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LICENSE.md

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+# Task-material license
+
+The original PhysClosureBench task specifications, grading rubrics, resource-limit descriptions, and explanatory text in this package are licensed under the [Creative Commons Attribution 4.0 International license (CC BY 4.0)](https://creativecommons.org/licenses/by/4.0/).
+
+The [full legal terms](https://creativecommons.org/licenses/by/4.0/legalcode) govern reuse. Give appropriate credit to the PhysClosureBench contributors, retain the license notice and link, and indicate any changes. Attribution must not imply endorsement.
+
+For attribution, identify PhysClosureBench and link to its associated paper: [From Research Goals to Scientific Closure: Evaluating Agents Through Evidence-Supported Physics Research](https://arxiv.org/abs/2610.21767).
+
+This grant applies only to rights held by the PhysClosureBench contributors. It does not license the cited third-party papers, figures, code, or other third-party materials. Their respective rights and licenses remain applicable. Source citations and links do not imply permission to reproduce those works.
+
+This is a task-material license, not an extension of the execution framework's software license. No MIT license is applied to these task materials by reference to that framework.

README.md

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----
-license: mit
----
+# PhysClosureBench — Complete 50-Case Materials
+
+[Paper](https://arxiv.org/abs/2610.21767)
+
+This collection provides the task specifications and complete case-specific grading materials for all 50 PhysClosureBench research tasks.
+
+Each case directory contains `task.md`, `grading_rubric.md`, `grading_rubric.json`, `resource_limits.json`, and `sources.md`. The Markdown and JSON rubrics contain the same twenty half-point criteria, task-specific RC0–RC4 requirements, scientific dependencies, accepted equivalent evidence, and applicability conditions.
+
+Task specifications, resource limits, and [common submission requirements](submission_requirements.md) are agent inputs. Rubrics and scientific source references are evaluator materials and must not be supplied as task inputs.
+
+Shared grading instructions, independent first-pass assessment, targeted review, focused adjudication, and output conventions are described in the accompanying paper's **Appendix H**. The machine-readable first-pass output schema is provided at [grading/first_pass_output.schema.json](grading/first_pass_output.schema.json). Research Closure is assessed separately from the additive atomic score; it is not a score cap or a score-based classification.
+
+The [source-publication index](case_source_publications.pdf) links all 50 cases to their source publications. Scientific reference locations are also given in each case's `sources.md`; source publications and their figures are not reproduced in this collection.
+
+## Resource limits
+
+Each task has one `resource_limits.json` file. `time_limit_minutes` covers all candidate work, including planning, derivation, coding, computation, validation, interpretation, and final-file preparation. CPU cores specify the maximum allocation, not a prescribed numerical strategy. Network access is disabled. There is no separate aggregate CPU-hour ceiling.
+
+`temporary_storage_gib` is temporary disk space, not RAM; 1 GiB equals 2^30 bytes. `available_memory_gib`, where provided, is an approximate RAM availability estimate, not an enforced limit. An unspecified task-specific RAM limit does not imply unlimited physical memory. Collection after the work deadline provides no additional working time.
+
+## Case index
+
+| Case | Research task | CPU cores | Time limit (minutes) | Case materials |
+| --- | --- | ---: | ---: | --- |
+| [Case01](cases/case01/task.md) | Phase characterization in a weak-pulse/strong-field ionization model | 8 | 30 | [Resource limits](cases/case01/resource_limits.json) · [Rubric](cases/case01/grading_rubric.md) · [Sources](cases/case01/sources.md) |
+| [Case02](cases/case02/task.md) | Multiphoton ionization from driven scattering responses | 16 | 30 | [Resource limits](cases/case02/resource_limits.json) · [Rubric](cases/case02/grading_rubric.md) · [Sources](cases/case02/sources.md) |
+| [Case03](cases/case03/task.md) | Time-domain sampling of semiclassical photoelectron momentum distributions | 32 | 240 | [Resource limits](cases/case03/resource_limits.json) · [Rubric](cases/case03/grading_rubric.md) · [Sources](cases/case03/sources.md) |
+| [Case04](cases/case04/task.md) | Quantum radiation from a strongly driven two-level system | 8 | 30 | [Resource limits](cases/case04/resource_limits.json) · [Rubric](cases/case04/grading_rubric.md) · [Sources](cases/case04/sources.md) |
+| [Case05](cases/case05/task.md) | Topological edge states in finite-chain high-harmonic generation | 32 | 45 | [Resource limits](cases/case05/resource_limits.json) · [Rubric](cases/case05/grading_rubric.md) · [Sources](cases/case05/sources.md) |
+| [Case06](cases/case06/task.md) | Causal time-domain inference in a driven three-state system | 8 | 45 | [Resource limits](cases/case06/resource_limits.json) · [Rubric](cases/case06/grading_rubric.md) · [Sources](cases/case06/sources.md) |
+| [Case07](cases/case07/task.md) | Nonlinear radiation and field-state dynamics in a quantized two-level model | 8 | 45 | [Resource limits](cases/case07/resource_limits.json) · [Rubric](cases/case07/grading_rubric.md) · [Sources](cases/case07/sources.md) |
+| [Case08](cases/case08/task.md) | Timing information in molecular photoionization | 32 | 60 | [Resource limits](cases/case08/resource_limits.json) · [Rubric](cases/case08/grading_rubric.md) · [Sources](cases/case08/sources.md) |
+| [Case09](cases/case09/task.md) | High-harmonic emission from a one-dimensional periodic system | 16 | 30 | [Resource limits](cases/case09/resource_limits.json) · [Rubric](cases/case09/grading_rubric.md) · [Sources](cases/case09/sources.md) |
+| [Case10](cases/case10/task.md) | Harmonic radiation from driven few-level systems | 8 | 30 | [Resource limits](cases/case10/resource_limits.json) · [Rubric](cases/case10/grading_rubric.md) · [Sources](cases/case10/sources.md) |
+| [Case11](cases/case11/task.md) | Channel-resolved high-harmonic generation in driven two-band solids | 16 | 60 | [Resource limits](cases/case11/resource_limits.json) · [Rubric](cases/case11/grading_rubric.md) · [Sources](cases/case11/sources.md) |
+| [Case12](cases/case12/task.md) | Selective high-energy harmonic response in a weakly inhomogeneous field | 16 | 60 | [Resource limits](cases/case12/resource_limits.json) · [Rubric](cases/case12/grading_rubric.md) · [Sources](cases/case12/sources.md) |
+| [Case13](cases/case13/task.md) | Interpreting high-harmonic emission from a driven periodic system | 8 | 45 | [Resource limits](cases/case13/resource_limits.json) · [Rubric](cases/case13/grading_rubric.md) · [Sources](cases/case13/sources.md) |
+| [Case14](cases/case14/task.md) | Two-centre structure in nondipole strong-field ionization | 8 | 45 | [Resource limits](cases/case14/resource_limits.json) · [Rubric](cases/case14/grading_rubric.md) · [Sources](cases/case14/sources.md) |
+| [Case15](cases/case15/task.md) | Resolving molecular photoemission timing from nondipole momentum signals | 8 | 60 | [Resource limits](cases/case15/resource_limits.json) · [Rubric](cases/case15/grading_rubric.md) · [Sources](cases/case15/sources.md) |
+| [Case16](cases/case16/task.md) | Spectral confinement of phase-matched slow electrons | 8 | 45 | [Resource limits](cases/case16/resource_limits.json) · [Rubric](cases/case16/grading_rubric.md) · [Sources](cases/case16/sources.md) |
+| [Case17](cases/case17/task.md) | Gap and drive dependence of high-harmonic emission in two quantum models | 16 | 45 | [Resource limits](cases/case17/resource_limits.json) · [Rubric](cases/case17/grading_rubric.md) · [Sources](cases/case17/sources.md) |
+| [Case18](cases/case18/task.md) | Coupling and polarization as controls of dimer high-harmonic emission | 8 | 45 | [Resource limits](cases/case18/resource_limits.json) · [Rubric](cases/case18/grading_rubric.md) · [Sources](cases/case18/sources.md) |
+| [Case19](cases/case19/task.md) | Dissociation dynamics in a spatially nonuniform optical field | 16 | 60 | [Resource limits](cases/case19/resource_limits.json) · [Rubric](cases/case19/grading_rubric.md) · [Sources](cases/case19/sources.md) |
+| [Case20](cases/case20/task.md) | Diagnosing correlated resonances in high-harmonic emission | 32 | 90 | [Resource limits](cases/case20/resource_limits.json) · [Rubric](cases/case20/grading_rubric.md) · [Sources](cases/case20/sources.md) |
+| [Case21](cases/case21/task.md) | Can smooth single-lobe fields generate spectral interference? | 8 | 45 | [Resource limits](cases/case21/resource_limits.json) · [Rubric](cases/case21/grading_rubric.md) · [Sources](cases/case21/sources.md) |
+| [Case22](cases/case22/task.md) | Can pulse polarity control vacuum-pair acceleration and yield? | 8 | 60 | [Resource limits](cases/case22/resource_limits.json) · [Rubric](cases/case22/grading_rubric.md) · [Sources](cases/case22/sources.md) |
+| [Case23](cases/case23/task.md) | Can a bosonic environment enhance or suppress strong-field ionization? | 8 | 45 | [Resource limits](cases/case23/resource_limits.json) · [Rubric](cases/case23/grading_rubric.md) · [Sources](cases/case23/sources.md) |
+| [Case24](cases/case24/task.md) | When does a weak-field hierarchy faithfully describe assisted pair production? | 8 | 60 | [Resource limits](cases/case24/resource_limits.json) · [Rubric](cases/case24/grading_rubric.md) · [Sources](cases/case24/sources.md) |
+| [Case25](cases/case25/task.md) | How is the quantum state of a driving field encoded in crystal high-harmonic radiation? | 8 | 60 | [Resource limits](cases/case25/resource_limits.json) · [Rubric](cases/case25/grading_rubric.md) · [Sources](cases/case25/sources.md) |
+| [Case26](cases/case26/task.md) | Ellipticity-dependent high-harmonic emission from graphene | 16 | 90 | [Resource limits](cases/case26/resource_limits.json) · [Rubric](cases/case26/grading_rubric.md) · [Sources](cases/case26/sources.md) |
+| [Case27](cases/case27/task.md) | What can complex saddle structure establish about a short-pulse attoclock? | 8 | 60 | [Resource limits](cases/case27/resource_limits.json) · [Rubric](cases/case27/grading_rubric.md) · [Sources](cases/case27/sources.md) |
+| [Case28](cases/case28/task.md) | Field-dependent high-harmonic generation in a periodic crystal | 16 | 60 | [Resource limits](cases/case28/resource_limits.json) · [Rubric](cases/case28/grading_rubric.md) · [Sources](cases/case28/sources.md) |
+| [Case29](cases/case29/task.md) | Resonant EUV high-harmonic spectroscopy of correlated helium | 32 | 90 | [Resource limits](cases/case29/resource_limits.json) · [Rubric](cases/case29/grading_rubric.md) · [Sources](cases/case29/sources.md) |
+| [Case30](cases/case30/task.md) | When can a scattering model account for an attoclock offset? | 8 | 45 | [Resource limits](cases/case30/resource_limits.json) · [Rubric](cases/case30/grading_rubric.md) · [Sources](cases/case30/sources.md) |
+| [Case31](cases/case31/task.md) | Coulomb-sensitive semiclassical modelling of strong-field photoelectron interference | 96 | 360 | [Resource limits](cases/case31/resource_limits.json) · [Rubric](cases/case31/grading_rubric.md) · [Sources](cases/case31/sources.md) |
+| [Case32](cases/case32/task.md) | Diagnosing coupled electron-nuclear dynamics through molecular high-harmonic spectra | 96 | 720 | [Resource limits](cases/case32/resource_limits.json) · [Rubric](cases/case32/grading_rubric.md) · [Sources](cases/case32/sources.md) |
+| [Case33](cases/case33/task.md) | Single-atom recollision beyond the dipole approximation | 8 | 45 | [Resource limits](cases/case33/resource_limits.json) · [Rubric](cases/case33/grading_rubric.md) · [Sources](cases/case33/sources.md) |
+| [Case34](cases/case34/task.md) | Quantum-informed trajectory modelling of strong-field photoelectron spectra | 96 | 180 | [Resource limits](cases/case34/resource_limits.json) · [Rubric](cases/case34/grading_rubric.md) · [Sources](cases/case34/sources.md) |
+| [Case35](cases/case35/task.md) | Testing phase-space descriptions of quantum-light high-harmonic generation | 96 | 120 | [Resource limits](cases/case35/resource_limits.json) · [Rubric](cases/case35/grading_rubric.md) · [Sources](cases/case35/sources.md) |
+| [Case36](cases/case36/task.md) | Temporal control of solid-state high-harmonic emission with a shaped driver | 8 | 45 | [Resource limits](cases/case36/resource_limits.json) · [Rubric](cases/case36/grading_rubric.md) · [Sources](cases/case36/sources.md) |
+| [Case37](cases/case37/task.md) | Recoil and coupling in free-electron photon statistics | 8 | 45 | [Resource limits](cases/case37/resource_limits.json) · [Rubric](cases/case37/grading_rubric.md) · [Sources](cases/case37/sources.md) |
+| [Case38](cases/case38/task.md) | Valley-resolved and Brillouin-zone-integrated topological high-harmonic emission | 16 | 90 | [Resource limits](cases/case38/resource_limits.json) · [Rubric](cases/case38/grading_rubric.md) · [Sources](cases/case38/sources.md) |
+| [Case39](cases/case39/task.md) | Atomic high-harmonic generation in a quantized optical cavity | 96 | 120 | [Resource limits](cases/case39/resource_limits.json) · [Rubric](cases/case39/grading_rubric.md) · [Sources](cases/case39/sources.md) |
+| [Case40](cases/case40/task.md) | Photon-momentum partition in direct strong-field ionization | 16 | 90 | [Resource limits](cases/case40/resource_limits.json) · [Rubric](cases/case40/grading_rubric.md) · [Sources](cases/case40/sources.md) |
+| [Case41](cases/case41/task.md) | State-resolved longitudinal momentum transfer in light-front tunnelling | 96 | 180 | [Resource limits](cases/case41/resource_limits.json) · [Rubric](cases/case41/grading_rubric.md) · [Sources](cases/case41/sources.md) |
+| [Case42](cases/case42/task.md) | Collective response of optically structured superconducting order | 96 | 180 | [Resource limits](cases/case42/resource_limits.json) · [Rubric](cases/case42/grading_rubric.md) · [Sources](cases/case42/sources.md) |
+| [Case43](cases/case43/task.md) | Quantum-statistical radiation pressure in strong-field ionization | 32 | 90 | [Resource limits](cases/case43/resource_limits.json) · [Rubric](cases/case43/grading_rubric.md) · [Sources](cases/case43/sources.md) |
+| [Case44](cases/case44/task.md) | Interaction-shaped diffraction of two trapped atoms | 8 | 45 | [Resource limits](cases/case44/resource_limits.json) · [Rubric](cases/case44/grading_rubric.md) · [Sources](cases/case44/sources.md) |
+| [Case45](cases/case45/task.md) | Near-resonant ionization beyond a resonant two-state description | 32 | 90 | [Resource limits](cases/case45/resource_limits.json) · [Rubric](cases/case45/grading_rubric.md) · [Sources](cases/case45/sources.md) |
+| [Case46](cases/case46/task.md) | Carrier-envelope control of directional above-threshold ionization | 16 | 90 | [Resource limits](cases/case46/resource_limits.json) · [Rubric](cases/case46/grading_rubric.md) · [Sources](cases/case46/sources.md) |
+| [Case47](cases/case47/task.md) | Complete intermediate propagation in strong-field detachment | 8 | 45 | [Resource limits](cases/case47/resource_limits.json) · [Rubric](cases/case47/grading_rubric.md) · [Sources](cases/case47/sources.md) |
+| [Case48](cases/case48/task.md) | Benchmarking approximations to quantum light emitted by a driven correlated chain | 16 | 60 | [Resource limits](cases/case48/resource_limits.json) · [Rubric](cases/case48/grading_rubric.md) · [Sources](cases/case48/sources.md) |
+| [Case49](cases/case49/task.md) | Interferometric recovery of a direct-SFA photoelectron wave packet | 8 | 60 | [Resource limits](cases/case49/resource_limits.json) · [Rubric](cases/case49/grading_rubric.md) · [Sources](cases/case49/sources.md) |
+| [Case50](cases/case50/task.md) | The role of spin in relativistic three-photon standing-wave diffraction | 8 | 45 | [Resource limits](cases/case50/resource_limits.json) · [Rubric](cases/case50/grading_rubric.md) · [Sources](cases/case50/sources.md) |
+
+## License
+
+Original task materials are licensed under CC BY 4.0; see [Task-material license](LICENSE.md) for attribution and third-party exclusions. The software framework's MIT license does not apply to these materials.

case_source_publications.pdf

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+version https://git-lfs.github.com/spec/v1
+oid sha256:0114fd6643672b8615c93415f64938d1bf666e89dcef412b41cfc2ef358c0285
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cases/case01/grading_rubric.json

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+{
+  "case_id": "Case01",
+  "title": "Case01 — Carrier-Envelope-Phase Characterization for an Isolated Attosecond Pulse by Angular Streaking",
+  "atoms": [
+    {
+      "criterion_id": "F1",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.",
+      "award_conditions": [
+        "The two finite-support physical fields share time origin, helicity, intensity units and CEP convention; their vector potential obeys E=-dA/dt."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article p.203601-2, Eq.(1) and Fig.1(a): finite-support circular pulses, intensity-to-field convention and combined waveform."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F2",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.",
+      "award_conditions": [
+        "A standard hydrogen-1s ADK relative rate uses the instantaneous combined magnitude and is accumulated without depletion; release maps to no-Coulomb drift momentum and angle using the same vector potential."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F1 (Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.)",
+        "Preserve independently valid work in O2, O3, O4, I2, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning \"At the moment\": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32]."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F3",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.",
+      "award_conditions": [
+        "The final SFA probability is the squared modulus of one coherent combined-field amplitude with consistent action and dipole; an incoherent sum of isolated pulse probabilities does not qualify."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F1 (Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.)",
+        "Preserve independently valid work in O1, I1, M1, M2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article pp.203601-2-3, Eqs.(2)-(4), Fig.2(c,h): one combined-field SFA amplitude; its interference contribution is signed, not a probability or two independently propagated single-pulse yields."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "O1",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.",
+      "award_conditions": [
+        "Submitted combined-field and release-weight/drift evidence is reconstructible and exposes the physical nonlinear modulation and angular distribution; causal explanation is not required by this Output item.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.); F2 (Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.)",
+        "Preserve independently valid work in O2, O3, O4, I2, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning \"At the moment\": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32]."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O2",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.",
+      "award_conditions": [
+        "The submitted 67 nm final signal is nonnegative, ring-supported and angularly modulated, with genuine multi-CEP recalculation and an exposed phase-observable relation.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.)",
+        "Preserve independently valid work in O1, O3, O4, I3, M1, M2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article p.203601-3, Fig.2(a-d), especially final total (d), and adjacent ring/modulation discussion. These are 67 nm fixed-phase SFA anchors; genuine multi-CEP recalculation is a task-defined inference duty, not an existing source phase-map target."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O3",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present attribution evidence separating a genuine phase-linked two-pulse effect from single-pulse background, normalization and display choices. A chosen canonical signed contribution must permit both positive and negative regions.",
+      "award_conditions": [
+        "Candidate-presented controls distinguish two-pulse phase attribution from isolated-pulse background and normalization/display effects; a chosen interference cross term retains its signed positive and negative regions.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.)",
+        "Preserve independently valid work in O1, O2, O4, I3, M1, M2, M4, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article pp.203601-2-3, Eqs.(2)-(4), Fig.2(c,h): one combined-field SFA amplitude; its interference contribution is signed, not a probability or two independently propagated single-pulse yields."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O4",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present the 100 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, using the same diagnostic definition as at 67 nm.",
+      "award_conditions": [
+        "The 100 nm final coherent signal and genuine CEP recalculations use the same diagnostic definition as 67 nm, with reconstructible case-specific response.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.)",
+        "Preserve independently valid work in O1, O2, O3, I2, M1, M2, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article p.203601-3, Fig.2(f-i), especially 100 nm total (i), compared with 67 nm Fig.2(a-d); p.203601-2 states wavelength generality. Applying one diagnostic across genuine CEP recalculations is task-defined."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "I1",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify in the submitted release evidence how the weak IAP changes nonlinear tunnelling weights through the combined-field magnitude, and identify the release-to-detection mapping through the subsequent vector potential.",
+      "award_conditions": [
+        "The candidate identifies specific changes of combined magnitude and nonlinear release weights and the subsequent vector-potential mapping in their own evidence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O1 (Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.)",
+        "Preserve independently valid work in O2, O3, O4, I2, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning \"At the moment\": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32]."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I2",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify phase-bearing structure, genuine CEP response, and its visibility or ambiguity against background in the submitted 67 nm final and attribution evidence.",
+      "award_conditions": [
+        "The candidate identifies genuine 67 nm CEP-sensitive structure and its background visibility or ambiguity from final and attribution evidence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O3 (Present attribution evidence separating a genuine phase-linked two-pulse effect from single-pulse background, normalization and display choices. A chosen canonical signed contribution must permit both positive and negative regions.)",
+        "Preserve independently valid work in I3, M6, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article p.203601-3, Fig.2(a-d), especially final total (d), and adjacent ring/modulation discussion. These are 67 nm fixed-phase SFA anchors; genuine multi-CEP recalculation is a task-defined inference duty, not an existing source phase-map target."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I3",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify case-specific responses and cross-wavelength usability differences of the same diagnostic from genuine 67 nm and 100 nm CEP recalculations; two fixed-phase summaries are insufficient.",
+      "award_conditions": [
+        "The candidate identifies wavelength-specific response and comparative usability from both recalculated phase families, not only two fixed-phase images."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O4 (Present the 100 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, using the same diagnostic definition as at 67 nm.)",
+        "Preserve independently valid work in I2, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article p.203601-3, Fig.2(f-i), especially 100 nm total (i), compared with 67 nm Fig.2(a-d); p.203601-2 states wavelength generality. Applying one diagnostic across genuine CEP recalculations is task-defined."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M1",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain with concrete combined-field and release features how strong tunnelling nonlinearity makes the weak IAP observable in the release weights.",
+      "award_conditions": [
+        "Parallel/antiparallel field features in the submitted calculation are linked to the strong nonlinear tunnelling response that amplifies the weak IAP effect."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.); O1 (Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.); I1 (Identify in the submitted release evidence how the weak IAP changes nonlinear tunnelling weights through the combined-field magnitude, and identify the release-to-detection mapping through the subsequent vector potential.)",
+        "Preserve independently valid work in O2, O3, O4, I2, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning \"At the moment\": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32]."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M2",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Close the angular-streaking causal chain from release information through vector potential/drift momentum to final detection direction, rather than equating instantaneous field angle with detected electron angle.",
+      "award_conditions": [
+        "The candidate connects release weighting to later vector-potential acceleration and final momentum angle; instantaneous field angle is not substituted for detection angle."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.); O1 (Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.); I1 (Identify in the submitted release evidence how the weak IAP changes nonlinear tunnelling weights through the combined-field magnitude, and identify the release-to-detection mapping through the subsequent vector potential.)",
+        "Preserve independently valid work in O2, O3, O4, I2, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning \"At the moment\": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32]."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M3",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use attribution evidence to explain which part of the final coherent signal carries two-pulse phase information and why it is not a single-pulse, normalization or display effect.",
+      "award_conditions": [
+        "Attribution evidence supports a causal two-pulse phase contribution in the complete signal and excludes a single-pulse or display-only explanation."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.); O3 (Present attribution evidence separating a genuine phase-linked two-pulse effect from single-pulse background, normalization and display choices. A chosen canonical signed contribution must permit both positive and negative regions.); I2 (Identify phase-bearing structure, genuine CEP response, and its visibility or ambiguity against background in the submitted 67 nm final and attribution evidence.)",
+        "Preserve independently valid work in O4, I3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article pp.203601-2-3, Eqs.(2)-(4), Fig.2(c,h): one combined-field SFA amplitude; its interference contribution is signed, not a probability or two independently propagated single-pulse yields."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M4",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Define a reconstructible CEP diagnostic and establish its phase-observable mapping and discriminating power through genuine multi-phase calculation.",
+      "award_conditions": [
+        "The chosen diagnostic has a reconstructible mathematical definition and phase-to-observable mapping established by actual recalculation at multiple phases."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); I2 (Identify phase-bearing structure, genuine CEP response, and its visibility or ambiguity against background in the submitted 67 nm final and attribution evidence.)",
+        "Preserve independently valid work in O4, I3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article pp.203601-3-4, Fig.3(a) and paragraphs defining angular integration and CEP dependence; pp.203601-2-3, Eq.(4), Fig.2(d,i). Fig.3(a) is a hydrogen 100 nm TDSE phase map: it motivates phase-sensitive inference but does not prescribe the different ADK/SFA diagnostic or its geometry."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M5",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Assess diagnostic visibility in the complete nonnegative observable, ambiguity or non-uniqueness, and the CEP resolution or characterization actually supported.",
+      "award_conditions": [
+        "The final nonnegative signal supports the stated diagnostic visibility, ambiguities and achievable CEP discrimination; noiseless self-interpolation alone is not physical resolution."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O3 (Present attribution evidence separating a genuine phase-linked two-pulse effect from single-pulse background, normalization and display choices. A chosen canonical signed contribution must permit both positive and negative regions.); I2 (Identify phase-bearing structure, genuine CEP response, and its visibility or ambiguity against background in the submitted 67 nm final and attribution evidence.)",
+        "Preserve independently valid work in O4, I3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article pp.203601-3-4, Fig.3(a) and paragraphs defining angular integration and CEP dependence; pp.203601-2-3, Eq.(4), Fig.2(d,i). Fig.3(a) is a hydrogen 100 nm TDSE phase map: it motivates phase-sensitive inference but does not prescribe the different ADK/SFA diagnostic or its geometry."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M6",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Determine from the two wavelength-specific calculations whether the same diagnostic remains applicable and explain the case-specific differences; fixed-phase summaries do not establish cross-wavelength phase characterization.",
+      "award_conditions": [
+        "Both wavelength calculations establish whether the same diagnostic transfers and explain case-dependent changes within their actual phase domain."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O4 (Present the 100 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, using the same diagnostic definition as at 67 nm.); I3 (Identify case-specific responses and cross-wavelength usability differences of the same diagnostic from genuine 67 nm and 100 nm CEP recalculations; two fixed-phase summaries are insufficient.)",
+        "Preserve independently valid work in I2, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article p.203601-3, Fig.2(f-i), especially 100 nm total (i), compared with 67 nm Fig.2(a-d); p.203601-2 states wavelength generality. Applying one diagnostic across genuine CEP recalculations is task-defined."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M7",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "State a final CEP-characterization conclusion commensurate with the ADK/SFA evidence, distinguishing model-level characterization from experimental quantitative or unique inversion claims.",
+      "award_conditions": [
+        "The final characterization claim follows the ADK/SFA evidence and distinguishes model-level discrimination from experimental accuracy or unique inversion."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: M4 (Define a reconstructible CEP diagnostic and establish its phase-observable mapping and discriminating power through genuine multi-phase calculation.); M5 (Assess diagnostic visibility in the complete nonnegative observable, ambiguity or non-uniqueness, and the CEP resolution or characterization actually supported.); M6 (Determine from the two wavelength-specific calculations whether the same diagnostic remains applicable and explain the case-specific differences; fixed-phase summaries do not establish cross-wavelength phase characterization.)",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article pp.203601-3-4, Fig.3(a) and paragraphs defining angular integration and CEP dependence; pp.203601-2-3, Eq.(4), Fig.2(d,i). Fig.3(a) is a hydrogen 100 nm TDSE phase map: it motivates phase-sensitive inference but does not prescribe the different ADK/SFA diagnostic or its geometry."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M8",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Reconcile field, ADK, SFA, attribution and final-diagnostic evidence; investigate material conflicts before concluding, and distinguish a genuine negative result from information lost by observable compression.",
+      "award_conditions": [
+        "The candidate reconciles field, release, coherent SFA and attribution evidence, investigating material conflicts and distinguishing a true null result from diagnostic compression."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: M1 (Explain with concrete combined-field and release features how strong tunnelling nonlinearity makes the weak IAP observable in the release weights.); M2 (Close the angular-streaking causal chain from release information through vector potential/drift momentum to final detection direction, rather than equating instantaneous field angle with detected electron angle.); M3 (Use attribution evidence to explain which part of the final coherent signal carries two-pulse phase information and why it is not a single-pulse, normalization or display effect.); M4 (Define a reconstructible CEP diagnostic and establish its phase-observable mapping and discriminating power through genuine multi-phase calculation.)",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article pp.203601-3-4, Fig.3(a) and paragraphs defining angular integration and CEP dependence; pp.203601-2-3, Eq.(4), Fig.2(d,i). Fig.3(a) is a hydrogen 100 nm TDSE phase map: it motivates phase-sensitive inference but does not prescribe the different ADK/SFA diagnostic or its geometry."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V1",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Positively state the model and evidence domain: hydrogen 1s, the specified two pulses, the no-depletion/no-Coulomb ADK baseline, coherent final SFA, and the actually sampled wavelength/CEP range.",
+      "award_conditions": [
+        "The candidate positively declares hydrogen 1s, specified pulses, no-depletion/no-Coulomb release model, coherent SFA, and calculated CEP/wavelength domain."
+      ],
+      "applicability_and_na": [
+        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article pp.203601-2-4, Eqs.(2)-(5), discussion distinguishing explanatory SFA from quantitative TDSE and Fig.4(a,b) noise examples. The positive stated model domain and risk-triggered validation are task/evaluation duties; neither TDSE nor these particular noise controls is compulsory."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V2",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "When the submitted method, data, anomaly or claim exposes a material risk, exclude a concrete alternative with discriminating evidence or narrow the threatened conclusion; omission of an examiner-preferred check alone does not trigger this obligation.",
+      "award_conditions": [
+        "If an actual conclusion-threatening risk is triggered, discriminating evidence excludes the concrete alternative or the claim is narrowed; an untriggered assessable item remains N/A with fixed credit."
+      ],
+      "applicability_and_na": [
+        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
+        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.",
+        "A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.",
+        "No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase."
+      ],
+      "source_support": [
+        "He et al. (2016), article pp.203601-2-4, Eqs.(2)-(5), discussion distinguishing explanatory SFA from quantitative TDSE and Fig.4(a,b) noise examples. The positive stated model domain and risk-triggered validation are task/evaluation duties; neither TDSE nor these particular noise controls is compulsory."
+      ],
+      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    }
+  ],
+  "case_scientific_rules": [
+    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
+    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
+    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
+    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
+    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
+    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
+    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
+    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
+    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
+    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
+    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
+    "The ADK and coherent SFA branches retain independent credit when the other fails. A failed 100 nm branch blocks cross-wavelength conclusions, not independently established 67 nm attribution or diagnostic conclusions.",
+    "A tiny noiseless same-model interpolation error is not by itself physical CEP resolution. Null response must not be inferred solely from a compressed diagnostic while information survives in the underlying signal.",
+    "Do not grade absolute photoelectron yield, exact peak-to-valley ratio, crop, annotation, colours or pixels. Noise, clipping or resolution matters only when it changes the physical signal or obscures a material claim.",
+    "The canonical route superposes the two physical fields, uses one consistent vector potential with $\\mathbf E=-d\\mathbf A/dt$, and applies a standard hydrogen-$1s$ ADK relative rate to the instantaneous combined-field magnitude. Under the task scope, release is accumulated without depletion and the no-Coulomb drift direction is obtained from the vector potential at release. A consistently opposite global momentum convention is equivalent after the corresponding angular transformation.",
+    "At the SFA level, the canonical source route evaluates one coherent two-pulse amplitude. Linearity in its electric-field factor permits IAP-driven and IR-driven component amplitudes only while they retain the same combined-field phase, vector potentials, and dipole argument. Their modulus-square expansion contains two nonnegative self terms and the signed contribution",
+    "$$\nC(\\mathbf p)=2\\operatorname{Re}\\!\\left[\nM_{\\mathrm{IAP}}(\\mathbf p)M_{\\mathrm{IR}}^*(\\mathbf p)\n\\right].\n$$",
+    "Students need not use or submit this decomposition. A replacement must still separate a genuine phase-linked two-pulse effect from the final coherent signal, single-pulse background, normalization changes, and numerical artefacts.",
+    "For the 67 nm reference case, parallel and antiparallel portions of the two fields respectively alter the combined magnitude. The nonlinear tunnelling response makes the weak IAP visible in the release weighting, and the later field maps release information into a detected direction.",
+    "The canonical 67 nm drift-angle result has a strong nonuniform topology with a dominant sector, flanking structures, intervening depressions, and a broad opposite-side minimum after any allowed global angular transformation.",
+    "The canonical signed SFA contribution contains both positive and negative momentum regions. It has a finer sequence of alternating sectors for 67 nm and fewer/broader sectors for 100 nm. The corresponding full distributions are nonnegative, ring-supported, angularly modulated, and case-specific.",
+    "Changing `theta_IAP` must change a phase-bearing final signal if the proposed characterization route is working. The source directly presents a CEP-dependent angular map for the 100 nm hydrogen case at the TDSE level. This supports the scientific need for a phase variation; neither that TDSE map nor its stripe geometry is a visual or quantitative target for the student's different ADK/SFA calculation.",
+    "The source states that the principle is not restricted to one IAP wavelength. In this examination abstraction, 67 nm and 100 nm test whether one diagnostic remains usable across wavelength; they are not two independent projects.",
+    "The source supplies the physical reason that CEP information can enter the angular signal, while the task asks the student to construct an ADK/SFA-level phase study. The phase scan is necessary evidence for answering the research question, not a request to reproduce the source TDSE phase image. Grade the mathematical validity of the student's chosen diagnostic, consistent recalculation of the stated model across phase, the physical credibility of the resolved response, and whether the evidence supports the claim made. Do not compare its image, stripe count, slope, contrast, or layout with the source TDSE panel.",
+    "An examiner-side calculation may be used to audit task feasibility or diagnose a suspected implementation error, but it must not become a hidden pixel template, fixed diagnostic, phase grid, or expected curve. ",
+    "For F1-F3/O1-O4/M1-M4, the source convention (article p.203601-2, Eqs.(1)-(4)) is\n$$M(\\mathbf p)=-i\\int dt\\,e^{i\\phi(t)}\\mathbf d[\\mathbf p+\\mathbf A(t)]\\cdot\\mathbf E(t),\\quad\n\\phi(t)=I_p(t-t_0)+\\frac12\\int_{t_0}^{t}[\\mathbf p+\\mathbf A(s)]^2ds,$$\n$$\\mathbf E=\\mathbf E_{\\rm IAP}+\\mathbf E_{\\rm IR}=-\\dot{\\mathbf A},\\quad I_p=0.5,\\quad\n\\mathbf d(\\mathbf k)\\propto\\frac{\\mathbf k}{(k^2+2I_p)^3}.$$\nThe common dipole scale is free. In the usual electron convention with zero final vector potential, the no-Coulomb zero-launch drift is $\\mathbf p_\\infty=-\\mathbf A(t_r)$; an opposite global momentum convention requires the matching angular transformation. A hydrogen-1s relative ADK form is $w(F)\\propto F^{-1}\\exp[-2/(3F)]$, $F=|\\mathbf E(t_r)|$, within the stipulated tunnelling baseline. The source cites ADK rather than printing this rate. The already stated signed cross term is the algebraic expansion of this one amplitude; components retain the same combined-field action and dipole.\n\nThe physical finite-support source pulse is $\\mathbf E_i(t)=E_{0i}[\\cos(\\omega_it+\\theta_i)\\hat x-\\sin(\\omega_it+\\theta_i)\\hat y]\\cos^2(\\pi t/\\tau_i)$ for $|t|<\\tau_i/2$, zero otherwise, with $E_{0i}=\\sqrt{I_i/(3.51\\times10^{16}\\,{\\rm W\\,cm^{-2}})}$ in atomic units. These are source Eq.(1), not a vector-potential envelope substituted for the physical field."
+  ],
+  "closure_requirements": {
+    "RC0": [
+      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
+      "Required indispensable claim CL0, central physical object: all of: F1 (Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.); F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC1": [
+      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
+      "Required co primary claim CL1, indispensable material component: all of: F2 (Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.); O1 (Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL2, indispensable material component: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O4 (Present the 100 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, using the same diagnostic definition as at 67 nm.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC2": [
+      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
+      "Required co primary claim CL1, principal mechanism or commissioned conclusion: all of: M1 (Explain with concrete combined-field and release features how strong tunnelling nonlinearity makes the weak IAP observable in the release weights.); M2 (Close the angular-streaking causal chain from release information through vector potential/drift momentum to final detection direction, rather than equating instantaneous field angle with detected electron angle.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M3 (Use attribution evidence to explain which part of the final coherent signal carries two-pulse phase information and why it is not a single-pulse, normalization or display effect.); M4 (Define a reconstructible CEP diagnostic and establish its phase-observable mapping and discriminating power through genuine multi-phase calculation.); M5 (Assess diagnostic visibility in the complete nonnegative observable, ambiguity or non-uniqueness, and the CEP resolution or characterization actually supported.); M6 (Determine from the two wavelength-specific calculations whether the same diagnostic remains applicable and explain the case-specific differences; fixed-phase summaries do not establish cross-wavelength phase characterization.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL3, principal mechanism or commissioned conclusion: all of: M7 (State a final CEP-characterization conclusion commensurate with the ADK/SFA evidence, distinguishing model-level characterization from experimental quantitative or unique inversion claims.); M8 (Reconcile field, ADK, SFA, attribution and final-diagnostic evidence; investigate material conflicts before concluding, and distinguish a genuine negative result from information lost by observable compression.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC3": [
+      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
+      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
+      "Required co primary claim CL3, material validation/scope: V2 (When the submitted method, data, anomaly or claim exposes a material risk, exclude a concrete alternative with discriminating evidence or narrow the threatened conclusion; omission of an examiner-preferred check alone does not trigger this obligation.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC4": [
+      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
+      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
+      "Close CL0 central physical object: all of: F1 (Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.); F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.).",
+      "Close CL1 indispensable material component: all of: F2 (Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.); O1 (Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.).",
+      "Close CL1 principal mechanism or commissioned conclusion: all of: M1 (Explain with concrete combined-field and release features how strong tunnelling nonlinearity makes the weak IAP observable in the release weights.); M2 (Close the angular-streaking causal chain from release information through vector potential/drift momentum to final detection direction, rather than equating instantaneous field angle with detected electron angle.).",
+      "Close CL2 indispensable material component: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O4 (Present the 100 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, using the same diagnostic definition as at 67 nm.).",
+      "Close CL2 principal mechanism or commissioned conclusion: all of: M3 (Use attribution evidence to explain which part of the final coherent signal carries two-pulse phase information and why it is not a single-pulse, normalization or display effect.); M4 (Define a reconstructible CEP diagnostic and establish its phase-observable mapping and discriminating power through genuine multi-phase calculation.); M5 (Assess diagnostic visibility in the complete nonnegative observable, ambiguity or non-uniqueness, and the CEP resolution or characterization actually supported.); M6 (Determine from the two wavelength-specific calculations whether the same diagnostic remains applicable and explain the case-specific differences; fixed-phase summaries do not establish cross-wavelength phase characterization.).",
+      "Close CL3 principal mechanism or commissioned conclusion: all of: M7 (State a final CEP-characterization conclusion commensurate with the ADK/SFA evidence, distinguishing model-level characterization from experimental quantitative or unique inversion claims.); M8 (Reconcile field, ADK, SFA, attribution and final-diagnostic evidence; investigate material conflicts before concluding, and distinguish a genuine negative result from information lost by observable compression.).",
+      "Close CL3 material validation/scope: V2 (When the submitted method, data, anomaly or claim exposes a material risk, exclude a concrete alternative with discriminating evidence or narrow the threatened conclusion; omission of an examiner-preferred check alone does not trigger this obligation.)."
+    ]
+  },
+  "references": [
+    {
+      "citation": "Pei-Lun He, Camilo Ruiz, and Feng He. 2016. *Carrier-Envelope-Phase Characterization for an Isolated Attosecond Pulse by Angular Streaking*. *Physical Review Letters*, 116, 203601.",
+      "url": "https://doi.org/10.1103/PhysRevLett.116.203601",
+      "scientific_scope": "Carrier-Envelope-Phase Characterization for an Isolated Attosecond Pulse by Angular Streaking",
+      "anchors": [
+        "He et al. (2016), article p.203601-2, Eq.(1) and Fig.1(a): finite-support circular pulses, intensity-to-field convention and combined waveform.",
+        "He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning \"At the moment\": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32].",
+        "He et al. (2016), article pp.203601-2-3, Eqs.(2)-(4), Fig.2(c,h): one combined-field SFA amplitude; its interference contribution is signed, not a probability or two independently propagated single-pulse yields.",
+        "He et al. (2016), article p.203601-3, Fig.2(a-d), especially final total (d), and adjacent ring/modulation discussion. These are 67 nm fixed-phase SFA anchors; genuine multi-CEP recalculation is a task-defined inference duty, not an existing source phase-map target.",
+        "He et al. (2016), article p.203601-3, Fig.2(f-i), especially 100 nm total (i), compared with 67 nm Fig.2(a-d); p.203601-2 states wavelength generality. Applying one diagnostic across genuine CEP recalculations is task-defined.",
+        "He et al. (2016), article pp.203601-3-4, Fig.3(a) and paragraphs defining angular integration and CEP dependence; pp.203601-2-3, Eq.(4), Fig.2(d,i). Fig.3(a) is a hydrogen 100 nm TDSE phase map: it motivates phase-sensitive inference but does not prescribe the different ADK/SFA diagnostic or its geometry.",
+        "He et al. (2016), article pp.203601-2-4, Eqs.(2)-(5), discussion distinguishing explanatory SFA from quantitative TDSE and Fig.4(a,b) noise examples. The positive stated model domain and risk-triggered validation are task/evaluation duties; neither TDSE nor these particular noise controls is compulsory."
+      ]
+    }
+  ]
+}

cases/case01/grading_rubric.md

@@ -0,0 +1,856 @@
+# Grading Rubric — Case01
+
+Case01 — Carrier-Envelope-Phase Characterization for an Isolated Attosecond Pulse by Angular Streaking
+
+## Atomic Scoring Criteria
+
+Each criterion awards 0 or 0.5 points, for a maximum of 10. Explicit N/A rules apply where stated.
+
+### F1 — F — 0.5 points
+
+**Scientific requirement**
+
+Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.
+
+**Conditions for credit**
+
+- The two finite-support physical fields share time origin, helicity, intensity units and CEP convention; their vector potential obeys E=-dA/dt.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article p.203601-2, Eq.(1) and Fig.1(a): finite-support circular pulses, intensity-to-field convention and combined waveform.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F2 — F — 0.5 points
+
+**Scientific requirement**
+
+Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.
+
+**Conditions for credit**
+
+- A standard hydrogen-1s ADK relative rate uses the instantaneous combined magnitude and is accumulated without depletion; release maps to no-Coulomb drift momentum and angle using the same vector potential.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F1 (Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.)
+
+- Preserve independently valid work in O2, O3, O4, I2, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning "At the moment": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32].
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F3 — F — 0.5 points
+
+**Scientific requirement**
+
+Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.
+
+**Conditions for credit**
+
+- The final SFA probability is the squared modulus of one coherent combined-field amplitude with consistent action and dipole; an incoherent sum of isolated pulse probabilities does not qualify.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F1 (Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.)
+
+- Preserve independently valid work in O1, I1, M1, M2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article pp.203601-2-3, Eqs.(2)-(4), Fig.2(c,h): one combined-field SFA amplitude; its interference contribution is signed, not a probability or two independently propagated single-pulse yields.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### O1 — O — 0.5 points
+
+**Scientific requirement**
+
+Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.
+
+**Conditions for credit**
+
+- Submitted combined-field and release-weight/drift evidence is reconstructible and exposes the physical nonlinear modulation and angular distribution; causal explanation is not required by this Output item.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.); F2 (Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.)
+
+- Preserve independently valid work in O2, O3, O4, I2, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning "At the moment": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32].
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O2 — O — 0.5 points
+
+**Scientific requirement**
+
+Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.
+
+**Conditions for credit**
+
+- The submitted 67 nm final signal is nonnegative, ring-supported and angularly modulated, with genuine multi-CEP recalculation and an exposed phase-observable relation.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.)
+
+- Preserve independently valid work in O1, O3, O4, I3, M1, M2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article p.203601-3, Fig.2(a-d), especially final total (d), and adjacent ring/modulation discussion. These are 67 nm fixed-phase SFA anchors; genuine multi-CEP recalculation is a task-defined inference duty, not an existing source phase-map target.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O3 — O — 0.5 points
+
+**Scientific requirement**
+
+Present attribution evidence separating a genuine phase-linked two-pulse effect from single-pulse background, normalization and display choices. A chosen canonical signed contribution must permit both positive and negative regions.
+
+**Conditions for credit**
+
+- Candidate-presented controls distinguish two-pulse phase attribution from isolated-pulse background and normalization/display effects; a chosen interference cross term retains its signed positive and negative regions.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.)
+
+- Preserve independently valid work in O1, O2, O4, I3, M1, M2, M4, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article pp.203601-2-3, Eqs.(2)-(4), Fig.2(c,h): one combined-field SFA amplitude; its interference contribution is signed, not a probability or two independently propagated single-pulse yields.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O4 — O — 0.5 points
+
+**Scientific requirement**
+
+Present the 100 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, using the same diagnostic definition as at 67 nm.
+
+**Conditions for credit**
+
+- The 100 nm final coherent signal and genuine CEP recalculations use the same diagnostic definition as 67 nm, with reconstructible case-specific response.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.)
+
+- Preserve independently valid work in O1, O2, O3, I2, M1, M2, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article p.203601-3, Fig.2(f-i), especially 100 nm total (i), compared with 67 nm Fig.2(a-d); p.203601-2 states wavelength generality. Applying one diagnostic across genuine CEP recalculations is task-defined.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### I1 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify in the submitted release evidence how the weak IAP changes nonlinear tunnelling weights through the combined-field magnitude, and identify the release-to-detection mapping through the subsequent vector potential.
+
+**Conditions for credit**
+
+- The candidate identifies specific changes of combined magnitude and nonlinear release weights and the subsequent vector-potential mapping in their own evidence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O1 (Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.)
+
+- Preserve independently valid work in O2, O3, O4, I2, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning "At the moment": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32].
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I2 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify phase-bearing structure, genuine CEP response, and its visibility or ambiguity against background in the submitted 67 nm final and attribution evidence.
+
+**Conditions for credit**
+
+- The candidate identifies genuine 67 nm CEP-sensitive structure and its background visibility or ambiguity from final and attribution evidence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O3 (Present attribution evidence separating a genuine phase-linked two-pulse effect from single-pulse background, normalization and display choices. A chosen canonical signed contribution must permit both positive and negative regions.)
+
+- Preserve independently valid work in I3, M6, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article p.203601-3, Fig.2(a-d), especially final total (d), and adjacent ring/modulation discussion. These are 67 nm fixed-phase SFA anchors; genuine multi-CEP recalculation is a task-defined inference duty, not an existing source phase-map target.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I3 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify case-specific responses and cross-wavelength usability differences of the same diagnostic from genuine 67 nm and 100 nm CEP recalculations; two fixed-phase summaries are insufficient.
+
+**Conditions for credit**
+
+- The candidate identifies wavelength-specific response and comparative usability from both recalculated phase families, not only two fixed-phase images.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O4 (Present the 100 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, using the same diagnostic definition as at 67 nm.)
+
+- Preserve independently valid work in I2, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article p.203601-3, Fig.2(f-i), especially 100 nm total (i), compared with 67 nm Fig.2(a-d); p.203601-2 states wavelength generality. Applying one diagnostic across genuine CEP recalculations is task-defined.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M1 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain with concrete combined-field and release features how strong tunnelling nonlinearity makes the weak IAP observable in the release weights.
+
+**Conditions for credit**
+
+- Parallel/antiparallel field features in the submitted calculation are linked to the strong nonlinear tunnelling response that amplifies the weak IAP effect.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.); O1 (Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.); I1 (Identify in the submitted release evidence how the weak IAP changes nonlinear tunnelling weights through the combined-field magnitude, and identify the release-to-detection mapping through the subsequent vector potential.)
+
+- Preserve independently valid work in O2, O3, O4, I2, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning "At the moment": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32].
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M2 — M — 0.5 points
+
+**Scientific requirement**
+
+Close the angular-streaking causal chain from release information through vector potential/drift momentum to final detection direction, rather than equating instantaneous field angle with detected electron angle.
+
+**Conditions for credit**
+
+- The candidate connects release weighting to later vector-potential acceleration and final momentum angle; instantaneous field angle is not substituted for detection angle.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.); O1 (Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.); I1 (Identify in the submitted release evidence how the weak IAP changes nonlinear tunnelling weights through the combined-field magnitude, and identify the release-to-detection mapping through the subsequent vector potential.)
+
+- Preserve independently valid work in O2, O3, O4, I2, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning "At the moment": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32].
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M3 — M — 0.5 points
+
+**Scientific requirement**
+
+Use attribution evidence to explain which part of the final coherent signal carries two-pulse phase information and why it is not a single-pulse, normalization or display effect.
+
+**Conditions for credit**
+
+- Attribution evidence supports a causal two-pulse phase contribution in the complete signal and excludes a single-pulse or display-only explanation.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.); O3 (Present attribution evidence separating a genuine phase-linked two-pulse effect from single-pulse background, normalization and display choices. A chosen canonical signed contribution must permit both positive and negative regions.); I2 (Identify phase-bearing structure, genuine CEP response, and its visibility or ambiguity against background in the submitted 67 nm final and attribution evidence.)
+
+- Preserve independently valid work in O4, I3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article pp.203601-2-3, Eqs.(2)-(4), Fig.2(c,h): one combined-field SFA amplitude; its interference contribution is signed, not a probability or two independently propagated single-pulse yields.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M4 — M — 0.5 points
+
+**Scientific requirement**
+
+Define a reconstructible CEP diagnostic and establish its phase-observable mapping and discriminating power through genuine multi-phase calculation.
+
+**Conditions for credit**
+
+- The chosen diagnostic has a reconstructible mathematical definition and phase-to-observable mapping established by actual recalculation at multiple phases.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); I2 (Identify phase-bearing structure, genuine CEP response, and its visibility or ambiguity against background in the submitted 67 nm final and attribution evidence.)
+
+- Preserve independently valid work in O4, I3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article pp.203601-3-4, Fig.3(a) and paragraphs defining angular integration and CEP dependence; pp.203601-2-3, Eq.(4), Fig.2(d,i). Fig.3(a) is a hydrogen 100 nm TDSE phase map: it motivates phase-sensitive inference but does not prescribe the different ADK/SFA diagnostic or its geometry.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M5 — M — 0.5 points
+
+**Scientific requirement**
+
+Assess diagnostic visibility in the complete nonnegative observable, ambiguity or non-uniqueness, and the CEP resolution or characterization actually supported.
+
+**Conditions for credit**
+
+- The final nonnegative signal supports the stated diagnostic visibility, ambiguities and achievable CEP discrimination; noiseless self-interpolation alone is not physical resolution.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O3 (Present attribution evidence separating a genuine phase-linked two-pulse effect from single-pulse background, normalization and display choices. A chosen canonical signed contribution must permit both positive and negative regions.); I2 (Identify phase-bearing structure, genuine CEP response, and its visibility or ambiguity against background in the submitted 67 nm final and attribution evidence.)
+
+- Preserve independently valid work in O4, I3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article pp.203601-3-4, Fig.3(a) and paragraphs defining angular integration and CEP dependence; pp.203601-2-3, Eq.(4), Fig.2(d,i). Fig.3(a) is a hydrogen 100 nm TDSE phase map: it motivates phase-sensitive inference but does not prescribe the different ADK/SFA diagnostic or its geometry.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M6 — M — 0.5 points
+
+**Scientific requirement**
+
+Determine from the two wavelength-specific calculations whether the same diagnostic remains applicable and explain the case-specific differences; fixed-phase summaries do not establish cross-wavelength phase characterization.
+
+**Conditions for credit**
+
+- Both wavelength calculations establish whether the same diagnostic transfers and explain case-dependent changes within their actual phase domain.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O4 (Present the 100 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, using the same diagnostic definition as at 67 nm.); I3 (Identify case-specific responses and cross-wavelength usability differences of the same diagnostic from genuine 67 nm and 100 nm CEP recalculations; two fixed-phase summaries are insufficient.)
+
+- Preserve independently valid work in I2, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article p.203601-3, Fig.2(f-i), especially 100 nm total (i), compared with 67 nm Fig.2(a-d); p.203601-2 states wavelength generality. Applying one diagnostic across genuine CEP recalculations is task-defined.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M7 — M — 0.5 points
+
+**Scientific requirement**
+
+State a final CEP-characterization conclusion commensurate with the ADK/SFA evidence, distinguishing model-level characterization from experimental quantitative or unique inversion claims.
+
+**Conditions for credit**
+
+- The final characterization claim follows the ADK/SFA evidence and distinguishes model-level discrimination from experimental accuracy or unique inversion.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: M4 (Define a reconstructible CEP diagnostic and establish its phase-observable mapping and discriminating power through genuine multi-phase calculation.); M5 (Assess diagnostic visibility in the complete nonnegative observable, ambiguity or non-uniqueness, and the CEP resolution or characterization actually supported.); M6 (Determine from the two wavelength-specific calculations whether the same diagnostic remains applicable and explain the case-specific differences; fixed-phase summaries do not establish cross-wavelength phase characterization.)
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article pp.203601-3-4, Fig.3(a) and paragraphs defining angular integration and CEP dependence; pp.203601-2-3, Eq.(4), Fig.2(d,i). Fig.3(a) is a hydrogen 100 nm TDSE phase map: it motivates phase-sensitive inference but does not prescribe the different ADK/SFA diagnostic or its geometry.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M8 — M — 0.5 points
+
+**Scientific requirement**
+
+Reconcile field, ADK, SFA, attribution and final-diagnostic evidence; investigate material conflicts before concluding, and distinguish a genuine negative result from information lost by observable compression.
+
+**Conditions for credit**
+
+- The candidate reconciles field, release, coherent SFA and attribution evidence, investigating material conflicts and distinguishing a true null result from diagnostic compression.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: M1 (Explain with concrete combined-field and release features how strong tunnelling nonlinearity makes the weak IAP observable in the release weights.); M2 (Close the angular-streaking causal chain from release information through vector potential/drift momentum to final detection direction, rather than equating instantaneous field angle with detected electron angle.); M3 (Use attribution evidence to explain which part of the final coherent signal carries two-pulse phase information and why it is not a single-pulse, normalization or display effect.); M4 (Define a reconstructible CEP diagnostic and establish its phase-observable mapping and discriminating power through genuine multi-phase calculation.)
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article pp.203601-3-4, Fig.3(a) and paragraphs defining angular integration and CEP dependence; pp.203601-2-3, Eq.(4), Fig.2(d,i). Fig.3(a) is a hydrogen 100 nm TDSE phase map: it motivates phase-sensitive inference but does not prescribe the different ADK/SFA diagnostic or its geometry.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V1 — V — 0.5 points
+
+**Scientific requirement**
+
+Positively state the model and evidence domain: hydrogen 1s, the specified two pulses, the no-depletion/no-Coulomb ADK baseline, coherent final SFA, and the actually sampled wavelength/CEP range.
+
+**Conditions for credit**
+
+- The candidate positively declares hydrogen 1s, specified pulses, no-depletion/no-Coulomb release model, coherent SFA, and calculated CEP/wavelength domain.
+
+**Applicability and N/A**
+
+- This positive scientific scope/evidence duty is unconditional; N/A is not permitted.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article pp.203601-2-4, Eqs.(2)-(5), discussion distinguishing explanatory SFA from quantitative TDSE and Fig.4(a,b) noise examples. The positive stated model domain and risk-triggered validation are task/evaluation duties; neither TDSE nor these particular noise controls is compulsory.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V2 — V — 0.5 points
+
+**Scientific requirement**
+
+When the submitted method, data, anomaly or claim exposes a material risk, exclude a concrete alternative with discriminating evidence or narrow the threatened conclusion; omission of an examiner-preferred check alone does not trigger this obligation.
+
+**Conditions for credit**
+
+- If an actual conclusion-threatening risk is triggered, discriminating evidence excludes the concrete alternative or the claim is narrowed; an untriggered assessable item remains N/A with fixed credit.
+
+**Applicability and N/A**
+
+- Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.
+
+- If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent global phase, angular origin, momentum sign, helicity, gauge and common-scale transformations are accepted after their physical mapping is established.
+
+- A functionally equivalent causal control may replace the component split. If used, C(p)=2 Re[M_IAP(p) M_IR(p)*] is signed and both amplitudes must retain the same combined-field phase, vector potential and dipole argument.
+
+- No fixed phase grid, diagnostic, six-figure package or resemblance to a TDSE phase image is required; the ADK/SFA model must actually be recalculated at each tested phase.
+
+**Scientific source locations**
+
+- He et al. (2016), article pp.203601-2-4, Eqs.(2)-(5), discussion distinguishing explanatory SFA from quantitative TDSE and Fig.4(a,b) noise examples. The positive stated model domain and risk-triggered validation are task/evaluation duties; neither TDSE nor these particular noise controls is compulsory.
+
+**Research Closure relation**
+
+Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+## Research Closure Requirements
+
+### RC0
+
+- The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.
+
+- Required indispensable claim CL0, central physical object: all of: F1 (Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.); F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC1
+
+- With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.
+
+- Required co primary claim CL1, indispensable material component: all of: F2 (Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.); O1 (Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL2, indispensable material component: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O4 (Present the 100 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, using the same diagnostic definition as at 67 nm.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC2
+
+- With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.
+
+- Required co primary claim CL1, principal mechanism or commissioned conclusion: all of: M1 (Explain with concrete combined-field and release features how strong tunnelling nonlinearity makes the weak IAP observable in the release weights.); M2 (Close the angular-streaking causal chain from release information through vector potential/drift momentum to final detection direction, rather than equating instantaneous field angle with detected electron angle.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M3 (Use attribution evidence to explain which part of the final coherent signal carries two-pulse phase information and why it is not a single-pulse, normalization or display effect.); M4 (Define a reconstructible CEP diagnostic and establish its phase-observable mapping and discriminating power through genuine multi-phase calculation.); M5 (Assess diagnostic visibility in the complete nonnegative observable, ambiguity or non-uniqueness, and the CEP resolution or characterization actually supported.); M6 (Determine from the two wavelength-specific calculations whether the same diagnostic remains applicable and explain the case-specific differences; fixed-phase summaries do not establish cross-wavelength phase characterization.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL3, principal mechanism or commissioned conclusion: all of: M7 (State a final CEP-characterization conclusion commensurate with the ADK/SFA evidence, distinguishing model-level characterization from experimental quantitative or unique inversion claims.); M8 (Reconcile field, ADK, SFA, attribution and final-diagnostic evidence; investigate material conflicts before concluding, and distinguish a genuine negative result from information lost by observable compression.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC3
+
+- With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.
+
+- Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.
+
+- Required co primary claim CL3, material validation/scope: V2 (When the submitted method, data, anomaly or claim exposes a material risk, exclude a concrete alternative with discriminating evidence or narrow the threatened conclusion; omission of an examiner-preferred check alone does not trigger this obligation.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC4
+
+- All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.
+
+- Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.
+
+- Close CL0 central physical object: all of: F1 (Establish the joint physical driver from the two supplied finite-support pulses on one time origin, consistently treating electric field, vector potential, phase, momentum axes, helicity and units.); F3 (Construct one coherent two-pulse final SFA amplitude and final momentum/angular distribution with the same combined field, vector potential and dipole argument; do not add unrelated pulse probabilities.).
+
+- Close CL1 indispensable material component: all of: F2 (Select a standard hydrogen-1s ADK relative rate and construct a computable release-weight-to-no-Coulomb-drift-momentum/angle route without depletion or post-release Coulomb interaction.); O1 (Present physically valid, sufficiently exposed and reconstructible combined-field and ADK release-weight/drift-direction evidence. This output criterion does not itself require the release or detection-direction causal explanation.).
+
+- Close CL1 principal mechanism or commissioned conclusion: all of: M1 (Explain with concrete combined-field and release features how strong tunnelling nonlinearity makes the weak IAP observable in the release weights.); M2 (Close the angular-streaking causal chain from release information through vector potential/drift momentum to final detection direction, rather than equating instantaneous field angle with detected electron angle.).
+
+- Close CL2 indispensable material component: all of: O2 (Present the 67 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, exposing a reconstructible phase-observable relation.); O4 (Present the 100 nm coherent, nonnegative, ring-supported, angularly modulated final photoelectron distribution at a reference phase and through genuine multi-CEP recalculation, using the same diagnostic definition as at 67 nm.).
+
+- Close CL2 principal mechanism or commissioned conclusion: all of: M3 (Use attribution evidence to explain which part of the final coherent signal carries two-pulse phase information and why it is not a single-pulse, normalization or display effect.); M4 (Define a reconstructible CEP diagnostic and establish its phase-observable mapping and discriminating power through genuine multi-phase calculation.); M5 (Assess diagnostic visibility in the complete nonnegative observable, ambiguity or non-uniqueness, and the CEP resolution or characterization actually supported.); M6 (Determine from the two wavelength-specific calculations whether the same diagnostic remains applicable and explain the case-specific differences; fixed-phase summaries do not establish cross-wavelength phase characterization.).
+
+- Close CL3 principal mechanism or commissioned conclusion: all of: M7 (State a final CEP-characterization conclusion commensurate with the ADK/SFA evidence, distinguishing model-level characterization from experimental quantitative or unique inversion claims.); M8 (Reconcile field, ADK, SFA, attribution and final-diagnostic evidence; investigate material conflicts before concluding, and distinguish a genuine negative result from information lost by observable compression.).
+
+- Close CL3 material validation/scope: V2 (When the submitted method, data, anomaly or claim exposes a material risk, exclude a concrete alternative with discriminating evidence or narrow the threatened conclusion; omission of an examiner-preferred check alone does not trigger this obligation.).
+
+## Applicability and Equivalent Evidence
+
+- Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.
+
+- Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.
+
+- For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.
+
+- Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.
+
+- Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.
+
+- Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.
+
+- Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.
+
+- Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.
+
+- Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.
+
+- Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.
+
+- A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.
+
+- The ADK and coherent SFA branches retain independent credit when the other fails. A failed 100 nm branch blocks cross-wavelength conclusions, not independently established 67 nm attribution or diagnostic conclusions.
+
+- A tiny noiseless same-model interpolation error is not by itself physical CEP resolution. Null response must not be inferred solely from a compressed diagnostic while information survives in the underlying signal.
+
+- Do not grade absolute photoelectron yield, exact peak-to-valley ratio, crop, annotation, colours or pixels. Noise, clipping or resolution matters only when it changes the physical signal or obscures a material claim.
+
+- The canonical route superposes the two physical fields, uses one consistent vector potential with $\mathbf E=-d\mathbf A/dt$, and applies a standard hydrogen-$1s$ ADK relative rate to the instantaneous combined-field magnitude. Under the task scope, release is accumulated without depletion and the no-Coulomb drift direction is obtained from the vector potential at release. A consistently opposite global momentum convention is equivalent after the corresponding angular transformation.
+
+- At the SFA level, the canonical source route evaluates one coherent two-pulse amplitude. Linearity in its electric-field factor permits IAP-driven and IR-driven component amplitudes only while they retain the same combined-field phase, vector potentials, and dipole argument. Their modulus-square expansion contains two nonnegative self terms and the signed contribution
+
+$$
+C(\mathbf p)=2\operatorname{Re}\!\left[
+M_{\mathrm{IAP}}(\mathbf p)M_{\mathrm{IR}}^*(\mathbf p)
+\right].
+$$
+
+- Students need not use or submit this decomposition. A replacement must still separate a genuine phase-linked two-pulse effect from the final coherent signal, single-pulse background, normalization changes, and numerical artefacts.
+
+- For the 67 nm reference case, parallel and antiparallel portions of the two fields respectively alter the combined magnitude. The nonlinear tunnelling response makes the weak IAP visible in the release weighting, and the later field maps release information into a detected direction.
+
+- The canonical 67 nm drift-angle result has a strong nonuniform topology with a dominant sector, flanking structures, intervening depressions, and a broad opposite-side minimum after any allowed global angular transformation.
+
+- The canonical signed SFA contribution contains both positive and negative momentum regions. It has a finer sequence of alternating sectors for 67 nm and fewer/broader sectors for 100 nm. The corresponding full distributions are nonnegative, ring-supported, angularly modulated, and case-specific.
+
+- Changing `theta_IAP` must change a phase-bearing final signal if the proposed characterization route is working. The source directly presents a CEP-dependent angular map for the 100 nm hydrogen case at the TDSE level. This supports the scientific need for a phase variation; neither that TDSE map nor its stripe geometry is a visual or quantitative target for the student's different ADK/SFA calculation.
+
+- The source states that the principle is not restricted to one IAP wavelength. In this examination abstraction, 67 nm and 100 nm test whether one diagnostic remains usable across wavelength; they are not two independent projects.
+
+- The source supplies the physical reason that CEP information can enter the angular signal, while the task asks the student to construct an ADK/SFA-level phase study. The phase scan is necessary evidence for answering the research question, not a request to reproduce the source TDSE phase image. Grade the mathematical validity of the student's chosen diagnostic, consistent recalculation of the stated model across phase, the physical credibility of the resolved response, and whether the evidence supports the claim made. Do not compare its image, stripe count, slope, contrast, or layout with the source TDSE panel.
+
+- An examiner-side calculation may be used to audit task feasibility or diagnose a suspected implementation error, but it must not become a hidden pixel template, fixed diagnostic, phase grid, or expected curve. 
+
+For F1-F3/O1-O4/M1-M4, the source convention (article p.203601-2, Eqs.(1)-(4)) is
+$$M(\mathbf p)=-i\int dt\,e^{i\phi(t)}\mathbf d[\mathbf p+\mathbf A(t)]\cdot\mathbf E(t),\quad
+\phi(t)=I_p(t-t_0)+\frac12\int_{t_0}^{t}[\mathbf p+\mathbf A(s)]^2ds,$$
+$$\mathbf E=\mathbf E_{\rm IAP}+\mathbf E_{\rm IR}=-\dot{\mathbf A},\quad I_p=0.5,\quad
+\mathbf d(\mathbf k)\propto\frac{\mathbf k}{(k^2+2I_p)^3}.$$
+The common dipole scale is free. In the usual electron convention with zero final vector potential, the no-Coulomb zero-launch drift is $\mathbf p_\infty=-\mathbf A(t_r)$; an opposite global momentum convention requires the matching angular transformation. A hydrogen-1s relative ADK form is $w(F)\propto F^{-1}\exp[-2/(3F)]$, $F=|\mathbf E(t_r)|$, within the stipulated tunnelling baseline. The source cites ADK rather than printing this rate. The already stated signed cross term is the algebraic expansion of this one amplitude; components retain the same combined-field action and dipole.
+
+The physical finite-support source pulse is $\mathbf E_i(t)=E_{0i}[\cos(\omega_it+\theta_i)\hat x-\sin(\omega_it+\theta_i)\hat y]\cos^2(\pi t/\tau_i)$ for $|t|<\tau_i/2$, zero otherwise, with $E_{0i}=\sqrt{I_i/(3.51\times10^{16}\,{\rm W\,cm^{-2}})}$ in atomic units. These are source Eq.(1), not a vector-potential envelope substituted for the physical field.

cases/case01/resource_limits.json

@@ -0,0 +1,8 @@
+{
+  "cpu_cores": 8,
+  "nodes": 1,
+  "time_limit_minutes": 30,
+  "network_access": "disabled",
+  "temporary_storage_gib": 64,
+  "memory_policy": "No separate task-specific RAM limit is specified."
+}

cases/case01/sources.md

@@ -0,0 +1,36 @@
+# Scientific Sources — Case01
+
+## References
+
+Pei-Lun He, Camilo Ruiz, and Feng He. 2016. *Carrier-Envelope-Phase Characterization for an Isolated Attosecond Pulse by Angular Streaking*. *Physical Review Letters*, 116, 203601. [Source](https://doi.org/10.1103/PhysRevLett.116.203601)
+
+Carrier-Envelope-Phase Characterization for an Isolated Attosecond Pulse by Angular Streaking
+
+## Criterion-to-source crosswalk
+
+Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.
+
+| Criteria | Source locations, scientific use and limits |
+|---|---|
+| F1 | He et al. (2016), article p.203601-2, Eq.(1) and Fig.1(a): finite-support circular pulses, intensity-to-field convention and combined waveform. |
+| F2, O1, I1, M1, M2 | He et al. (2016), article p.203601-2, Fig.1(a,b) and paragraph beginning "At the moment": parallel/antiparallel field addition modulates nonlinear ADK release, and subsequent vector-potential streaking maps release to detection direction. The ADK reference is their Ref.[32]. |
+| F3, O3, M3 | He et al. (2016), article pp.203601-2-3, Eqs.(2)-(4), Fig.2(c,h): one combined-field SFA amplitude; its interference contribution is signed, not a probability or two independently propagated single-pulse yields. |
+| O2, I2 | He et al. (2016), article p.203601-3, Fig.2(a-d), especially final total (d), and adjacent ring/modulation discussion. These are 67 nm fixed-phase SFA anchors; genuine multi-CEP recalculation is a task-defined inference duty, not an existing source phase-map target. |
+| O4, I3, M6 | He et al. (2016), article p.203601-3, Fig.2(f-i), especially 100 nm total (i), compared with 67 nm Fig.2(a-d); p.203601-2 states wavelength generality. Applying one diagnostic across genuine CEP recalculations is task-defined. |
+| M4, M5, M7, M8 | He et al. (2016), article pp.203601-3-4, Fig.3(a) and paragraphs defining angular integration and CEP dependence; pp.203601-2-3, Eq.(4), Fig.2(d,i). Fig.3(a) is a hydrogen 100 nm TDSE phase map: it motivates phase-sensitive inference but does not prescribe the different ADK/SFA diagnostic or its geometry. |
+| V1, V2 | He et al. (2016), article pp.203601-2-4, Eqs.(2)-(5), discussion distinguishing explanatory SFA from quantitative TDSE and Fig.4(a,b) noise examples. The positive stated model domain and risk-triggered validation are task/evaluation duties; neither TDSE nor these particular noise controls is compulsory. |
+
+## Formula and convention notes
+
+For F1-F3/O1-O4/M1-M4, the source convention (article p.203601-2, Eqs.(1)-(4)) is
+$$M(\mathbf p)=-i\int dt\,e^{i\phi(t)}\mathbf d[\mathbf p+\mathbf A(t)]\cdot\mathbf E(t),\quad
+\phi(t)=I_p(t-t_0)+\frac12\int_{t_0}^{t}[\mathbf p+\mathbf A(s)]^2ds,$$
+$$\mathbf E=\mathbf E_{\rm IAP}+\mathbf E_{\rm IR}=-\dot{\mathbf A},\quad I_p=0.5,\quad
+\mathbf d(\mathbf k)\propto\frac{\mathbf k}{(k^2+2I_p)^3}.$$
+The common dipole scale is free. In the usual electron convention with zero final vector potential, the no-Coulomb zero-launch drift is $\mathbf p_\infty=-\mathbf A(t_r)$; an opposite global momentum convention requires the matching angular transformation. A hydrogen-1s relative ADK form is $w(F)\propto F^{-1}\exp[-2/(3F)]$, $F=|\mathbf E(t_r)|$, within the stipulated tunnelling baseline. The source cites ADK rather than printing this rate. The already stated signed cross term is the algebraic expansion of this one amplitude; components retain the same combined-field action and dipole.
+
+The physical finite-support source pulse is $\mathbf E_i(t)=E_{0i}[\cos(\omega_it+\theta_i)\hat x-\sin(\omega_it+\theta_i)\hat y]\cos^2(\pi t/\tau_i)$ for $|t|<\tau_i/2$, zero otherwise, with $E_{0i}=\sqrt{I_i/(3.51\times10^{16}\,{\rm W\,cm^{-2}})}$ in atomic units. These are source Eq.(1), not a vector-potential envelope substituted for the physical field.
+
+## Scope of the source anchors
+
+The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.

cases/case01/task.md

@@ -0,0 +1,117 @@
+# Phase characterization in a weak-pulse/strong-field ionization model
+
+## Background
+
+Directly characterizing the carrier-envelope phase (CEP) of a weak circularly
+polarized isolated attosecond pulse (IAP) is difficult because the pulse does
+not by itself provide the strongly nonlinear response used in established
+infrared CEP measurements. Consider ground-state hydrogen exposed to the weak
+IAP together with a much stronger, phase-stable circularly polarized infrared
+(IR) field, with the emitted photoelectrons observed in the laser-polarization
+plane.
+
+## Research problem
+
+Develop and assess a reproducible angular-streaking strategy for characterizing
+the absolute IAP CEP, within the stated laboratory phase convention, from the
+final photoelectron momentum or angular distribution in this two-pulse
+configuration. Treat the known IR phase as the phase reference.
+Demonstrate, by varying the IAP CEP, whether a usable phase-to-observable
+relation can be established and whether the same diagnostic remains applicable
+at both specified IAP wavelengths. Determine the level of CEP characterization
+supported by the stated model and your calculated evidence.
+
+How the strategy is constructed and substantiated is for you to decide. Assess
+its success from the calculated evidence rather than assuming it in advance.
+
+## Physical inputs
+
+Use atomic units in the field and strong-field calculations. For each
+individual pulse $i\in\{\mathrm{IAP},\mathrm{IR}\}$, use the source-stated
+finite-support field
+
+$$
+\mathbf E_i(t)=E_{0,i}
+\left[
+\cos(\omega_i t+\theta_i)\,\hat{\mathbf x}
+-\sin(\omega_i t+\theta_i)\,\hat{\mathbf y}
+\right]
+\cos^2\!\left(\frac{\pi t}{\tau_i}\right),
+\qquad |t|<\frac{\tau_i}{2},
+$$
+
+and $\mathbf E_i(t)=0$ outside this support. The two pulse envelopes share the
+same time origin. The fields rotate clockwise in the $x$-$y$ plane under this
+convention.
+
+| Quantity | Value or condition |
+|---|---|
+| Target | Ground-state hydrogen ($1s$) |
+| Ionization potential | $I_p=0.5$ a.u. |
+| IAP wavelengths | 67 nm and 100 nm |
+| IR wavelength | 800 nm |
+| Peak intensities | $I_{\mathrm{IAP}}=2\times10^{11}\,\mathrm{W/cm^2}$ and $I_{\mathrm{IR}}=2\times10^{14}\,\mathrm{W/cm^2}$ |
+| Field amplitudes | $E_{0,i}=\sqrt{I_i/(3.51\times10^{16})}$ a.u. |
+| Pulse durations | Four optical cycles, $\tau_i=4(2\pi/\omega_i)$ |
+| Carrier frequencies | $\omega_i=2\pi c/\lambda_i$, converted consistently to atomic units |
+| Phase reference | $\theta_{\mathrm{IR}}=0$; $\theta_{\mathrm{IAP}}$ is the characterization variable |
+| Momentum domain of interest | Laser-polarization plane, $p_z=0$ |
+
+State any conversion constants and phase, vector-potential, momentum-axis, and
+angular conventions used in your work.
+
+## Model scope
+
+Use a standard ground-state-hydrogen ($1s$) ADK treatment as the simplified
+tunnelling baseline and a standard strong-field approximation (SFA) for the
+coherent final photoelectron calculation. Select and cite the precise standard
+formulations you use. In the ADK-level model, neglect ground-state depletion
+and post-release Coulomb action. Do not add a full TDSE calculation to the
+required task.
+
+All numerical and diagnostic choices not fixed above are yours. The same
+physical and phase conventions must be used consistently, and the same
+diagnostic strategy must be tested at both IAP wavelengths. Any normalization
+or display scaling must be declared and kept common wherever relative
+magnitudes are used as scientific evidence. Absolute photoelectron yield is
+not a grading target unless it is fixed by the formulation you adopt.
+
+You are responsible for checking that your numerical results are sufficiently
+reliable and reproducible to support the conclusions you report. No particular
+grid, solver, convergence sequence, error metric, or validation procedure is
+prescribed.
+
+## Submission
+
+Submit a self-contained scientific report and an offline reproduction package
+containing the code, the numerical data underlying the reported evidence, the
+a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge, and concise run and environment information. The
+scientific organization of the report and supporting evidence, as well as
+filenames below the common top-level collection entry points, are yours. No
+full exploratory history or examiner-selected numerical method is required.
+
+The active examination resources and limits are defined in the companion
+`resource_limits.json`. All retained production calculations must run
+within that fixed allocation and active wall time. More expensive modelling
+does not receive additional credit.
+
+## Reference and integrity policy
+
+This examination is conducted without network access or live literature
+retrieval. You may rely on your existing general scientific knowledge and, if any are
+explicitly supplied with the examination, on those offline materials or
+software documentation. Record every such source actually consulted. For formulas,
+methods, constants, or conventions used from general knowledge rather than a
+consulted source, state enough of the method basis, definition, value, units,
+and convention to make the calculation auditable; do not invent a citation.
+You are not required to identify or prove a publication date or to retrieve
+literature during the examination.
+
+The hidden target article and its identifying metadata, figures or captions,
+supplementary material, author code or data, target-specific reproduction
+code, solution or scoring material, online solutions, and worked
+reproductions of this case must not be used. All submitted scientific figures
+and numerical data must be generated by your own implementation of the stated
+problem.
+
+See [submission requirements](../../submission_requirements.md) for the common submission entry points.

cases/case02/grading_rubric.json

@@ -0,0 +1,606 @@
+{
+  "case_id": "Case02",
+  "title": "Case02 — Calculation of multiphoton ionization amplitudes and cross sections of few-electron atoms",
+  "atoms": [
+    {
+      "criterion_id": "F1",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.",
+      "award_conditions": [
+        "The hydrogen-1s ordered hierarchy applies D=p_z exactly once with unit coefficient at each photon step; order and E1 channel parity are consistent."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article pp.043108-3-4, Eqs.(19),(20),(28)-(30), velocity-form paragraph following Eq.(21): ordered unit-coefficient dipole-response hierarchy."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F2",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.",
+      "award_conditions": [
+        "All open intermediate energies and the selected final energy occur in the outgoing Coulomb representation, and a determinate common complex system isolates the final coefficient."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.)",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F3",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.",
+      "award_conditions": [
+        "The isolated final coefficient maps to absolute generalized partial cross sections with declared Coulomb normalization and K-dependent units; independently normalized shapes do not qualify."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.)",
+        "Preserve independently valid work in I3, M3, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article pp.043108-2-5, Eqs.(11)-(15),(26),(27),(31) and SI-unit paragraph: Coulomb amplitude normalization and absolute order-dependent generalized cross sections."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "O4",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.",
+      "award_conditions": [
+        "All K=4 E1-allowed final waves are presented in absolute units over a domain sufficient for claimed openings and off-pole high-energy behavior.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.)",
+        "Preserve independently valid work in O1, O2, O3, I3, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-5, Fig.2(b,c) and Sec.III.A threshold paragraphs: intermediate openings near 6.8/13.6 eV for K=3 and 4.5/6.8/13.6 eV for K=4, with off-pole high-energy decline."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O1",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.",
+      "award_conditions": [
+        "Absolute K=2 s/d partial cross sections and their arithmetic total are reconstructible with correct normalization and stable material structure.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.)",
+        "Preserve independently valid work in O2, O3, O4, I1, I3, M1, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-5, Fig.2(a), Eq.(31) and first Sec.III.A paragraph: hydrogen two-photon s/d partial cross sections and their arithmetic total; E1 channel parity extends to the higher orders in Fig.2(b,c)."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O2",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present reconstructible absolute K=3 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.",
+      "award_conditions": [
+        "All K=3 E1-allowed final waves are presented in absolute units over a domain sufficient for claimed openings and off-pole high-energy behavior.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.)",
+        "Preserve independently valid work in O1, O3, O4, I3, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-5, Fig.2(b,c) and Sec.III.A threshold paragraphs: intermediate openings near 6.8/13.6 eV for K=3 and 4.5/6.8/13.6 eV for K=4, with off-pole high-energy decline."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O3",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.",
+      "award_conditions": [
+        "A genuinely open-intermediate complex radial response and a common multi-wave reconstruction expose both components in the unscaled asymptotic region using one coefficient set.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.)",
+        "Preserve independently valid work in O1, O2, O4, I1, I2, M1, M2, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "I1",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify threshold/structure sequences organized by successive intermediate continuum openings, and off-pole high-energy decline, in the submitted K=3/4 absolute families.",
+      "award_conditions": [
+        "The candidate identifies intermediate-opening sequences and high-energy off-pole decline in their K=3/4 absolute families."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.)",
+        "Preserve independently valid work in O1, O3, I3, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-5, Fig.2(b,c) and Sec.III.A threshold paragraphs: intermediate openings near 6.8/13.6 eV for K=3 and 4.5/6.8/13.6 eV for K=4, with off-pole high-energy decline."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I2",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify the E1-allowed final partial-wave sets for K=2,3,4, the K=2 total, and correct order/channel binding across the submitted families.",
+      "award_conditions": [
+        "The candidate identifies K=2 l=0,2; K=3 l=1,3; K=4 l=0,2,4 and the K=2 arithmetic total with correct order binding."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O1 (Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.)",
+        "Preserve independently valid work in O3, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-5, Fig.2(a), Eq.(31) and first Sec.III.A paragraph: hydrogen two-photon s/d partial cross sections and their arithmetic total; E1 channel parity extends to the higher orders in Fig.2(b,c)."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I3",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify common multi-wave beating/asymptotic content caused by the open intermediate channel, the selected final coefficient, and the unscaled radial region actually supporting the identification.",
+      "award_conditions": [
+        "The candidate identifies common complex beating, the selected final component and the actual unscaled region supporting that interpretation."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.)",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M1",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use energy conservation and the submitted K=3/4 structures to explain which intermediate absorption steps open and how they organize the observed sequences.",
+      "award_conditions": [
+        "Energy conservation at successive absorption steps explains the observed K=3/4 threshold sequence and which intermediate continua open."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.); I1 (Identify threshold/structure sequences organized by successive intermediate continuum openings, and off-pole high-energy decline, in the submitted K=3/4 absolute families.)",
+        "Preserve independently valid work in O1, O3, I3, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-5, Fig.2(b,c) and Sec.III.A threshold paragraphs: intermediate openings near 6.8/13.6 eV for K=3 and 4.5/6.8/13.6 eV for K=4, with off-pole high-energy decline."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M2",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain the allowed final waves, K=2 arithmetic total and retained off-pole high-energy behavior from absolute data rather than channel-free plot description.",
+      "award_conditions": [
+        "The candidate explains E1 final-channel parity, K=2 summation and off-pole decline using their absolute data rather than channel-free descriptions."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); O1 (Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.); I2 (Identify the E1-allowed final partial-wave sets for K=2,3,4, the K=2 total, and correct order/channel binding across the submitted families.)",
+        "Preserve independently valid work in O3, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-5, Fig.2(a), Eq.(31) and first Sec.III.A paragraph: hydrogen two-photon s/d partial cross sections and their arithmetic total; E1 channel parity extends to the higher orders in Fig.2(b,c)."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M3",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain why a single outgoing final wave is insufficient with an open intermediate continuum and why open intermediate and selected final energy Coulomb waves must coexist.",
+      "award_conditions": [
+        "The nonlocalized continuum driving term is connected to simultaneous intermediate- and final-energy outgoing waves; a lone final wave is shown insufficient."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.); O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.); I3 (Identify common multi-wave beating/asymptotic content caused by the open intermediate channel, the selected final coefficient, and the unscaled radial region actually supporting the identification.)",
+        "Preserve independently valid work in O1, O2, O4, M1, M2, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M4",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain how the common multi-wave coefficient system isolates the final outgoing coefficient and connects it to absolute cross sections; Wronskian, direct complex fit, surface relation and functionally equivalent extraction are accepted.",
+      "award_conditions": [
+        "The candidate explains how the common coefficient system distinguishes the final outgoing coefficient and connects it to absolute cross sections."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.); O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.); I3 (Identify common multi-wave beating/asymptotic content caused by the open intermediate channel, the selected final coefficient, and the unscaled radial region actually supporting the identification.)",
+        "Preserve independently valid work in O1, O2, O4, M1, M2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M5",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use one coefficient set to explain both real and imaginary response components and determine whether the fixed-wave-number Coulomb representation holds; separately fitting the components does not establish the common complex structure.",
+      "award_conditions": [
+        "One complex coefficient set explains real and imaginary radial components and supports or bounds the fixed-wave-number representation."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.); I3 (Identify common multi-wave beating/asymptotic content caused by the open intermediate channel, the selected final coefficient, and the unscaled radial region actually supporting the identification.)",
+        "Preserve independently valid work in O1, O2, O4, M1, M2, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M6",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain why coefficient recovery is supported only in the unscaled asymptotic region; distinguish ECS-contour response from real-axis continuation and state the boundary near exact bound poles or continuum resonances.",
+      "award_conditions": [
+        "Coefficient recovery is justified only in an unscaled asymptotic region; ECS-contour damping, real-axis continuation and near-pole limitations are distinguished."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.); I3 (Identify common multi-wave beating/asymptotic content caused by the open intermediate channel, the selected final coefficient, and the unscaled radial region actually supporting the identification.)",
+        "Preserve independently valid work in O1, O2, O4, M1, M2, M3, M4, M5, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article pp.043108-2-5, Eq.(9), paragraph preceding Eq.(12), Fig.1 caption, Sec.III.A pole limitation: extraction inside unscaled asymptotic space; exact bound poles are outside the unmodified real-energy perturbative prescription."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M7",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Close the dimensional and normalization chain from selected final coefficient through declared Coulomb normalization and order-dependent units to absolute K-photon cross sections; independently normalized curves are insufficient.",
+      "award_conditions": [
+        "The coefficient, Coulomb normalization, photon order and units form one absolute dimensional chain without arbitrary channel-by-channel rescaling."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.); O1 (Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.)",
+        "Preserve independently valid work in O3, I3, M3, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article pp.043108-2-5, Eqs.(11)-(15),(26),(27),(31) and SI-unit paragraph: Coulomb amplitude normalization and absolute order-dependent generalized cross sections."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M8",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Synthesize the absolute partial-wave families and open-intermediate complex response into a supported off-pole, perturbative single-electron-ejection extraction conclusion, without assuming every outgoing fit is meaningful.",
+      "award_conditions": [
+        "The absolute partial families and open-intermediate reconstruction jointly support a bounded off-pole, perturbative single-electron-ejection extraction conclusion."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: M3 (Explain why a single outgoing final wave is insufficient with an open intermediate continuum and why open intermediate and selected final energy Coulomb waves must coexist.); M4 (Explain how the common multi-wave coefficient system isolates the final outgoing coefficient and connects it to absolute cross sections; Wronskian, direct complex fit, surface relation and functionally equivalent extraction are accepted.); M5 (Use one coefficient set to explain both real and imaginary response components and determine whether the fixed-wave-number Coulomb representation holds; separately fitting the components does not establish the common complex structure.); M7 (Close the dimensional and normalization chain from selected final coefficient through declared Coulomb normalization and order-dependent units to absolute K-photon cross sections; independently normalized curves are insufficient.)",
+        "Preserve independently valid work in O1, O2, O3, O4, I1, I2, I3, M1, M2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article pp.043108-4-5, Eqs.(23)-(31), Fig.1 and Sec.III.A discussion of radial extent/collocation resolution; p.043108-9, Sec.IV limits the extraction to single-electron ejection. Evidence synthesis and triggered alternative tests are task-defined, not prescribed source solver settings."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V1",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Positively restrict the conclusion to the specified hydrogen single-electron ionization, ordered perturbation theory, real-energy off-pole response, sampled energy domain and selected unscaled asymptotic region.",
+      "award_conditions": [
+        "The candidate positively states hydrogen single-electron ionization, ordered perturbation, real-energy off-pole domain and actual unscaled recovery interval."
+      ],
+      "applicability_and_na": [
+        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article pp.043108-2-5, Eq.(9), paragraph preceding Eq.(12), Fig.1 caption, Sec.III.A pole limitation: extraction inside unscaled asymptotic space; exact bound poles are outside the unmodified real-energy perturbative prescription."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V2",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "When the fit, data, region, anomaly or conclusion exposes a material risk, challenge omitted open waves, coefficient non-identifiability, recovery-region contamination or normalization freedom with discriminating evidence, or narrow the claim; a missing prescribed convergence sequence alone is insufficient.",
+      "award_conditions": [
+        "When a material risk is exposed, capable evidence challenges omitted waves, coefficient degeneracy, region contamination or normalization freedom, or the claim is narrowed; otherwise N/A."
+      ],
+      "applicability_and_na": [
+        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
+        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.",
+        "Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.",
+        "The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.",
+        "A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets."
+      ],
+      "source_support": [
+        "Mihelic and Horvat (2021), article pp.043108-4-5, Eqs.(23)-(31), Fig.1 and Sec.III.A discussion of radial extent/collocation resolution; p.043108-9, Sec.IV limits the extraction to single-electron ejection. Evidence synthesis and triggered alternative tests are task-defined, not prescribed source solver settings."
+      ],
+      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    }
+  ],
+  "case_scientific_rules": [
+    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
+    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
+    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
+    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
+    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
+    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
+    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
+    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
+    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
+    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
+    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
+    "The E1-allowed families are K=2: l=0,2; K=3: l=1,3; K=4: l=0,2,4. The K=2 arithmetic total has only one scoring and indispensable-component owner, O1.",
+    "A local presentation or low-energy resolution gap in K=3 does not erase independent channel identity, absolute normalization or a correctly bounded inference supported by the valid remaining evidence.",
+    "The overall extraction synthesis requires the common multi-wave representation, final-coefficient isolation, common complex reconstruction and absolute normalization. Supporting fine opening sequences, family interpretation and recovery-region explanation retain independent scoring; they are not silently promoted to additional all-or-nothing central gates.",
+    "The canonical construction solves the ordered hierarchy",
+    "$$\n(E_0+j\\omega-H)\\widehat\\Psi_j=D\\widehat\\Psi_{j-1},\n\\qquad j=1,\\ldots,K,\n$$",
+    "with one unit-coefficient application of $D=p_z$ at each step. In an open partial wave, the large-radius radial response is a linear combination of the outgoing Coulomb waves associated with every open intermediate energy and the selected final energy. Wronskians sampled at several radii in the unscaled asymptotic region determine the coefficients; the coefficient of the final wave gives the ionization amplitude and hence the conventional generalized cross section. Equivalent direct linear fits or surface-flux formulations are acceptable only when they recover the same outgoing coefficient and absolute normalization.",
+    "the two-photon family contains $\\ell=0,2$ partial cross sections and their arithmetic total;",
+    "the three-photon family contains $\\ell=1,3$ and resolves sequences approaching about 6.8 and 13.6 eV, associated with the successive opening of intermediate ATI steps;",
+    "the four-photon family contains $\\ell=0,2,4$ and resolves corresponding sequences approaching about 4.5, 6.8 and 13.6 eV;",
+    "away from resonant poles, the selected ATI branches decrease at high photon energy over the retained range; exact pole heights are not finite physical anchors;",
+    "the source's canonical $K=2$, $\\omega=1$ a.u., $(\\ell,m)=(2,0)$ example has a beat-like unscaled complex radial response described by one common pair of outgoing Coulomb waves with $k=1$ and $k=\\sqrt3$; this is a reference anchor, not the only acceptable student-selected open-intermediate response;",
+    "coefficient recovery must use the unscaled region. The damped computed ECS response beyond $R_0$ and a real-axis analytic continuation are different objects and their post-$R_0$ difference is not fit evidence.",
+    "For F2-F3/M4-M7, article pp.043108-3-5, Eqs.(14),(23)-(31), define\n$$H_\\ell(k;r)=e^{-i\\eta_\\ell(k)}[F_\\ell(k;r)+iG_\\ell(k;r)],\\quad\n\\widehat P_\\ell(r)\\sim\\sum_q A_{\\ell q}H_\\ell(k_q;r),\\quad k_q=\\sqrt{2(E_0+j_q\\omega)}>0.$$\nWith the article's outgoing Coulomb convention and final index $n$,\n$$B_\\ell=i^{-\\ell+1}\\sqrt{\\frac{k_n}{2\\pi}}A_{\\ell n},\\qquad\n\\sigma^{(K)}_\\ell=2\\pi\\left(\\frac{2\\pi}{c\\omega}\\right)^K|B_\\ell|^2.$$\nThe SI conversion factor is $a_0^{2K}t_0^{K-1}$, giving area$^K$ time$^{K-1}$. The canonical extraction uses $M_{pq}=W\\{F_\\ell(k_n;r),H_\\ell(k_q;r)\\}_{r_p}$ and $b_p=W\\{F_\\ell(k_n;r),\\widehat P_\\ell(r)\\}_{r_p}$, with $W\\{f,g\\}=fg'-f'g$ and $r_p<R_0$ in the asymptotic region. A common complex direct fit or equivalent surface relation is accepted when it isolates the same absolutely normalized coefficient."
+  ],
+  "closure_requirements": {
+    "RC0": [
+      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
+      "Required indispensable claim CL0, central physical object: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC1": [
+      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
+      "Required co primary claim CL1, indispensable material component: all of: O1 (Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.); O2 (Present reconstructible absolute K=3 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL2, indispensable material component: all of: O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC2": [
+      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
+      "Required co primary claim CL1, principal mechanism or commissioned conclusion: all of: M7 (Close the dimensional and normalization chain from selected final coefficient through declared Coulomb normalization and order-dependent units to absolute K-photon cross sections; independently normalized curves are insufficient.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M3 (Explain why a single outgoing final wave is insufficient with an open intermediate continuum and why open intermediate and selected final energy Coulomb waves must coexist.); M4 (Explain how the common multi-wave coefficient system isolates the final outgoing coefficient and connects it to absolute cross sections; Wronskian, direct complex fit, surface relation and functionally equivalent extraction are accepted.); M5 (Use one coefficient set to explain both real and imaginary response components and determine whether the fixed-wave-number Coulomb representation holds; separately fitting the components does not establish the common complex structure.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL3, principal mechanism or commissioned conclusion: M8 (Synthesize the absolute partial-wave families and open-intermediate complex response into a supported off-pole, perturbative single-electron-ejection extraction conclusion, without assuming every outgoing fit is meaningful.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC3": [
+      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
+      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
+      "Required co primary claim CL3, material validation/scope: V2 (When the fit, data, region, anomaly or conclusion exposes a material risk, challenge omitted open waves, coefficient non-identifiability, recovery-region contamination or normalization freedom with discriminating evidence, or narrow the claim; a missing prescribed convergence sequence alone is insufficient.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC4": [
+      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
+      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
+      "Close CL0 central physical object: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.).",
+      "Close CL1 indispensable material component: all of: O1 (Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.); O2 (Present reconstructible absolute K=3 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.).",
+      "Close CL1 principal mechanism or commissioned conclusion: all of: M7 (Close the dimensional and normalization chain from selected final coefficient through declared Coulomb normalization and order-dependent units to absolute K-photon cross sections; independently normalized curves are insufficient.).",
+      "Close CL2 indispensable material component: all of: O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.).",
+      "Close CL2 principal mechanism or commissioned conclusion: all of: M3 (Explain why a single outgoing final wave is insufficient with an open intermediate continuum and why open intermediate and selected final energy Coulomb waves must coexist.); M4 (Explain how the common multi-wave coefficient system isolates the final outgoing coefficient and connects it to absolute cross sections; Wronskian, direct complex fit, surface relation and functionally equivalent extraction are accepted.); M5 (Use one coefficient set to explain both real and imaginary response components and determine whether the fixed-wave-number Coulomb representation holds; separately fitting the components does not establish the common complex structure.).",
+      "Close CL3 principal mechanism or commissioned conclusion: M8 (Synthesize the absolute partial-wave families and open-intermediate complex response into a supported off-pole, perturbative single-electron-ejection extraction conclusion, without assuming every outgoing fit is meaningful.).",
+      "Close CL3 material validation/scope: V2 (When the fit, data, region, anomaly or conclusion exposes a material risk, challenge omitted open waves, coefficient non-identifiability, recovery-region contamination or normalization freedom with discriminating evidence, or narrow the claim; a missing prescribed convergence sequence alone is insufficient.)."
+    ]
+  },
+  "references": [
+    {
+      "citation": "Andrej Mihelič and Martin Horvat. 2021. *Calculation of multiphoton ionization amplitudes and cross sections of few-electron atoms*. *Physical Review A*, 103, 043108.",
+      "url": "https://doi.org/10.1103/PhysRevA.103.043108",
+      "scientific_scope": "Calculation of multiphoton ionization amplitudes and cross sections of few-electron atoms",
+      "anchors": [
+        "Mihelic and Horvat (2021), article pp.043108-3-4, Eqs.(19),(20),(28)-(30), velocity-form paragraph following Eq.(21): ordered unit-coefficient dipole-response hierarchy.",
+        "Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory.",
+        "Mihelic and Horvat (2021), article pp.043108-2-5, Eqs.(11)-(15),(26),(27),(31) and SI-unit paragraph: Coulomb amplitude normalization and absolute order-dependent generalized cross sections.",
+        "Mihelic and Horvat (2021), article p.043108-5, Fig.2(a), Eq.(31) and first Sec.III.A paragraph: hydrogen two-photon s/d partial cross sections and their arithmetic total; E1 channel parity extends to the higher orders in Fig.2(b,c).",
+        "Mihelic and Horvat (2021), article p.043108-5, Fig.2(b,c) and Sec.III.A threshold paragraphs: intermediate openings near 6.8/13.6 eV for K=3 and 4.5/6.8/13.6 eV for K=4, with off-pole high-energy decline.",
+        "Mihelic and Horvat (2021), article pp.043108-2-5, Eq.(9), paragraph preceding Eq.(12), Fig.1 caption, Sec.III.A pole limitation: extraction inside unscaled asymptotic space; exact bound poles are outside the unmodified real-energy perturbative prescription.",
+        "Mihelic and Horvat (2021), article pp.043108-4-5, Eqs.(23)-(31), Fig.1 and Sec.III.A discussion of radial extent/collocation resolution; p.043108-9, Sec.IV limits the extraction to single-electron ejection. Evidence synthesis and triggered alternative tests are task-defined, not prescribed source solver settings."
+      ]
+    }
+  ]
+}

cases/case02/grading_rubric.md

@@ -0,0 +1,890 @@
+# Grading Rubric — Case02
+
+Case02 — Calculation of multiphoton ionization amplitudes and cross sections of few-electron atoms
+
+## Atomic Scoring Criteria
+
+Each criterion awards 0 or 0.5 points, for a maximum of 10. Explicit N/A rules apply where stated.
+
+### F1 — F — 0.5 points
+
+**Scientific requirement**
+
+Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.
+
+**Conditions for credit**
+
+- The hydrogen-1s ordered hierarchy applies D=p_z exactly once with unit coefficient at each photon step; order and E1 channel parity are consistent.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article pp.043108-3-4, Eqs.(19),(20),(28)-(30), velocity-form paragraph following Eq.(21): ordered unit-coefficient dipole-response hierarchy.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F2 — F — 0.5 points
+
+**Scientific requirement**
+
+For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.
+
+**Conditions for credit**
+
+- All open intermediate energies and the selected final energy occur in the outgoing Coulomb representation, and a determinate common complex system isolates the final coefficient.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.)
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F3 — F — 0.5 points
+
+**Scientific requirement**
+
+Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.
+
+**Conditions for credit**
+
+- The isolated final coefficient maps to absolute generalized partial cross sections with declared Coulomb normalization and K-dependent units; independently normalized shapes do not qualify.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.)
+
+- Preserve independently valid work in I3, M3, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article pp.043108-2-5, Eqs.(11)-(15),(26),(27),(31) and SI-unit paragraph: Coulomb amplitude normalization and absolute order-dependent generalized cross sections.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### O4 — O — 0.5 points
+
+**Scientific requirement**
+
+Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.
+
+**Conditions for credit**
+
+- All K=4 E1-allowed final waves are presented in absolute units over a domain sufficient for claimed openings and off-pole high-energy behavior.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.)
+
+- Preserve independently valid work in O1, O2, O3, I3, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-5, Fig.2(b,c) and Sec.III.A threshold paragraphs: intermediate openings near 6.8/13.6 eV for K=3 and 4.5/6.8/13.6 eV for K=4, with off-pole high-energy decline.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O1 — O — 0.5 points
+
+**Scientific requirement**
+
+Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.
+
+**Conditions for credit**
+
+- Absolute K=2 s/d partial cross sections and their arithmetic total are reconstructible with correct normalization and stable material structure.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.)
+
+- Preserve independently valid work in O2, O3, O4, I1, I3, M1, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-5, Fig.2(a), Eq.(31) and first Sec.III.A paragraph: hydrogen two-photon s/d partial cross sections and their arithmetic total; E1 channel parity extends to the higher orders in Fig.2(b,c).
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O2 — O — 0.5 points
+
+**Scientific requirement**
+
+Present reconstructible absolute K=3 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.
+
+**Conditions for credit**
+
+- All K=3 E1-allowed final waves are presented in absolute units over a domain sufficient for claimed openings and off-pole high-energy behavior.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.)
+
+- Preserve independently valid work in O1, O3, O4, I3, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-5, Fig.2(b,c) and Sec.III.A threshold paragraphs: intermediate openings near 6.8/13.6 eV for K=3 and 4.5/6.8/13.6 eV for K=4, with off-pole high-energy decline.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O3 — O — 0.5 points
+
+**Scientific requirement**
+
+Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.
+
+**Conditions for credit**
+
+- A genuinely open-intermediate complex radial response and a common multi-wave reconstruction expose both components in the unscaled asymptotic region using one coefficient set.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.)
+
+- Preserve independently valid work in O1, O2, O4, I1, I2, M1, M2, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### I1 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify threshold/structure sequences organized by successive intermediate continuum openings, and off-pole high-energy decline, in the submitted K=3/4 absolute families.
+
+**Conditions for credit**
+
+- The candidate identifies intermediate-opening sequences and high-energy off-pole decline in their K=3/4 absolute families.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.)
+
+- Preserve independently valid work in O1, O3, I3, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-5, Fig.2(b,c) and Sec.III.A threshold paragraphs: intermediate openings near 6.8/13.6 eV for K=3 and 4.5/6.8/13.6 eV for K=4, with off-pole high-energy decline.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I2 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify the E1-allowed final partial-wave sets for K=2,3,4, the K=2 total, and correct order/channel binding across the submitted families.
+
+**Conditions for credit**
+
+- The candidate identifies K=2 l=0,2; K=3 l=1,3; K=4 l=0,2,4 and the K=2 arithmetic total with correct order binding.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O1 (Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.)
+
+- Preserve independently valid work in O3, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-5, Fig.2(a), Eq.(31) and first Sec.III.A paragraph: hydrogen two-photon s/d partial cross sections and their arithmetic total; E1 channel parity extends to the higher orders in Fig.2(b,c).
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I3 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify common multi-wave beating/asymptotic content caused by the open intermediate channel, the selected final coefficient, and the unscaled radial region actually supporting the identification.
+
+**Conditions for credit**
+
+- The candidate identifies common complex beating, the selected final component and the actual unscaled region supporting that interpretation.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.)
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M1 — M — 0.5 points
+
+**Scientific requirement**
+
+Use energy conservation and the submitted K=3/4 structures to explain which intermediate absorption steps open and how they organize the observed sequences.
+
+**Conditions for credit**
+
+- Energy conservation at successive absorption steps explains the observed K=3/4 threshold sequence and which intermediate continua open.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.); I1 (Identify threshold/structure sequences organized by successive intermediate continuum openings, and off-pole high-energy decline, in the submitted K=3/4 absolute families.)
+
+- Preserve independently valid work in O1, O3, I3, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-5, Fig.2(b,c) and Sec.III.A threshold paragraphs: intermediate openings near 6.8/13.6 eV for K=3 and 4.5/6.8/13.6 eV for K=4, with off-pole high-energy decline.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M2 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain the allowed final waves, K=2 arithmetic total and retained off-pole high-energy behavior from absolute data rather than channel-free plot description.
+
+**Conditions for credit**
+
+- The candidate explains E1 final-channel parity, K=2 summation and off-pole decline using their absolute data rather than channel-free descriptions.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); O1 (Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.); I2 (Identify the E1-allowed final partial-wave sets for K=2,3,4, the K=2 total, and correct order/channel binding across the submitted families.)
+
+- Preserve independently valid work in O3, I3, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-5, Fig.2(a), Eq.(31) and first Sec.III.A paragraph: hydrogen two-photon s/d partial cross sections and their arithmetic total; E1 channel parity extends to the higher orders in Fig.2(b,c).
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M3 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain why a single outgoing final wave is insufficient with an open intermediate continuum and why open intermediate and selected final energy Coulomb waves must coexist.
+
+**Conditions for credit**
+
+- The nonlocalized continuum driving term is connected to simultaneous intermediate- and final-energy outgoing waves; a lone final wave is shown insufficient.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.); O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.); I3 (Identify common multi-wave beating/asymptotic content caused by the open intermediate channel, the selected final coefficient, and the unscaled radial region actually supporting the identification.)
+
+- Preserve independently valid work in O1, O2, O4, M1, M2, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M4 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain how the common multi-wave coefficient system isolates the final outgoing coefficient and connects it to absolute cross sections; Wronskian, direct complex fit, surface relation and functionally equivalent extraction are accepted.
+
+**Conditions for credit**
+
+- The candidate explains how the common coefficient system distinguishes the final outgoing coefficient and connects it to absolute cross sections.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.); O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.); I3 (Identify common multi-wave beating/asymptotic content caused by the open intermediate channel, the selected final coefficient, and the unscaled radial region actually supporting the identification.)
+
+- Preserve independently valid work in O1, O2, O4, M1, M2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M5 — M — 0.5 points
+
+**Scientific requirement**
+
+Use one coefficient set to explain both real and imaginary response components and determine whether the fixed-wave-number Coulomb representation holds; separately fitting the components does not establish the common complex structure.
+
+**Conditions for credit**
+
+- One complex coefficient set explains real and imaginary radial components and supports or bounds the fixed-wave-number representation.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.); I3 (Identify common multi-wave beating/asymptotic content caused by the open intermediate channel, the selected final coefficient, and the unscaled radial region actually supporting the identification.)
+
+- Preserve independently valid work in O1, O2, O4, M1, M2, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M6 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain why coefficient recovery is supported only in the unscaled asymptotic region; distinguish ECS-contour response from real-axis continuation and state the boundary near exact bound poles or continuum resonances.
+
+**Conditions for credit**
+
+- Coefficient recovery is justified only in an unscaled asymptotic region; ECS-contour damping, real-axis continuation and near-pole limitations are distinguished.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.); I3 (Identify common multi-wave beating/asymptotic content caused by the open intermediate channel, the selected final coefficient, and the unscaled radial region actually supporting the identification.)
+
+- Preserve independently valid work in O1, O2, O4, M1, M2, M3, M4, M5, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article pp.043108-2-5, Eq.(9), paragraph preceding Eq.(12), Fig.1 caption, Sec.III.A pole limitation: extraction inside unscaled asymptotic space; exact bound poles are outside the unmodified real-energy perturbative prescription.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M7 — M — 0.5 points
+
+**Scientific requirement**
+
+Close the dimensional and normalization chain from selected final coefficient through declared Coulomb normalization and order-dependent units to absolute K-photon cross sections; independently normalized curves are insufficient.
+
+**Conditions for credit**
+
+- The coefficient, Coulomb normalization, photon order and units form one absolute dimensional chain without arbitrary channel-by-channel rescaling.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.); O1 (Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.)
+
+- Preserve independently valid work in O3, I3, M3, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article pp.043108-2-5, Eqs.(11)-(15),(26),(27),(31) and SI-unit paragraph: Coulomb amplitude normalization and absolute order-dependent generalized cross sections.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M8 — M — 0.5 points
+
+**Scientific requirement**
+
+Synthesize the absolute partial-wave families and open-intermediate complex response into a supported off-pole, perturbative single-electron-ejection extraction conclusion, without assuming every outgoing fit is meaningful.
+
+**Conditions for credit**
+
+- The absolute partial families and open-intermediate reconstruction jointly support a bounded off-pole, perturbative single-electron-ejection extraction conclusion.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: M3 (Explain why a single outgoing final wave is insufficient with an open intermediate continuum and why open intermediate and selected final energy Coulomb waves must coexist.); M4 (Explain how the common multi-wave coefficient system isolates the final outgoing coefficient and connects it to absolute cross sections; Wronskian, direct complex fit, surface relation and functionally equivalent extraction are accepted.); M5 (Use one coefficient set to explain both real and imaginary response components and determine whether the fixed-wave-number Coulomb representation holds; separately fitting the components does not establish the common complex structure.); M7 (Close the dimensional and normalization chain from selected final coefficient through declared Coulomb normalization and order-dependent units to absolute K-photon cross sections; independently normalized curves are insufficient.)
+
+- Preserve independently valid work in O1, O2, O3, O4, I1, I2, I3, M1, M2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article pp.043108-4-5, Eqs.(23)-(31), Fig.1 and Sec.III.A discussion of radial extent/collocation resolution; p.043108-9, Sec.IV limits the extraction to single-electron ejection. Evidence synthesis and triggered alternative tests are task-defined, not prescribed source solver settings.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V1 — V — 0.5 points
+
+**Scientific requirement**
+
+Positively restrict the conclusion to the specified hydrogen single-electron ionization, ordered perturbation theory, real-energy off-pole response, sampled energy domain and selected unscaled asymptotic region.
+
+**Conditions for credit**
+
+- The candidate positively states hydrogen single-electron ionization, ordered perturbation, real-energy off-pole domain and actual unscaled recovery interval.
+
+**Applicability and N/A**
+
+- This positive scientific scope/evidence duty is unconditional; N/A is not permitted.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article pp.043108-2-5, Eq.(9), paragraph preceding Eq.(12), Fig.1 caption, Sec.III.A pole limitation: extraction inside unscaled asymptotic space; exact bound poles are outside the unmodified real-energy perturbative prescription.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V2 — V — 0.5 points
+
+**Scientific requirement**
+
+When the fit, data, region, anomaly or conclusion exposes a material risk, challenge omitted open waves, coefficient non-identifiability, recovery-region contamination or normalization freedom with discriminating evidence, or narrow the claim; a missing prescribed convergence sequence alone is insufficient.
+
+**Conditions for credit**
+
+- When a material risk is exposed, capable evidence challenges omitted waves, coefficient degeneracy, region contamination or normalization freedom, or the claim is narrowed; otherwise N/A.
+
+**Applicability and N/A**
+
+- Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.
+
+- If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Globally equivalent Coulomb phases, radial signs and plotting conventions are accepted after alignment.
+
+- Wronskians, direct complex fits and equivalent surface-flux relations are accepted only when they recover the same outgoing final coefficient and absolute Coulomb normalization.
+
+- The open-intermediate radial case is student-selected: K=2, omega=1 a.u., l=2 is canonical but not compulsory. The real and imaginary parts must use one coefficient set.
+
+- A broadened response can provide secondary evidence but cannot replace the primary real-energy off-pole object. Exact pole heights, source plot bounds, basis and layout are not targets.
+
+**Scientific source locations**
+
+- Mihelic and Horvat (2021), article pp.043108-4-5, Eqs.(23)-(31), Fig.1 and Sec.III.A discussion of radial extent/collocation resolution; p.043108-9, Sec.IV limits the extraction to single-electron ejection. Evidence synthesis and triggered alternative tests are task-defined, not prescribed source solver settings.
+
+**Research Closure relation**
+
+Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+## Research Closure Requirements
+
+### RC0
+
+- The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.
+
+- Required indispensable claim CL0, central physical object: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC1
+
+- With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.
+
+- Required co primary claim CL1, indispensable material component: all of: O1 (Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.); O2 (Present reconstructible absolute K=3 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL2, indispensable material component: all of: O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC2
+
+- With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.
+
+- Required co primary claim CL1, principal mechanism or commissioned conclusion: all of: M7 (Close the dimensional and normalization chain from selected final coefficient through declared Coulomb normalization and order-dependent units to absolute K-photon cross sections; independently normalized curves are insufficient.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M3 (Explain why a single outgoing final wave is insufficient with an open intermediate continuum and why open intermediate and selected final energy Coulomb waves must coexist.); M4 (Explain how the common multi-wave coefficient system isolates the final outgoing coefficient and connects it to absolute cross sections; Wronskian, direct complex fit, surface relation and functionally equivalent extraction are accepted.); M5 (Use one coefficient set to explain both real and imaginary response components and determine whether the fixed-wave-number Coulomb representation holds; separately fitting the components does not establish the common complex structure.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL3, principal mechanism or commissioned conclusion: M8 (Synthesize the absolute partial-wave families and open-intermediate complex response into a supported off-pole, perturbative single-electron-ejection extraction conclusion, without assuming every outgoing fit is meaningful.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC3
+
+- With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.
+
+- Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.
+
+- Required co primary claim CL3, material validation/scope: V2 (When the fit, data, region, anomaly or conclusion exposes a material risk, challenge omitted open waves, coefficient non-identifiability, recovery-region contamination or normalization freedom with discriminating evidence, or narrow the claim; a missing prescribed convergence sequence alone is insufficient.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC4
+
+- All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.
+
+- Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.
+
+- Close CL0 central physical object: all of: F1 (Establish the ordered hydrogen-1s K-photon driven-response hierarchy with velocity-form D=p_z, one unit-coefficient application of D per step, and correct photon-order/E1-channel binding.); F2 (For an open intermediate continuum, construct the multi-wave Coulomb asymptote containing every open intermediate wave and the selected final wave, and a determinate extraction uniquely isolating the final coefficient.); F3 (Convert the isolated outgoing final coefficient to absolute partial generalized cross sections under declared Coulomb normalization, cross-section convention and photon-order units. The K=2 arithmetic total belongs to O1 alone.).
+
+- Close CL1 indispensable material component: all of: O1 (Present reconstructible absolute K=2 l=0 and l=2 partial cross sections and their arithmetic total, with correct case binding, stable large-scale structure and absolute normalization.); O2 (Present reconstructible absolute K=3 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.); O4 (Present reconstructible absolute K=4 cross sections for all E1-allowed partial waves over a chosen energy domain sufficient for the claimed channel openings and off-pole high-energy behavior.).
+
+- Close CL1 principal mechanism or commissioned conclusion: all of: M7 (Close the dimensional and normalization chain from selected final coefficient through declared Coulomb normalization and order-dependent units to absolute K-photon cross sections; independently normalized curves are insufficient.).
+
+- Close CL2 indispensable material component: all of: O3 (Present a genuinely open-intermediate complex radial response and one common multi-wave outgoing reconstruction using the same coefficients for real and imaginary parts, with reconstructible data in the unscaled asymptotic region.).
+
+- Close CL2 principal mechanism or commissioned conclusion: all of: M3 (Explain why a single outgoing final wave is insufficient with an open intermediate continuum and why open intermediate and selected final energy Coulomb waves must coexist.); M4 (Explain how the common multi-wave coefficient system isolates the final outgoing coefficient and connects it to absolute cross sections; Wronskian, direct complex fit, surface relation and functionally equivalent extraction are accepted.); M5 (Use one coefficient set to explain both real and imaginary response components and determine whether the fixed-wave-number Coulomb representation holds; separately fitting the components does not establish the common complex structure.).
+
+- Close CL3 principal mechanism or commissioned conclusion: M8 (Synthesize the absolute partial-wave families and open-intermediate complex response into a supported off-pole, perturbative single-electron-ejection extraction conclusion, without assuming every outgoing fit is meaningful.).
+
+- Close CL3 material validation/scope: V2 (When the fit, data, region, anomaly or conclusion exposes a material risk, challenge omitted open waves, coefficient non-identifiability, recovery-region contamination or normalization freedom with discriminating evidence, or narrow the claim; a missing prescribed convergence sequence alone is insufficient.).
+
+## Applicability and Equivalent Evidence
+
+- Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.
+
+- Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.
+
+- For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.
+
+- Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.
+
+- Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.
+
+- Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.
+
+- Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.
+
+- Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.
+
+- Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.
+
+- Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.
+
+- A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.
+
+- The E1-allowed families are K=2: l=0,2; K=3: l=1,3; K=4: l=0,2,4. The K=2 arithmetic total has only one scoring and indispensable-component owner, O1.
+
+- A local presentation or low-energy resolution gap in K=3 does not erase independent channel identity, absolute normalization or a correctly bounded inference supported by the valid remaining evidence.
+
+- The overall extraction synthesis requires the common multi-wave representation, final-coefficient isolation, common complex reconstruction and absolute normalization. Supporting fine opening sequences, family interpretation and recovery-region explanation retain independent scoring; they are not silently promoted to additional all-or-nothing central gates.
+
+- The canonical construction solves the ordered hierarchy
+
+$$
+(E_0+j\omega-H)\widehat\Psi_j=D\widehat\Psi_{j-1},
+\qquad j=1,\ldots,K,
+$$
+
+- with one unit-coefficient application of $D=p_z$ at each step. In an open partial wave, the large-radius radial response is a linear combination of the outgoing Coulomb waves associated with every open intermediate energy and the selected final energy. Wronskians sampled at several radii in the unscaled asymptotic region determine the coefficients; the coefficient of the final wave gives the ionization amplitude and hence the conventional generalized cross section. Equivalent direct linear fits or surface-flux formulations are acceptable only when they recover the same outgoing coefficient and absolute normalization.
+
+- the two-photon family contains $\ell=0,2$ partial cross sections and their arithmetic total;
+
+- the three-photon family contains $\ell=1,3$ and resolves sequences approaching about 6.8 and 13.6 eV, associated with the successive opening of intermediate ATI steps;
+
+- the four-photon family contains $\ell=0,2,4$ and resolves corresponding sequences approaching about 4.5, 6.8 and 13.6 eV;
+
+- away from resonant poles, the selected ATI branches decrease at high photon energy over the retained range; exact pole heights are not finite physical anchors;
+
+- the source's canonical $K=2$, $\omega=1$ a.u., $(\ell,m)=(2,0)$ example has a beat-like unscaled complex radial response described by one common pair of outgoing Coulomb waves with $k=1$ and $k=\sqrt3$; this is a reference anchor, not the only acceptable student-selected open-intermediate response;
+
+- coefficient recovery must use the unscaled region. The damped computed ECS response beyond $R_0$ and a real-axis analytic continuation are different objects and their post-$R_0$ difference is not fit evidence.
+
+For F2-F3/M4-M7, article pp.043108-3-5, Eqs.(14),(23)-(31), define
+$$H_\ell(k;r)=e^{-i\eta_\ell(k)}[F_\ell(k;r)+iG_\ell(k;r)],\quad
+\widehat P_\ell(r)\sim\sum_q A_{\ell q}H_\ell(k_q;r),\quad k_q=\sqrt{2(E_0+j_q\omega)}>0.$$
+With the article's outgoing Coulomb convention and final index $n$,
+$$B_\ell=i^{-\ell+1}\sqrt{\frac{k_n}{2\pi}}A_{\ell n},\qquad
+\sigma^{(K)}_\ell=2\pi\left(\frac{2\pi}{c\omega}\right)^K|B_\ell|^2.$$
+The SI conversion factor is $a_0^{2K}t_0^{K-1}$, giving area$^K$ time$^{K-1}$. The canonical extraction uses $M_{pq}=W\{F_\ell(k_n;r),H_\ell(k_q;r)\}_{r_p}$ and $b_p=W\{F_\ell(k_n;r),\widehat P_\ell(r)\}_{r_p}$, with $W\{f,g\}=fg'-f'g$ and $r_p<R_0$ in the asymptotic region. A common complex direct fit or equivalent surface relation is accepted when it isolates the same absolutely normalized coefficient.

cases/case02/resource_limits.json

@@ -0,0 +1,8 @@
+{
+  "cpu_cores": 16,
+  "nodes": 1,
+  "time_limit_minutes": 30,
+  "network_access": "disabled",
+  "temporary_storage_gib": 64,
+  "memory_policy": "No separate task-specific RAM limit is specified."
+}

cases/case02/sources.md

@@ -0,0 +1,35 @@
+# Scientific Sources — Case02
+
+## References
+
+Andrej Mihelič and Martin Horvat. 2021. *Calculation of multiphoton ionization amplitudes and cross sections of few-electron atoms*. *Physical Review A*, 103, 043108. [Source](https://doi.org/10.1103/PhysRevA.103.043108)
+
+Calculation of multiphoton ionization amplitudes and cross sections of few-electron atoms
+
+## Criterion-to-source crosswalk
+
+Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.
+
+| Criteria | Source locations, scientific use and limits |
+|---|---|
+| F1 | Mihelic and Horvat (2021), article pp.043108-3-4, Eqs.(19),(20),(28)-(30), velocity-form paragraph following Eq.(21): ordered unit-coefficient dipole-response hierarchy. |
+| F2, O3, I3, M3, M4, M5 | Mihelic and Horvat (2021), article p.043108-4, Fig.1 and Eqs.(22)-(26): open-intermediate multi-wave asymptote and one complex coefficient system isolating the final wave. The two-wave omega=1 example is illustrative, not mandatory. |
+| F3, M7 | Mihelic and Horvat (2021), article pp.043108-2-5, Eqs.(11)-(15),(26),(27),(31) and SI-unit paragraph: Coulomb amplitude normalization and absolute order-dependent generalized cross sections. |
+| O1, I2, M2 | Mihelic and Horvat (2021), article p.043108-5, Fig.2(a), Eq.(31) and first Sec.III.A paragraph: hydrogen two-photon s/d partial cross sections and their arithmetic total; E1 channel parity extends to the higher orders in Fig.2(b,c). |
+| O2, O4, I1, M1 | Mihelic and Horvat (2021), article p.043108-5, Fig.2(b,c) and Sec.III.A threshold paragraphs: intermediate openings near 6.8/13.6 eV for K=3 and 4.5/6.8/13.6 eV for K=4, with off-pole high-energy decline. |
+| M6, V1 | Mihelic and Horvat (2021), article pp.043108-2-5, Eq.(9), paragraph preceding Eq.(12), Fig.1 caption, Sec.III.A pole limitation: extraction inside unscaled asymptotic space; exact bound poles are outside the unmodified real-energy perturbative prescription. |
+| M8, V2 | Mihelic and Horvat (2021), article pp.043108-4-5, Eqs.(23)-(31), Fig.1 and Sec.III.A discussion of radial extent/collocation resolution; p.043108-9, Sec.IV limits the extraction to single-electron ejection. Evidence synthesis and triggered alternative tests are task-defined, not prescribed source solver settings. |
+
+## Formula and convention notes
+
+For F2-F3/M4-M7, article pp.043108-3-5, Eqs.(14),(23)-(31), define
+$$H_\ell(k;r)=e^{-i\eta_\ell(k)}[F_\ell(k;r)+iG_\ell(k;r)],\quad
+\widehat P_\ell(r)\sim\sum_q A_{\ell q}H_\ell(k_q;r),\quad k_q=\sqrt{2(E_0+j_q\omega)}>0.$$
+With the article's outgoing Coulomb convention and final index $n$,
+$$B_\ell=i^{-\ell+1}\sqrt{\frac{k_n}{2\pi}}A_{\ell n},\qquad
+\sigma^{(K)}_\ell=2\pi\left(\frac{2\pi}{c\omega}\right)^K|B_\ell|^2.$$
+The SI conversion factor is $a_0^{2K}t_0^{K-1}$, giving area$^K$ time$^{K-1}$. The canonical extraction uses $M_{pq}=W\{F_\ell(k_n;r),H_\ell(k_q;r)\}_{r_p}$ and $b_p=W\{F_\ell(k_n;r),\widehat P_\ell(r)\}_{r_p}$, with $W\{f,g\}=fg'-f'g$ and $r_p<R_0$ in the asymptotic region. A common complex direct fit or equivalent surface relation is accepted when it isolates the same absolutely normalized coefficient.
+
+## Scope of the source anchors
+
+The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.

cases/case02/task.md

@@ -0,0 +1,119 @@
+# Multiphoton ionization from driven scattering responses
+
+## Background
+
+Time-independent perturbation theory can avoid the long propagation times of
+a pulsed calculation, but multiphoton ionization becomes difficult once an
+intermediate absorption step is already in the continuum. A useful method
+must then recover absolute channel amplitudes from a driven scattering
+response without confusing open intermediate continua with the selected final
+photoelectron channel.
+
+## Research problem
+
+Develop and assess a time-independent method for extracting absolute
+generalized multiphoton ionization cross sections from driven responses of
+ground-state hydrogen. Apply it to two-, three-, and four-photon ionization,
+including photon-energy regions in which one or more intermediate steps are
+open. Determine what the resulting partial-wave family establishes about the
+opening of above-threshold pathways and whether the asymptotic content of a
+representative complex response supports the extraction principle.
+
+The derivation, numerical construction, choice of scientific evidence and
+organization of the argument are yours. Establish the validity and limits of
+the extraction from your calculated responses rather than assuming that an
+outgoing-wave fit is automatically meaningful.
+
+## Physical inputs
+
+Use atomic units internally. The target is hydrogen in its normalized,
+positive-real $1s$ ground state, with energy $E_0=-1/2$. The light is linearly
+polarized along $z$, and the interaction operator for each absorbed photon is
+the velocity-form dipole $D=p_z$.
+
+Treat the following photon orders:
+
+| Photon order | Conventional reported unit |
+|---|---|
+| $K=2$ | $\mathrm{cm^4\,s}$ |
+| $K=3$ | $\mathrm{cm^6\,s^2}$ |
+| $K=4$ | $\mathrm{cm^8\,s^3}$ |
+
+Resolve every electric-dipole-allowed final partial wave reached from the
+$1s$ state. For $K=2$, also report the arithmetic total of those partial
+cross sections. The allowed angular channels and their order dependence are
+part of your derivation.
+
+Choose an energetically allowed photon-energy domain sufficient to establish
+the channel-opening and high-energy claims you make. The primary graded
+objects are the real-energy, unbroadened perturbative responses away from
+exact bound-state poles. Exact pole samples may be omitted or explicitly
+flagged; do not replace the primary result with a phenomenologically
+broadened spectrum.
+
+As a method-level audit, also treat at least one student-chosen complex radial
+response for which an intermediate absorption step is open. Assess its
+outgoing Coulomb-wave content in the unscaled asymptotic region. Any real-axis
+continuation beyond the ECS onset must be distinguished from the computed
+response on the ECS contour.
+
+State the Coulomb-wave normalization, phase, radial-wave convention,
+atomic-unit conversion constants and generalized-cross-section convention
+used. Absolute cross sections, rather than independently normalized display
+curves, are the grading target.
+
+## Method boundary
+
+Use ordered time-independent perturbative driven equations and ECS outgoing
+boundary conditions. In the response convention for this task, every photon
+step consists of one application of $D$; do not insert an additional
+factorial, permutation, field-amplitude or order-dependent coefficient into
+the successive response states.
+
+You must derive the task-specific response hierarchy, the asymptotic
+coefficient extraction and the conversion from the selected outgoing
+coefficient to the reported cross section. Standard Coulomb functions, ECS,
+linear algebra and atomic-unit conversions may be selected and cited. No
+particular radial basis, knot sequence, ECS angle, box extent, sampling grid,
+fit implementation, solver, tolerance or plotting layout is prescribed.
+
+You are responsible for checking that the calculated evidence is sufficiently
+reliable and reproducible for the conclusions made. Numerical reliability has
+no separate deliverable or prescribed test sequence; it is reflected in the
+correctness and quality of the reported physical evidence.
+
+## Submission
+
+Submit one self-contained scientific report and an offline reproduction
+package containing the derivation, executable code, reconstructible absolute
+partial-cross-section data, the complex radial data and asymptotic
+reconstruction used in the method assessment, a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge, and
+concise run and environment information. The organization and number of
+figures are yours. No fixed file tree, filename scheme, complete exploratory
+history or examiner-selected diagnostic is required.
+
+The active examination resources and limits are defined in the companion
+`resource_limits.json`. All retained production calculations must run
+within that fixed allocation and active wall time. More expensive modelling
+does not receive additional credit.
+
+## Reference and integrity policy
+
+This examination is conducted without network access or live literature
+retrieval. You may rely on your existing general scientific knowledge and, if any are
+explicitly supplied with the examination, on those offline materials or
+software documentation. Record every such source actually consulted. For formulas,
+methods, constants, or conventions used from general knowledge rather than a
+consulted source, state enough of the method basis, definition, value, units,
+and convention to make the calculation auditable; do not invent a citation.
+You are not required to identify or prove a publication date or to retrieve
+literature during the examination.
+
+The hidden target article and its identifying metadata, figures or captions,
+supplementary material, author code or data, target-specific reproduction
+code, solution or scoring material, online solutions, and worked
+reproductions of this case must not be used. All submitted scientific figures
+and numerical data must be generated by your own implementation of the stated
+problem.
+
+See [submission requirements](../../submission_requirements.md) for the common submission entry points.

cases/case03/grading_rubric.json

@@ -0,0 +1,605 @@
+{
+  "case_id": "Case03",
+  "title": "Case03 — Efficient time-sampling method in Coulomb-corrected strong-field approximation",
+  "atoms": [
+    {
+      "criterion_id": "F1",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.",
+      "award_conditions": [
+        "All six signed-plane objects and coherent cell accumulation are defined, with absolute-area Jp/Jq separated from cell/proposal factors and normalization; determinant orientation is not a phase."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F2, O1, O2, O3, O4, O5, O6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F2",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.",
+      "award_conditions": [
+        "The declared phase, launch, propagation, asymptotic continuation and finite-tail equations distinguish adiabatic QTMC from q-labelled nonadiabatic CCSFA."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F1, O1, O2, O3, O4, O5, O6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-2-4, Eqs.(7)-(16),(22)-(28),(33)-(36): direct amplitude, nonadiabatic launch, Coulomb dynamics and -2/r action. Operational finite asymptotic/tail closure is supplied by Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40), not explicitly by Xiao et al."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "O1",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Reach the first-coverage milestone of the homogeneous no-Coulomb family N1 direct, N2 unweighted complex-time, N3 Jp-weighted complex-time: any one independently valid, reconstructible and adequately presented member suffices, without supplying the other members.",
+      "award_conditions": [
+        "At least one of N1/N2/N3 independently has a correct reconstructible and adequately presented no-Coulomb identity; no missing member is supplied by another.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F1, F2, O2, O3, I1, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O2",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Reach second coverage of N1 direct, N2 unweighted complex-time and N3 Jp-weighted complex-time: at least two independently object-valid, presentation-adequate and claim-adequate members share signed axes, pulse, phase and cell/binning conventions. No member supplies another.",
+      "award_conditions": [
+        "At least two independently valid N1/N2/N3 members are reconstructible and comparable in signed axes, pulse, phase and cell convention.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O1 (Reach the first-coverage milestone of the homogeneous no-Coulomb family N1 direct, N2 unweighted complex-time, N3 Jp-weighted complex-time: any one independently valid, reconstructible and adequately presented member suffices, without supplying the other members.)",
+        "Preserve independently valid work in F1, F2, O3, I1, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O3",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.",
+      "award_conditions": [
+        "All three N1/N2/N3 members are independently valid and comparable; N2 omits only Jp, retains the induced distortion, and N3 approaches direct N1 at demonstrated resolution.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O2 (Reach second coverage of N1 direct, N2 unweighted complex-time and N3 Jp-weighted complex-time: at least two independently object-valid, presentation-adequate and claim-adequate members share signed axes, pulse, phase and cell/binning conventions. No member supplies another.)",
+        "Preserve independently valid work in F1, F2, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O4",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.",
+      "award_conditions": [
+        "C1 is an independent coherent planar QTMC object with signed transverse launch, y=vy=py=0, regularized action and reached asymptotic-momentum bins; material support/envelope/arcs are resolved.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in O5, O6, I2, M3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-4,6, Eqs.(33),(34),(36), Fig.2(b): adiabatic planar QTMC with coherent final-momentum accumulation. The signed planar reduction and finite tail/asymptotic implementation follow the stated task and standard-method equivalence class."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O5",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.",
+      "award_conditions": [
+        "C2 actually samples q and solves contributing saddles under a declared converged prescription, uses nonadiabatic launch and common finite-tail/asymptotic treatment, and resolves material reached-momentum structure.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in O4, O6, I2, I3, M3, M4, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O6",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.",
+      "award_conditions": [
+        "C3 independently samples complex time with Jq and the same q-labelled saddle/launch/action/tail/bin identity as C2; C2 data cannot replace it.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in O4, O5, I2, M3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "I1",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify from submitted arrays/slices the nonuniform-measure failure of N2, including scarce support near px=0 when resolved, and convergence of N3 toward N1 under sampling/bin refinement, rather than generic image texture.",
+      "award_conditions": [
+        "The candidate identifies N2's nonuniform measure and resolved scarce support near px=0, and N3's convergence toward N1 using their own arrays or slices."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O3 (Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.)",
+        "Preserve independently valid work in F1, O1, O2, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I2",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify from reached-p_infinity data the common-q C2/C3 agreement in global support, envelope and resolved major rings/ridges, limiting fine-structure equivalence to actually resolved features.",
+      "award_conditions": [
+        "Candidate identification establishes C2/C3 agreement of global support, envelope and resolved major rings/ridges at reached asymptotic momentum, bounding fine-structure claims."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.); O6 (Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.)",
+        "Preserve independently valid work in O4, M3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I3",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify directly in C1 versus C2 the major CCSFA-family ridge/distribution shift toward larger final momentum relative to QTMC. Extend it to C3 only when I2 supports C2/C3 agreement; pointwise fringe matching is not required.",
+      "award_conditions": [
+        "The candidate identifies the direct C1/C2 local shift toward larger final momentum; extending it to C3 requires actual C2/C3 agreement."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O4 (Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.); O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.)",
+        "Preserve independently valid work in O6, I2, M4, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning \"In the present work\" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M1",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain how uniform sampling in (tr,ti) induces a nonuniform momentum measure rather than merely saying the weighted image is better.",
+      "award_conditions": [
+        "The time-to-momentum change of variables explains why uniform complex-time samples create a nonuniform momentum measure."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.)",
+        "Preserve independently valid work in F2, I1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M2",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain how the absolute-area Jacobian corrects the variable transformation and distinguish it from deterministic cell measure or Monte Carlo proposal weights.",
+      "award_conditions": [
+        "The absolute-area Jacobian is derived/interpreted as the measure correction, distinct from estimator proposal probabilities and deterministic cell factors."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.)",
+        "Preserve independently valid work in O1, I1, M1, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M3",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain C2/C3 as two sampling directions of the same q-labelled saddle/launch ensemble, with Jq correcting only sampling measure followed by common propagation and reached-p_infinity binning.",
+      "award_conditions": [
+        "The candidate explains common-q C2/C3 equivalence through a common saddle/launch ensemble, propagation and asymptotic bins, with Jq changing only sampling measure."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.); I2 (Identify from reached-p_infinity data the common-q C2/C3 agreement in global support, envelope and resolved major rings/ridges, limiting fine-structure equivalence to actually resolved features.)",
+        "Preserve independently valid work in O5, O6, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M4",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.",
+      "award_conditions": [
+        "The resolved local CCSFA shift is linked to its nonzero nonadiabatic longitudinal launch; the account is not asserted for the entire PMD."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.); I3 (Identify directly in C1 versus C2 the major CCSFA-family ridge/distribution shift toward larger final momentum relative to QTMC. Extend it to C3 only when I2 supports C2/C3 agreement; pointwise fringe matching is not required.)",
+        "Preserve independently valid work in I2, M3, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning \"In the present work\" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M5",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use convergence evidence to distinguish residual sample scarcity/bin asymmetry from physical structure and restrict N3 recovery of N1 to the resolved no-Coulomb validation; an unresolved map does not establish validation.",
+      "award_conditions": [
+        "Refinement evidence separates scarcity/bin asymmetry from physical structure and supports only resolved no-Coulomb recovery."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I1 (Identify from submitted arrays/slices the nonuniform-measure failure of N2, including scarce support near px=0 when resolved, and convergence of N3 toward N1 under sampling/bin refinement, rather than generic image texture.)",
+        "Preserve independently valid work in M1, M2, V1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M6",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Distinguish direct C1/C2 observations, extensions supported by C2/C3 agreement and unresolved fine structure; unresolved features cannot support a mechanism. Fine interference is optional strengthening evidence.",
+      "award_conditions": [
+        "Direct C1/C2 observation, inference via C2/C3 agreement and unresolved fine structure are distinguished; an unresolved fringe is not mechanism evidence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in I2, I3, M3, M4, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning \"In the present work\" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M7",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Form the commissioned QTMC-CCSFA family conclusion from the resolved direct C1/C2 shift and local launch mechanism; extend it to C3 only when independently demonstrated C2/C3 agreement permits.",
+      "award_conditions": [
+        "The family conclusion closes with the direct resolved shift and local launch mechanism; C3 is included only to the extent its independent agreement supports."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I3 (Identify directly in C1 versus C2 the major CCSFA-family ridge/distribution shift toward larger final momentum relative to QTMC. Extend it to C3 only when I2 supports C2/C3 agreement; pointwise fringe matching is not required.); M4 (Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.)",
+        "Preserve independently valid work in I2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning \"In the present work\" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V1",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Supply code/commands reproducing all six arrays, branch-specific numerical choices, raw cell/density conventions, separate cell/proposal factors, seeds/counts, normalization and claim-relevant stability evidence; judge implemented local parts without reward for resource consumption or duplicate penalties.",
+      "award_conditions": [
+        "Code/commands and branch-specific records reproduce six arrays, raw cell/density measures, separate estimator factors, seeds/counts and claim-relevant stability without rewarding resource use."
+      ],
+      "applicability_and_na": [
+        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F1, F2, O1, O2, O3, O4, O5, O6, I1, I2, I3, M1, M2, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article p.053310-6, Sec.III.A sampling/bin-error discussion and p.053310-7 Table I (efficiency context only); Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40) for finite post-pulse treatment. Reproduction records, compatible complex-estimator replica aggregation and risk-triggered checks are task-defined; no source sample count or runtime is a scoring target."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V2",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Only when estimator/Jacobian placement, saddle/contour consistency, replica aggregation, asymptotic/tail treatment or sampling-scarcity claims create a material threat to a central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.",
+      "award_conditions": [
+        "Only a concrete central risk in estimator weights, saddles, replicas, asymptotic tails or scarcity triggers discriminating validation; otherwise the assessable item is N/A."
+      ],
+      "applicability_and_na": [
+        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
+        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F1, F2, O1, O2, O3, O4, O5, O6, I1, I2, I3, M1, M2, M3, M4, M5, M6, M7, V1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
+        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
+        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
+      ],
+      "source_support": [
+        "Xiao et al. (2016), article p.053310-6, Sec.III.A sampling/bin-error discussion and p.053310-7 Table I (efficiency context only); Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40) for finite post-pulse treatment. Reproduction records, compatible complex-estimator replica aggregation and risk-triggered checks are task-defined; no source sample count or runtime is a scoring target."
+      ],
+      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    }
+  ],
+  "case_scientific_rules": [
+    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
+    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
+    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
+    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
+    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
+    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
+    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
+    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
+    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
+    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
+    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
+    "For the no-Coulomb map pz=-Ar(tr,ti), px=+/-sqrt(Ai(tr,ti)^2-2Ip), retain both signed branches and the admissible real domain. The CCSFA sampling map is to saddle/drift q, not asymptotic p_infinity.",
+    "Only the absolute area Jacobian Jp is omitted in N2; all saddle prefactors, phases and cell/proposal weights remain. Apply Ms_eff=Ms J in weighted branches, not sqrt(J), an arbitrary factor, an oriented-sign phase or an invented q-to-p_infinity Jacobian.",
+    "C2 samples q then solves roots and propagates; C3 samples complex time then maps to q. Both use the same nonadiabatic launch, action, contributing saddles, asymptotic map, tail convention and final cells. Ordinary CCSFA is not an asymptotic-momentum shooting problem.",
+    "Independent replicas must be combined at a compatible complex-estimator level before power. Duplicate seeds are not independent samples. Document proposed/sampled, propagated-root/trajectory and outgoing counts separately.",
+    "No-Coulomb coverage atoms are cumulative one/two/three-member milestones, not fixed assignments of N1, N2 and N3 to separate credits. Each Coulomb output C1, C2 and C3 is independently adjudicated.",
+    "Joint tail-parameter and cell-width stability must support relative phases and PMDs. An arbitrary finite-time momentum, literal divergent post-pulse integral, or branch-dependent cutoff determining the comparison is not equivalent.",
+    "When a major-feature mismatch would decide credit, compare like normalized objects against combined cell resolution and sampling uncertainty. No fixed image-correlation threshold is prescribed; unresolved physical-versus-numerical disagreement requires bounded review rather than an invented tolerance.",
+    "| ID | Mathematical object | Required branch identity | Normalization and units |\n|---|---|---|---|\n| N1 | Direct no-Coulomb $\\vert M(p_x,p_z)\\vert ^2$ from the finite-endpoint length-gauge SFA integral | Direct time integration; no Coulomb | Momentum in a.u.; yield in arbitrary units; one momentum-independent factor is free |\n| N2 | $\\vert \\sum_b a_s^{(\\mathrm{nc})}\\vert ^2$ from complex-time samples with $J_p=\\vert \\det\\partial(p_x,p_z)/\\partial(t_r,t_i)\\vert $ omitted and all other estimator weights retained | Same saddles/prefactor/phase/binning as N3 | Same as N1; `unweighted` omits only $J_p$ |\n| N3 | $\\vert \\sum_b a_s^{(\\mathrm{nc})}J_p\\vert ^2$ | Same physical branch as N2 with the absolute area Jacobian | Same as N1 |\n| C1 | Coherent planar QTMC PMD with $y=v_y=p_y=0$ | Standard stated one-component signed transverse-$p_x$ ADK/Landau initialization; retained post-release equations and $-2/r$ action; post-pulse Coulomb/Kepler map and finite regularized phase | Reached $\\mathbf p_\\infty$ in a.u.; yield in arbitrary units |\n| C2 | Coherent ordinary CCSFA PMD | Sample saddle/drift $\\mathbf q$, solve contributing saddle roots, propagate, map the end-of-pulse state to $\\mathbf p_\\infty$, and bin there; nonadiabatic launch | Same as C1 |\n| C3 | Coherent time-sampled CCSFA PMD | Complex-time sampling $\\rightarrow\\mathbf q$ with $J_q=\\vert \\det\\partial(q_x,q_z)/\\partial(t_r,t_i)\\vert $; same launch/action/post-pulse map and phase/saddles/$\\mathbf p_\\infty$ binning as C2 | Same as C1 |",
+    "The common physical construction for C1-C3 uses the planar reduction, a standard analytic Coulomb/Kepler end-of-pulse-to-asymptotic map or a demonstrated equivalent continuation, and a finite regularized post-pulse Coulomb phase within the tail-equivalence class stated in task. Cell-representative matching and trajectory-specific regularized actions are both acceptable when the submitted evidence shows that the selected tail and cell representation do not drive the claimed structures. Do not require a particular cutoff, radius, solver, grid, quadrature, caustic treatment, regularization, contour prescription, or root subset. Reject a comparison in which C2 and C3 use inconsistent declared saddle prescriptions, launch relations, asymptotic maps, Coulomb action factors, tail conventions, or $\\mathbf p_\\infty$ bin definitions. Saved raw arrays must identify cell-integrated versus density/average form, with deterministic cell measures or Monte Carlo proposal corrections documented separately from $J_p$ or $J_q$.",
+    "Uniform complex-time sampling maps nonuniformly into momentum space. Omitting the absolute area Jacobian produces the wrong measure; the most explicit source signal is scarce samples/noise near $p_x=0$, not a mandatory `boxy` appearance. Deterministic cell measure or Monte Carlo proposal correction remains separate from that Jacobian.",
+    "With the determinant and sufficient sampling, the time-sampled no-Coulomb result reproduces the direct SFA structures substantially better. Residual central noise and left-right asymmetry may remain at finite sampling/bin size.",
+    "Time-sampled CCSFA should reproduce ordinary CCSFA because both construct the same $\\mathbf q$-labelled saddle/launch ensemble, propagate it, and bin by reached $\\mathbf p_\\infty$; only the sampling direction and $J_q$ differ.",
+    "The source directly assigns the local larger-final-momentum shift to the ordinary CCSFA comparison relative to QTMC and connects it to nonzero initial longitudinal momentum in the nonadiabatic SFA launch. Applying that statement to the time-sampled result is conditional on demonstrated C2-C3 agreement.",
+    "When sufficiently resolved, finer structures absent from QTMC can be connected to an additional direct trajectory in CCSFA and the resulting intercycle interference. Such fine-fringe evidence may strengthen the analysis but is not required for full credit under this rubric; unresolved structure must not be used to support the mechanism.",
+    "Source anchors: article method section containing the direct SFA amplitude and saddle equations; time-sampling section defining the Jacobian and effective amplitude; no-Coulomb comparison caption and discussion; Coulomb comparison and trajectory-analysis discussion; runtime table; and Shvetsov-Shilovski et al. (2016), Section III.B, article p.013415-6, Eqs.(26)-(40), for the standard end-of-pulse Coulomb/Kepler asymptotic-momentum map and finite regularized post-pulse Coulomb phase.",
+    "The target article's printed antiderivative corresponding to its Eq. (31) has an erroneous factor of two in the two sideband numerators. Direct integration of the displayed pulse gives",
+    "$$\n  I_1(t)=-\\frac{A_0}{4}\\left[\n  \\frac{2\\cos(\\omega t+\\phi)}{\\omega}\n  +\\frac{\\cos((\\omega+2\\beta)t+\\phi)}{\\omega+2\\beta}\n  +\\frac{\\cos((\\omega-2\\beta)t+\\phi)}{\\omega-2\\beta}\n  \\right].\n  $$",
+    "The bracketed expression printed for the antiderivative corresponding to Eq. (32) differentiates to $A_z^2/2$ with its printed $A_0^2/64$ prefactor. For an antiderivative of $A_z^2$, the same bracket therefore carries $A_0^2/32$. The required integrals are derived or numerically evaluated from the stated pulse; these corrections clarify the mathematical identity and do not impose one antiderivative notation.",
+    "The target article invokes propagation to asymptotic momentum and an infinite post-release phase but does not itself give an operational finite post-pulse construction. Shvetsov-Shilovski et al. (2016) supplies one standard closure through the end-of-pulse energy, angular momentum and Runge--Lenz vector and the associated finite regularized phase. This reference establishes method provenance; it does not prescribe a unique reference or notation. A physically equivalent, declared and converged continuation receives full credit.",
+    "Full analysis credit requires the corresponding computed structure to be identifiable. A self-consistent explanation of a materially wrong PMD is not full-credit physics.",
+    "A student who correctly diagnoses nonconvergence may receive method/diagnostic credit but not credit for an unobserved source-supported conclusion.",
+    "Reasonable axis extensions, color maps, logarithmic transforms, common factors, and regions of interest are acceptable when the mathematical object and structures remain reviewable.",
+    "Do not require source annotations, panel letters, exact colors/crops, code-specific time windows, a particular root solver, grid, sample count, derivative formula, quadrature, cutoff, tolerance, optimization, or parallel strategy.",
+    "Do not prescribe an asymptotic-momentum shooting problem, a $\\mathbf q\\!\\to\\!\\mathbf p_\\infty$ Jacobian, root windows/seeds/tracker, bin grid, caustic solver, tail regularization, cutoff, radius, or quadrature.",
+    "Do not require a prescribed list of references, fixed file tree, numerical residual, or complete failed-run history.",
+    "For F1-F2/O1-O6/M1-M4, use article pp.053310-2-4, Eqs.(7),(8),(18)-(28),(33),(34),(36)-(38), with $\\mathbf q$ denoting the launch/saddle label in the Coulomb branches:\n$$[q_z+A_z(t_s)]^2+q_x^2+2I_p=0,\\quad\nq_z=-\\Re A_z(t_s),\\quad q_x=\\pm\\sqrt{[\\Im A_z(t_s)]^2-2I_p},$$\n$$\\mathbf v_0=\\mathbf q+\\mathbf A(t_r),\\quad\n\\mathbf r_0=\\Re\\int_{t_s}^{t_r}[\\mathbf q+\\mathbf A(s)]ds,\\quad\nJ_q=\\left|\\det\\frac{\\partial(q_x,q_z)}{\\partial(t_r,t_i)}\\right|.$$\nFor the no-Coulomb map replace q by final p. Both signed transverse branches must be represented. Subsequent Coulomb equations are $\\dot{\\mathbf r}=\\mathbf v$, $\\dot{\\mathbf v}=-\\mathbf E-\\mathbf r/r^3$. The retained continuum action uses $-\\int(v^2/2-2/r+I_p)dt$, rather than the source's $-1/r$ action. Its infinite tail must be replaced by a declared finite regularized phase. For a post-pulse outgoing Coulomb trajectory, $p_\\infty=\\sqrt{v_f^2-2/r_f}$; an analytic Kepler vector map or demonstrated equivalent continuation fixes direction. The q-to-p_infinity propagation map is not the time-to-q sampling Jacobian. The specified pulse antiderivatives, rather than the misprinted source Eqs.(31)-(32), determine the vector potential; directly integrating the stated pulse is equivalent.\n\nFor the standard post-pulse example, Shvetsov-Shilovski et al. (2016), article p.013415-6, Sec.III.B, Eqs.(26)-(40), gives for unit Coulomb charge\n$$\\mathbf L=\\mathbf r_f\\times\\mathbf v_f,\\quad\\mathbf a=\\mathbf v_f\\times\\mathbf L-\\mathbf r_f/r_f,\\quad\n\\mathbf p_\\infty=p_\\infty\\frac{p_\\infty(\\mathbf L\\times\\mathbf a)-\\mathbf a}{1+p_\\infty^2L^2}.$$\nWriting $E=p_\\infty^2/2>0$, $b=1/(2E)$ and $g=\\sqrt{1+2EL^2}$, one finite Coulomb tail contribution after removal of common divergent phases is\n$$\\widetilde\\Phi_C=-\\sqrt b\\left[\\ln g+\\operatorname{arsinh}\\frac{\\mathbf r_f\\cdot\\mathbf v_f}{g\\sqrt b}\\right].$$\nThis is a supported standard closure, not required notation or permission to replace the task's own launch/action identity. A declared converged equivalent continuation remains accepted. For the no-Coulomb direct reference, Xiao et al. article p.053310-2, Eqs.(7),(8), uses $M_{\\mathbf p}=i\\int_{t_0}^{t_f}dt\\,e^{i\\widetilde S_{\\mathbf p}(t)}\\langle\\mathbf p+\\mathbf A(t)|\\mathbf r\\cdot\\mathbf E(t)|\\psi_0\\rangle$, with $\\partial_t\\widetilde S_{\\mathbf p}=[\\mathbf p+\\mathbf A(t)]^2/2+I_p$ and one common finite endpoint convention."
+  ],
+  "closure_requirements": {
+    "RC0": [
+      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
+      "Required indispensable claim CL1, central physical object: all of: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.); F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC1": [
+      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
+      "Required indispensable claim CL1, indispensable material component: all of: O3 (Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.); O4 (Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.); O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.); O6 (Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC2": [
+      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
+      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M1 (Explain how uniform sampling in (tr,ti) induces a nonuniform momentum measure rather than merely saying the weighted image is better.); M2 (Explain how the absolute-area Jacobian corrects the variable transformation and distinguish it from deterministic cell measure or Monte Carlo proposal weights.); M5 (Use convergence evidence to distinguish residual sample scarcity/bin asymmetry from physical structure and restrict N3 recovery of N1 to the resolved no-Coulomb validation; an unresolved map does not establish validation.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL3, principal mechanism or commissioned conclusion: all of: M3 (Explain C2/C3 as two sampling directions of the same q-labelled saddle/launch ensemble, with Jq correcting only sampling measure followed by common propagation and reached-p_infinity binning.); M4 (Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.); M7 (Form the commissioned QTMC-CCSFA family conclusion from the resolved direct C1/C2 shift and local launch mechanism; extend it to C3 only when independently demonstrated C2/C3 agreement permits.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC3": [
+      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
+      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
+      "Required co primary claim CL3, material validation/scope: V2 (Only when estimator/Jacobian placement, saddle/contour consistency, replica aggregation, asymptotic/tail treatment or sampling-scarcity claims create a material threat to a central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC4": [
+      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
+      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
+      "Close CL1 central physical object: all of: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.); F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.).",
+      "Close CL1 indispensable material component: all of: O3 (Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.); O4 (Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.); O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.); O6 (Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.).",
+      "Close CL2 principal mechanism or commissioned conclusion: all of: M1 (Explain how uniform sampling in (tr,ti) induces a nonuniform momentum measure rather than merely saying the weighted image is better.); M2 (Explain how the absolute-area Jacobian corrects the variable transformation and distinguish it from deterministic cell measure or Monte Carlo proposal weights.); M5 (Use convergence evidence to distinguish residual sample scarcity/bin asymmetry from physical structure and restrict N3 recovery of N1 to the resolved no-Coulomb validation; an unresolved map does not establish validation.).",
+      "Close CL3 principal mechanism or commissioned conclusion: all of: M3 (Explain C2/C3 as two sampling directions of the same q-labelled saddle/launch ensemble, with Jq correcting only sampling measure followed by common propagation and reached-p_infinity binning.); M4 (Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.); M7 (Form the commissioned QTMC-CCSFA family conclusion from the resolved direct C1/C2 shift and local launch mechanism; extend it to C3 only when independently demonstrated C2/C3 agreement permits.).",
+      "Close CL3 material validation/scope: V2 (Only when estimator/Jacobian placement, saddle/contour consistency, replica aggregation, asymptotic/tail treatment or sampling-scarcity claims create a material threat to a central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.)."
+    ]
+  },
+  "references": [
+    {
+      "citation": "Xiang-Ru Xiao, Mu-Xue Wang, Wei-Hao Xiong, and Liang-You Peng. 2016. *Efficient time-sampling method in Coulomb-corrected strong-field approximation*. *Physical Review E*, 94, 053310.",
+      "url": "https://doi.org/10.1103/PhysRevE.94.053310",
+      "scientific_scope": "Efficient time-sampling method in Coulomb-corrected strong-field approximation",
+      "anchors": [
+        "Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases.",
+        "Xiao et al. (2016), article pp.053310-2-4, Eqs.(7)-(16),(22)-(28),(33)-(36): direct amplitude, nonadiabatic launch, Coulomb dynamics and -2/r action. Operational finite asymptotic/tail closure is supplied by Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40), not explicitly by Xiao et al.",
+        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations.",
+        "Xiao et al. (2016), article pp.053310-4,6, Eqs.(33),(34),(36), Fig.2(b): adiabatic planar QTMC with coherent final-momentum accumulation. The signed planar reduction and finite tail/asymptotic implementation follow the stated task and standard-method equivalence class.",
+        "Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit.",
+        "Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning \"In the present work\" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching.",
+        "Xiao et al. (2016), article p.053310-6, Sec.III.A sampling/bin-error discussion and p.053310-7 Table I (efficiency context only); Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40) for finite post-pulse treatment. Reproduction records, compatible complex-estimator replica aggregation and risk-triggered checks are task-defined; no source sample count or runtime is a scoring target."
+      ]
+    },
+    {
+      "citation": "N. I. Shvetsov-Shilovski, M. Lein, L. B. Madsen, E. Räsänen, C. Lemell, J. Burgdörfer, D. G. Arbó, and K. Tőkési. 2016. *Semiclassical two-step model for strong-field ionization*. *Physical Review A*, 94, 013415.",
+      "url": "https://doi.org/10.1103/PhysRevA.94.013415",
+      "scientific_scope": "Standard post-pulse Coulomb/Kepler asymptotic-momentum map and finite regularized Coulomb phase; equivalent declared converged continuations remain accepted.",
+      "anchors": [
+        "Article p.013415-6, Section III.B, Eqs.(26)-(29): end-of-pulse Coulomb/Kepler map; Eqs.(30)-(40): removal of common divergent phase and finite regularized tail."
+      ]
+    }
+  ]
+}

cases/case03/grading_rubric.md

@@ -0,0 +1,889 @@
+# Grading Rubric — Case03
+
+Case03 — Efficient time-sampling method in Coulomb-corrected strong-field approximation
+
+## Atomic Scoring Criteria
+
+Each criterion awards 0 or 0.5 points, for a maximum of 10. Explicit N/A rules apply where stated.
+
+### F1 — F — 0.5 points
+
+**Scientific requirement**
+
+State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.
+
+**Conditions for credit**
+
+- All six signed-plane objects and coherent cell accumulation are defined, with absolute-area Jp/Jq separated from cell/proposal factors and normalization; determinant orientation is not a phase.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F2, O1, O2, O3, O4, O5, O6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F2 — F — 0.5 points
+
+**Scientific requirement**
+
+State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.
+
+**Conditions for credit**
+
+- The declared phase, launch, propagation, asymptotic continuation and finite-tail equations distinguish adiabatic QTMC from q-labelled nonadiabatic CCSFA.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F1, O1, O2, O3, O4, O5, O6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-2-4, Eqs.(7)-(16),(22)-(28),(33)-(36): direct amplitude, nonadiabatic launch, Coulomb dynamics and -2/r action. Operational finite asymptotic/tail closure is supplied by Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40), not explicitly by Xiao et al.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### O1 — O — 0.5 points
+
+**Scientific requirement**
+
+Reach the first-coverage milestone of the homogeneous no-Coulomb family N1 direct, N2 unweighted complex-time, N3 Jp-weighted complex-time: any one independently valid, reconstructible and adequately presented member suffices, without supplying the other members.
+
+**Conditions for credit**
+
+- At least one of N1/N2/N3 independently has a correct reconstructible and adequately presented no-Coulomb identity; no missing member is supplied by another.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F1, F2, O2, O3, I1, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O2 — O — 0.5 points
+
+**Scientific requirement**
+
+Reach second coverage of N1 direct, N2 unweighted complex-time and N3 Jp-weighted complex-time: at least two independently object-valid, presentation-adequate and claim-adequate members share signed axes, pulse, phase and cell/binning conventions. No member supplies another.
+
+**Conditions for credit**
+
+- At least two independently valid N1/N2/N3 members are reconstructible and comparable in signed axes, pulse, phase and cell convention.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O1 (Reach the first-coverage milestone of the homogeneous no-Coulomb family N1 direct, N2 unweighted complex-time, N3 Jp-weighted complex-time: any one independently valid, reconstructible and adequately presented member suffices, without supplying the other members.)
+
+- Preserve independently valid work in F1, F2, O3, I1, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O3 — O — 0.5 points
+
+**Scientific requirement**
+
+Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.
+
+**Conditions for credit**
+
+- All three N1/N2/N3 members are independently valid and comparable; N2 omits only Jp, retains the induced distortion, and N3 approaches direct N1 at demonstrated resolution.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O2 (Reach second coverage of N1 direct, N2 unweighted complex-time and N3 Jp-weighted complex-time: at least two independently object-valid, presentation-adequate and claim-adequate members share signed axes, pulse, phase and cell/binning conventions. No member supplies another.)
+
+- Preserve independently valid work in F1, F2, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O4 — O — 0.5 points
+
+**Scientific requirement**
+
+Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.
+
+**Conditions for credit**
+
+- C1 is an independent coherent planar QTMC object with signed transverse launch, y=vy=py=0, regularized action and reached asymptotic-momentum bins; material support/envelope/arcs are resolved.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in O5, O6, I2, M3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-4,6, Eqs.(33),(34),(36), Fig.2(b): adiabatic planar QTMC with coherent final-momentum accumulation. The signed planar reduction and finite tail/asymptotic implementation follow the stated task and standard-method equivalence class.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O5 — O — 0.5 points
+
+**Scientific requirement**
+
+Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.
+
+**Conditions for credit**
+
+- C2 actually samples q and solves contributing saddles under a declared converged prescription, uses nonadiabatic launch and common finite-tail/asymptotic treatment, and resolves material reached-momentum structure.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in O4, O6, I2, I3, M3, M4, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O6 — O — 0.5 points
+
+**Scientific requirement**
+
+Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.
+
+**Conditions for credit**
+
+- C3 independently samples complex time with Jq and the same q-labelled saddle/launch/action/tail/bin identity as C2; C2 data cannot replace it.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in O4, O5, I2, M3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### I1 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify from submitted arrays/slices the nonuniform-measure failure of N2, including scarce support near px=0 when resolved, and convergence of N3 toward N1 under sampling/bin refinement, rather than generic image texture.
+
+**Conditions for credit**
+
+- The candidate identifies N2's nonuniform measure and resolved scarce support near px=0, and N3's convergence toward N1 using their own arrays or slices.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O3 (Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.)
+
+- Preserve independently valid work in F1, O1, O2, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I2 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify from reached-p_infinity data the common-q C2/C3 agreement in global support, envelope and resolved major rings/ridges, limiting fine-structure equivalence to actually resolved features.
+
+**Conditions for credit**
+
+- Candidate identification establishes C2/C3 agreement of global support, envelope and resolved major rings/ridges at reached asymptotic momentum, bounding fine-structure claims.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.); O6 (Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.)
+
+- Preserve independently valid work in O4, M3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I3 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify directly in C1 versus C2 the major CCSFA-family ridge/distribution shift toward larger final momentum relative to QTMC. Extend it to C3 only when I2 supports C2/C3 agreement; pointwise fringe matching is not required.
+
+**Conditions for credit**
+
+- The candidate identifies the direct C1/C2 local shift toward larger final momentum; extending it to C3 requires actual C2/C3 agreement.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O4 (Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.); O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.)
+
+- Preserve independently valid work in O6, I2, M4, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning "In the present work" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M1 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain how uniform sampling in (tr,ti) induces a nonuniform momentum measure rather than merely saying the weighted image is better.
+
+**Conditions for credit**
+
+- The time-to-momentum change of variables explains why uniform complex-time samples create a nonuniform momentum measure.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.)
+
+- Preserve independently valid work in F2, I1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M2 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain how the absolute-area Jacobian corrects the variable transformation and distinguish it from deterministic cell measure or Monte Carlo proposal weights.
+
+**Conditions for credit**
+
+- The absolute-area Jacobian is derived/interpreted as the measure correction, distinct from estimator proposal probabilities and deterministic cell factors.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.)
+
+- Preserve independently valid work in O1, I1, M1, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M3 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain C2/C3 as two sampling directions of the same q-labelled saddle/launch ensemble, with Jq correcting only sampling measure followed by common propagation and reached-p_infinity binning.
+
+**Conditions for credit**
+
+- The candidate explains common-q C2/C3 equivalence through a common saddle/launch ensemble, propagation and asymptotic bins, with Jq changing only sampling measure.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.); I2 (Identify from reached-p_infinity data the common-q C2/C3 agreement in global support, envelope and resolved major rings/ridges, limiting fine-structure equivalence to actually resolved features.)
+
+- Preserve independently valid work in O5, O6, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M4 — M — 0.5 points
+
+**Scientific requirement**
+
+Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.
+
+**Conditions for credit**
+
+- The resolved local CCSFA shift is linked to its nonzero nonadiabatic longitudinal launch; the account is not asserted for the entire PMD.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.); I3 (Identify directly in C1 versus C2 the major CCSFA-family ridge/distribution shift toward larger final momentum relative to QTMC. Extend it to C3 only when I2 supports C2/C3 agreement; pointwise fringe matching is not required.)
+
+- Preserve independently valid work in I2, M3, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning "In the present work" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M5 — M — 0.5 points
+
+**Scientific requirement**
+
+Use convergence evidence to distinguish residual sample scarcity/bin asymmetry from physical structure and restrict N3 recovery of N1 to the resolved no-Coulomb validation; an unresolved map does not establish validation.
+
+**Conditions for credit**
+
+- Refinement evidence separates scarcity/bin asymmetry from physical structure and supports only resolved no-Coulomb recovery.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I1 (Identify from submitted arrays/slices the nonuniform-measure failure of N2, including scarce support near px=0 when resolved, and convergence of N3 toward N1 under sampling/bin refinement, rather than generic image texture.)
+
+- Preserve independently valid work in M1, M2, V1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M6 — M — 0.5 points
+
+**Scientific requirement**
+
+Distinguish direct C1/C2 observations, extensions supported by C2/C3 agreement and unresolved fine structure; unresolved features cannot support a mechanism. Fine interference is optional strengthening evidence.
+
+**Conditions for credit**
+
+- Direct C1/C2 observation, inference via C2/C3 agreement and unresolved fine structure are distinguished; an unresolved fringe is not mechanism evidence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in I2, I3, M3, M4, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning "In the present work" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M7 — M — 0.5 points
+
+**Scientific requirement**
+
+Form the commissioned QTMC-CCSFA family conclusion from the resolved direct C1/C2 shift and local launch mechanism; extend it to C3 only when independently demonstrated C2/C3 agreement permits.
+
+**Conditions for credit**
+
+- The family conclusion closes with the direct resolved shift and local launch mechanism; C3 is included only to the extent its independent agreement supports.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: I3 (Identify directly in C1 versus C2 the major CCSFA-family ridge/distribution shift toward larger final momentum relative to QTMC. Extend it to C3 only when I2 supports C2/C3 agreement; pointwise fringe matching is not required.); M4 (Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.)
+
+- Preserve independently valid work in I2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning "In the present work" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V1 — V — 0.5 points
+
+**Scientific requirement**
+
+Supply code/commands reproducing all six arrays, branch-specific numerical choices, raw cell/density conventions, separate cell/proposal factors, seeds/counts, normalization and claim-relevant stability evidence; judge implemented local parts without reward for resource consumption or duplicate penalties.
+
+**Conditions for credit**
+
+- Code/commands and branch-specific records reproduce six arrays, raw cell/density measures, separate estimator factors, seeds/counts and claim-relevant stability without rewarding resource use.
+
+**Applicability and N/A**
+
+- This positive scientific scope/evidence duty is unconditional; N/A is not permitted.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F1, F2, O1, O2, O3, O4, O5, O6, I1, I2, I3, M1, M2, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article p.053310-6, Sec.III.A sampling/bin-error discussion and p.053310-7 Table I (efficiency context only); Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40) for finite post-pulse treatment. Reproduction records, compatible complex-estimator replica aggregation and risk-triggered checks are task-defined; no source sample count or runtime is a scoring target.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V2 — V — 0.5 points
+
+**Scientific requirement**
+
+Only when estimator/Jacobian placement, saddle/contour consistency, replica aggregation, asymptotic/tail treatment or sampling-scarcity claims create a material threat to a central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.
+
+**Conditions for credit**
+
+- Only a concrete central risk in estimator weights, saddles, replicas, asymptotic tails or scarcity triggers discriminating validation; otherwise the assessable item is N/A.
+
+**Applicability and N/A**
+
+- Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.
+
+- If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F1, F2, O1, O2, O3, O4, O5, O6, I1, I2, I3, M1, M2, M3, M4, M5, M6, M7, V1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.
+
+- A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.
+
+- Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable.
+
+**Scientific source locations**
+
+- Xiao et al. (2016), article p.053310-6, Sec.III.A sampling/bin-error discussion and p.053310-7 Table I (efficiency context only); Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40) for finite post-pulse treatment. Reproduction records, compatible complex-estimator replica aggregation and risk-triggered checks are task-defined; no source sample count or runtime is a scoring target.
+
+**Research Closure relation**
+
+Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+## Research Closure Requirements
+
+### RC0
+
+- The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.
+
+- Required indispensable claim CL1, central physical object: all of: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.); F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC1
+
+- With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.
+
+- Required indispensable claim CL1, indispensable material component: all of: O3 (Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.); O4 (Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.); O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.); O6 (Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC2
+
+- With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.
+
+- Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M1 (Explain how uniform sampling in (tr,ti) induces a nonuniform momentum measure rather than merely saying the weighted image is better.); M2 (Explain how the absolute-area Jacobian corrects the variable transformation and distinguish it from deterministic cell measure or Monte Carlo proposal weights.); M5 (Use convergence evidence to distinguish residual sample scarcity/bin asymmetry from physical structure and restrict N3 recovery of N1 to the resolved no-Coulomb validation; an unresolved map does not establish validation.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL3, principal mechanism or commissioned conclusion: all of: M3 (Explain C2/C3 as two sampling directions of the same q-labelled saddle/launch ensemble, with Jq correcting only sampling measure followed by common propagation and reached-p_infinity binning.); M4 (Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.); M7 (Form the commissioned QTMC-CCSFA family conclusion from the resolved direct C1/C2 shift and local launch mechanism; extend it to C3 only when independently demonstrated C2/C3 agreement permits.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC3
+
+- With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.
+
+- Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.
+
+- Required co primary claim CL3, material validation/scope: V2 (Only when estimator/Jacobian placement, saddle/contour consistency, replica aggregation, asymptotic/tail treatment or sampling-scarcity claims create a material threat to a central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC4
+
+- All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.
+
+- Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.
+
+- Close CL1 central physical object: all of: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.); F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.).
+
+- Close CL1 indispensable material component: all of: O3 (Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.); O4 (Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.); O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.); O6 (Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.).
+
+- Close CL2 principal mechanism or commissioned conclusion: all of: M1 (Explain how uniform sampling in (tr,ti) induces a nonuniform momentum measure rather than merely saying the weighted image is better.); M2 (Explain how the absolute-area Jacobian corrects the variable transformation and distinguish it from deterministic cell measure or Monte Carlo proposal weights.); M5 (Use convergence evidence to distinguish residual sample scarcity/bin asymmetry from physical structure and restrict N3 recovery of N1 to the resolved no-Coulomb validation; an unresolved map does not establish validation.).
+
+- Close CL3 principal mechanism or commissioned conclusion: all of: M3 (Explain C2/C3 as two sampling directions of the same q-labelled saddle/launch ensemble, with Jq correcting only sampling measure followed by common propagation and reached-p_infinity binning.); M4 (Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.); M7 (Form the commissioned QTMC-CCSFA family conclusion from the resolved direct C1/C2 shift and local launch mechanism; extend it to C3 only when independently demonstrated C2/C3 agreement permits.).
+
+- Close CL3 material validation/scope: V2 (Only when estimator/Jacobian placement, saddle/contour consistency, replica aggregation, asymptotic/tail treatment or sampling-scarcity claims create a material threat to a central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.).
+
+## Applicability and Equivalent Evidence
+
+- Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.
+
+- Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.
+
+- For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.
+
+- Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.
+
+- Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.
+
+- Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.
+
+- Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.
+
+- Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.
+
+- Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.
+
+- Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.
+
+- A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.
+
+- For the no-Coulomb map pz=-Ar(tr,ti), px=+/-sqrt(Ai(tr,ti)^2-2Ip), retain both signed branches and the admissible real domain. The CCSFA sampling map is to saddle/drift q, not asymptotic p_infinity.
+
+- Only the absolute area Jacobian Jp is omitted in N2; all saddle prefactors, phases and cell/proposal weights remain. Apply Ms_eff=Ms J in weighted branches, not sqrt(J), an arbitrary factor, an oriented-sign phase or an invented q-to-p_infinity Jacobian.
+
+- C2 samples q then solves roots and propagates; C3 samples complex time then maps to q. Both use the same nonadiabatic launch, action, contributing saddles, asymptotic map, tail convention and final cells. Ordinary CCSFA is not an asymptotic-momentum shooting problem.
+
+- Independent replicas must be combined at a compatible complex-estimator level before power. Duplicate seeds are not independent samples. Document proposed/sampled, propagated-root/trajectory and outgoing counts separately.
+
+- No-Coulomb coverage atoms are cumulative one/two/three-member milestones, not fixed assignments of N1, N2 and N3 to separate credits. Each Coulomb output C1, C2 and C3 is independently adjudicated.
+
+- Joint tail-parameter and cell-width stability must support relative phases and PMDs. An arbitrary finite-time momentum, literal divergent post-pulse integral, or branch-dependent cutoff determining the comparison is not equivalent.
+
+- When a major-feature mismatch would decide credit, compare like normalized objects against combined cell resolution and sampling uncertainty. No fixed image-correlation threshold is prescribed; unresolved physical-versus-numerical disagreement requires bounded review rather than an invented tolerance.
+
+| ID | Mathematical object | Required branch identity | Normalization and units |
+|---|---|---|---|
+| N1 | Direct no-Coulomb $\vert M(p_x,p_z)\vert ^2$ from the finite-endpoint length-gauge SFA integral | Direct time integration; no Coulomb | Momentum in a.u.; yield in arbitrary units; one momentum-independent factor is free |
+| N2 | $\vert \sum_b a_s^{(\mathrm{nc})}\vert ^2$ from complex-time samples with $J_p=\vert \det\partial(p_x,p_z)/\partial(t_r,t_i)\vert $ omitted and all other estimator weights retained | Same saddles/prefactor/phase/binning as N3 | Same as N1; `unweighted` omits only $J_p$ |
+| N3 | $\vert \sum_b a_s^{(\mathrm{nc})}J_p\vert ^2$ | Same physical branch as N2 with the absolute area Jacobian | Same as N1 |
+| C1 | Coherent planar QTMC PMD with $y=v_y=p_y=0$ | Standard stated one-component signed transverse-$p_x$ ADK/Landau initialization; retained post-release equations and $-2/r$ action; post-pulse Coulomb/Kepler map and finite regularized phase | Reached $\mathbf p_\infty$ in a.u.; yield in arbitrary units |
+| C2 | Coherent ordinary CCSFA PMD | Sample saddle/drift $\mathbf q$, solve contributing saddle roots, propagate, map the end-of-pulse state to $\mathbf p_\infty$, and bin there; nonadiabatic launch | Same as C1 |
+| C3 | Coherent time-sampled CCSFA PMD | Complex-time sampling $\rightarrow\mathbf q$ with $J_q=\vert \det\partial(q_x,q_z)/\partial(t_r,t_i)\vert $; same launch/action/post-pulse map and phase/saddles/$\mathbf p_\infty$ binning as C2 | Same as C1 |
+
+- The common physical construction for C1-C3 uses the planar reduction, a standard analytic Coulomb/Kepler end-of-pulse-to-asymptotic map or a demonstrated equivalent continuation, and a finite regularized post-pulse Coulomb phase within the tail-equivalence class stated in task. Cell-representative matching and trajectory-specific regularized actions are both acceptable when the submitted evidence shows that the selected tail and cell representation do not drive the claimed structures. Do not require a particular cutoff, radius, solver, grid, quadrature, caustic treatment, regularization, contour prescription, or root subset. Reject a comparison in which C2 and C3 use inconsistent declared saddle prescriptions, launch relations, asymptotic maps, Coulomb action factors, tail conventions, or $\mathbf p_\infty$ bin definitions. Saved raw arrays must identify cell-integrated versus density/average form, with deterministic cell measures or Monte Carlo proposal corrections documented separately from $J_p$ or $J_q$.
+
+- Uniform complex-time sampling maps nonuniformly into momentum space. Omitting the absolute area Jacobian produces the wrong measure; the most explicit source signal is scarce samples/noise near $p_x=0$, not a mandatory `boxy` appearance. Deterministic cell measure or Monte Carlo proposal correction remains separate from that Jacobian.
+
+- With the determinant and sufficient sampling, the time-sampled no-Coulomb result reproduces the direct SFA structures substantially better. Residual central noise and left-right asymmetry may remain at finite sampling/bin size.
+
+- Time-sampled CCSFA should reproduce ordinary CCSFA because both construct the same $\mathbf q$-labelled saddle/launch ensemble, propagate it, and bin by reached $\mathbf p_\infty$; only the sampling direction and $J_q$ differ.
+
+- The source directly assigns the local larger-final-momentum shift to the ordinary CCSFA comparison relative to QTMC and connects it to nonzero initial longitudinal momentum in the nonadiabatic SFA launch. Applying that statement to the time-sampled result is conditional on demonstrated C2-C3 agreement.
+
+- When sufficiently resolved, finer structures absent from QTMC can be connected to an additional direct trajectory in CCSFA and the resulting intercycle interference. Such fine-fringe evidence may strengthen the analysis but is not required for full credit under this rubric; unresolved structure must not be used to support the mechanism.
+
+- Source anchors: article method section containing the direct SFA amplitude and saddle equations; time-sampling section defining the Jacobian and effective amplitude; no-Coulomb comparison caption and discussion; Coulomb comparison and trajectory-analysis discussion; runtime table; and Shvetsov-Shilovski et al. (2016), Section III.B, article p.013415-6, Eqs.(26)-(40), for the standard end-of-pulse Coulomb/Kepler asymptotic-momentum map and finite regularized post-pulse Coulomb phase.
+
+- The target article's printed antiderivative corresponding to its Eq. (31) has an erroneous factor of two in the two sideband numerators. Direct integration of the displayed pulse gives
+
+$$
+  I_1(t)=-\frac{A_0}{4}\left[
+  \frac{2\cos(\omega t+\phi)}{\omega}
+  +\frac{\cos((\omega+2\beta)t+\phi)}{\omega+2\beta}
+  +\frac{\cos((\omega-2\beta)t+\phi)}{\omega-2\beta}
+  \right].
+  $$
+
+- The bracketed expression printed for the antiderivative corresponding to Eq. (32) differentiates to $A_z^2/2$ with its printed $A_0^2/64$ prefactor. For an antiderivative of $A_z^2$, the same bracket therefore carries $A_0^2/32$. The required integrals are derived or numerically evaluated from the stated pulse; these corrections clarify the mathematical identity and do not impose one antiderivative notation.
+
+- The target article invokes propagation to asymptotic momentum and an infinite post-release phase but does not itself give an operational finite post-pulse construction. Shvetsov-Shilovski et al. (2016) supplies one standard closure through the end-of-pulse energy, angular momentum and Runge--Lenz vector and the associated finite regularized phase. This reference establishes method provenance; it does not prescribe a unique reference or notation. A physically equivalent, declared and converged continuation receives full credit.
+
+- Full analysis credit requires the corresponding computed structure to be identifiable. A self-consistent explanation of a materially wrong PMD is not full-credit physics.
+
+- A student who correctly diagnoses nonconvergence may receive method/diagnostic credit but not credit for an unobserved source-supported conclusion.
+
+- Reasonable axis extensions, color maps, logarithmic transforms, common factors, and regions of interest are acceptable when the mathematical object and structures remain reviewable.
+
+- Do not require source annotations, panel letters, exact colors/crops, code-specific time windows, a particular root solver, grid, sample count, derivative formula, quadrature, cutoff, tolerance, optimization, or parallel strategy.
+
+- Do not prescribe an asymptotic-momentum shooting problem, a $\mathbf q\!\to\!\mathbf p_\infty$ Jacobian, root windows/seeds/tracker, bin grid, caustic solver, tail regularization, cutoff, radius, or quadrature.
+
+- Do not require a prescribed list of references, fixed file tree, numerical residual, or complete failed-run history.
+
+For F1-F2/O1-O6/M1-M4, use article pp.053310-2-4, Eqs.(7),(8),(18)-(28),(33),(34),(36)-(38), with $\mathbf q$ denoting the launch/saddle label in the Coulomb branches:
+$$[q_z+A_z(t_s)]^2+q_x^2+2I_p=0,\quad
+q_z=-\Re A_z(t_s),\quad q_x=\pm\sqrt{[\Im A_z(t_s)]^2-2I_p},$$
+$$\mathbf v_0=\mathbf q+\mathbf A(t_r),\quad
+\mathbf r_0=\Re\int_{t_s}^{t_r}[\mathbf q+\mathbf A(s)]ds,\quad
+J_q=\left|\det\frac{\partial(q_x,q_z)}{\partial(t_r,t_i)}\right|.$$
+For the no-Coulomb map replace q by final p. Both signed transverse branches must be represented. Subsequent Coulomb equations are $\dot{\mathbf r}=\mathbf v$, $\dot{\mathbf v}=-\mathbf E-\mathbf r/r^3$. The retained continuum action uses $-\int(v^2/2-2/r+I_p)dt$, rather than the source's $-1/r$ action. Its infinite tail must be replaced by a declared finite regularized phase. For a post-pulse outgoing Coulomb trajectory, $p_\infty=\sqrt{v_f^2-2/r_f}$; an analytic Kepler vector map or demonstrated equivalent continuation fixes direction. The q-to-p_infinity propagation map is not the time-to-q sampling Jacobian. The specified pulse antiderivatives, rather than the misprinted source Eqs.(31)-(32), determine the vector potential; directly integrating the stated pulse is equivalent.
+
+For the standard post-pulse example, Shvetsov-Shilovski et al. (2016), article p.013415-6, Sec.III.B, Eqs.(26)-(40), gives for unit Coulomb charge
+$$\mathbf L=\mathbf r_f\times\mathbf v_f,\quad\mathbf a=\mathbf v_f\times\mathbf L-\mathbf r_f/r_f,\quad
+\mathbf p_\infty=p_\infty\frac{p_\infty(\mathbf L\times\mathbf a)-\mathbf a}{1+p_\infty^2L^2}.$$
+Writing $E=p_\infty^2/2>0$, $b=1/(2E)$ and $g=\sqrt{1+2EL^2}$, one finite Coulomb tail contribution after removal of common divergent phases is
+$$\widetilde\Phi_C=-\sqrt b\left[\ln g+\operatorname{arsinh}\frac{\mathbf r_f\cdot\mathbf v_f}{g\sqrt b}\right].$$
+This is a supported standard closure, not required notation or permission to replace the task's own launch/action identity. A declared converged equivalent continuation remains accepted. For the no-Coulomb direct reference, Xiao et al. article p.053310-2, Eqs.(7),(8), uses $M_{\mathbf p}=i\int_{t_0}^{t_f}dt\,e^{i\widetilde S_{\mathbf p}(t)}\langle\mathbf p+\mathbf A(t)|\mathbf r\cdot\mathbf E(t)|\psi_0\rangle$, with $\partial_t\widetilde S_{\mathbf p}=[\mathbf p+\mathbf A(t)]^2/2+I_p$ and one common finite endpoint convention.

cases/case03/resource_limits.json

@@ -0,0 +1,10 @@
+{
+  "cpu_cores": 32,
+  "nodes": 1,
+  "time_limit_minutes": 240,
+  "network_access": "disabled",
+  "temporary_storage_gib": 50,
+  "available_memory_gib": 128,
+  "memory_policy": "Available RAM is approximate and advisory, not a task-specific enforced limit.",
+  "gpu_available": false
+}

cases/case03/sources.md

@@ -0,0 +1,46 @@
+# Scientific Sources — Case03
+
+## References
+
+Xiang-Ru Xiao, Mu-Xue Wang, Wei-Hao Xiong, and Liang-You Peng. 2016. *Efficient time-sampling method in Coulomb-corrected strong-field approximation*. *Physical Review E*, 94, 053310. [Source](https://doi.org/10.1103/PhysRevE.94.053310)
+
+Efficient time-sampling method in Coulomb-corrected strong-field approximation
+
+N. I. Shvetsov-Shilovski, M. Lein, L. B. Madsen, E. Räsänen, C. Lemell, J. Burgdörfer, D. G. Arbó, and K. Tőkési. 2016. *Semiclassical two-step model for strong-field ionization*. *Physical Review A*, 94, 013415. [Source](https://doi.org/10.1103/PhysRevA.94.013415)
+
+Standard post-pulse Coulomb/Kepler asymptotic-momentum map and finite regularized Coulomb phase; equivalent declared converged continuations remain accepted.
+
+## Criterion-to-source crosswalk
+
+Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.
+
+| Criteria | Source locations, scientific use and limits |
+|---|---|
+| F1, M1, M2 | Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases. |
+| F2 | Xiao et al. (2016), article pp.053310-2-4, Eqs.(7)-(16),(22)-(28),(33)-(36): direct amplitude, nonadiabatic launch, Coulomb dynamics and -2/r action. Operational finite asymptotic/tail closure is supplied by Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40), not explicitly by Xiao et al. |
+| O1, O2, O3, I1, M5 | Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations. |
+| O4 | Xiao et al. (2016), article pp.053310-4,6, Eqs.(33),(34),(36), Fig.2(b): adiabatic planar QTMC with coherent final-momentum accumulation. The signed planar reduction and finite tail/asymptotic implementation follow the stated task and standard-method equivalence class. |
+| O5, O6, I2, M3 | Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit. |
+| I3, M4, M6, M7 | Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning "In the present work" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching. |
+| V1, V2 | Xiao et al. (2016), article p.053310-6, Sec.III.A sampling/bin-error discussion and p.053310-7 Table I (efficiency context only); Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40) for finite post-pulse treatment. Reproduction records, compatible complex-estimator replica aggregation and risk-triggered checks are task-defined; no source sample count or runtime is a scoring target. |
+
+## Formula and convention notes
+
+For F1-F2/O1-O6/M1-M4, use article pp.053310-2-4, Eqs.(7),(8),(18)-(28),(33),(34),(36)-(38), with $\mathbf q$ denoting the launch/saddle label in the Coulomb branches:
+$$[q_z+A_z(t_s)]^2+q_x^2+2I_p=0,\quad
+q_z=-\Re A_z(t_s),\quad q_x=\pm\sqrt{[\Im A_z(t_s)]^2-2I_p},$$
+$$\mathbf v_0=\mathbf q+\mathbf A(t_r),\quad
+\mathbf r_0=\Re\int_{t_s}^{t_r}[\mathbf q+\mathbf A(s)]ds,\quad
+J_q=\left|\det\frac{\partial(q_x,q_z)}{\partial(t_r,t_i)}\right|.$$
+For the no-Coulomb map replace q by final p. Both signed transverse branches must be represented. Subsequent Coulomb equations are $\dot{\mathbf r}=\mathbf v$, $\dot{\mathbf v}=-\mathbf E-\mathbf r/r^3$. The retained continuum action uses $-\int(v^2/2-2/r+I_p)dt$, rather than the source's $-1/r$ action. Its infinite tail must be replaced by a declared finite regularized phase. For a post-pulse outgoing Coulomb trajectory, $p_\infty=\sqrt{v_f^2-2/r_f}$; an analytic Kepler vector map or demonstrated equivalent continuation fixes direction. The q-to-p_infinity propagation map is not the time-to-q sampling Jacobian. The specified pulse antiderivatives, rather than the misprinted source Eqs.(31)-(32), determine the vector potential; directly integrating the stated pulse is equivalent.
+
+For the standard post-pulse example, Shvetsov-Shilovski et al. (2016), article p.013415-6, Sec.III.B, Eqs.(26)-(40), gives for unit Coulomb charge
+$$\mathbf L=\mathbf r_f\times\mathbf v_f,\quad\mathbf a=\mathbf v_f\times\mathbf L-\mathbf r_f/r_f,\quad
+\mathbf p_\infty=p_\infty\frac{p_\infty(\mathbf L\times\mathbf a)-\mathbf a}{1+p_\infty^2L^2}.$$
+Writing $E=p_\infty^2/2>0$, $b=1/(2E)$ and $g=\sqrt{1+2EL^2}$, one finite Coulomb tail contribution after removal of common divergent phases is
+$$\widetilde\Phi_C=-\sqrt b\left[\ln g+\operatorname{arsinh}\frac{\mathbf r_f\cdot\mathbf v_f}{g\sqrt b}\right].$$
+This is a supported standard closure, not required notation or permission to replace the task's own launch/action identity. A declared converged equivalent continuation remains accepted. For the no-Coulomb direct reference, Xiao et al. article p.053310-2, Eqs.(7),(8), uses $M_{\mathbf p}=i\int_{t_0}^{t_f}dt\,e^{i\widetilde S_{\mathbf p}(t)}\langle\mathbf p+\mathbf A(t)|\mathbf r\cdot\mathbf E(t)|\psi_0\rangle$, with $\partial_t\widetilde S_{\mathbf p}=[\mathbf p+\mathbf A(t)]^2/2+I_p$ and one common finite endpoint convention.
+
+## Scope of the source anchors
+
+The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.

cases/case03/task.md

@@ -0,0 +1,215 @@
+# Time-domain sampling of semiclassical photoelectron momentum distributions
+
+Assessment issue date: 20 August 2026
+
+## Background
+
+Semiclassical strong-field models can represent an ionization amplitude either on a final-momentum grid or through complex ionization times followed by real-time trajectories. This project asks whether a change of sampling variables preserves a coherent two-dimensional photoelectron momentum distribution and how Coulomb-corrected and adiabatic trajectory models differ in the structures they produce.
+
+Use atomic units unless a quantity is explicitly given in SI units.
+
+## Research objective
+
+For hydrogen in the pulse defined below, calculate six photoelectron momentum distributions (PMDs) in the signed $(p_x,p_z)$ plane:
+
+1. a direct no-Coulomb SFA benchmark;
+2. a no-Coulomb complex-time-sampled PMD without the time-to-momentum change-of-variables factor;
+3. the corresponding no-Coulomb complex-time-sampled PMD with that factor;
+4. a Coulomb-including QTMC PMD;
+5. an ordinary momentum-sampled CCSFA PMD;
+6. a complex-time-sampled CCSFA PMD.
+
+The two CCSFA calculations must represent the same physical model and differ only in their sampling direction. The QTMC calculation uses its own standard adiabatic initialization, as described below.
+
+## Physical system and pulse
+
+Use hydrogen with $I_p=0.5$, a four-cycle linearly polarized pulse of wavelength $800\,\mathrm{nm}$ and peak intensity $1.0\times10^{14}\,\mathrm{W\,cm^{-2}}$, and polarization along $z$.
+
+Define
+
+$$
+\mathbf A(t)=A_0\cos^2(\beta t)\sin(\omega t+\phi)\,\hat{\mathbf e}_z,
+\qquad
+\mathbf E(t)=-\frac{d\mathbf A}{dt},
+$$
+
+with $N=4$, $T=2\pi N/\omega$, and $\beta=\pi/T=\omega/(2N)$. Convert the stated wavelength and intensity to atomic units using a standard convention and state the conversion used.
+
+Task convention: take $\phi=0$, use the pulse on the real interval $t_0=-T/2$ to $t_f=T/2$, and set it to zero outside that interval. At complex time, use the analytic continuation of the interior trigonometric expression; do not apply a real-time support test to a complex argument.
+
+## Starting relations and derivation targets
+
+### Direct no-Coulomb benchmark
+
+Use the length-gauge SFA amplitude
+
+$$
+M(\mathbf p)=i\int_{t_0}^{t_f}dt'\,
+e^{i\widetilde S_{\mathbf p}(t')}
+\left\langle \mathbf p+\mathbf A(t')\middle|\mathbf r\cdot\mathbf E(t')\middle|1s\right\rangle,
+$$
+
+with the finite-endpoint phase convention
+
+$$
+\widetilde S_{\mathbf p}(t')=-\int_{t'}^{t_f}d\tau
+\left\{\frac{[\mathbf p+\mathbf A(\tau)]^2}{2}+I_p\right\}.
+$$
+
+Derive or state the standard plane-wave hydrogen-$1s$ length-gauge dipole and its continuum normalization. If you take the expression from examiner-supplied offline material, cite that source. A momentum-independent common amplitude factor is immaterial, but the momentum dependence and phase convention must be retained.
+
+The direct benchmark is $|M(\mathbf p)|^2$ evaluated on a converged signed $(p_x,p_z)$ grid with $p_y=0$.
+
+### Complex saddles and time sampling
+
+The complex ionization times $t_s=t_r+i t_i$ satisfy
+
+$$
+\frac{1}{2}[p_z+A_z(t_s)]^2+\frac{1}{2}p_x^2+I_p=0.
+$$
+
+Write $A_z(t_s)=A_r(t_r,t_i)+iA_i(t_r,t_i)$. Starting from this equation, derive the map from a sampled pair $(t_r,t_i)$ to the real momentum components and the absolute area Jacobian
+
+$$
+J_p=\left|\det\frac{\partial(p_x,p_z)}{\partial(t_r,t_i)}\right|.
+$$
+
+Retain both signed transverse solutions wherever the derived momentum is real; discard only inadmissible samples and document the criterion. Derive the expanded expression for $J_p$ rather than taking it as supplied. The sign of the oriented determinant is not an additional physical phase.
+
+For a saddle contribution use
+
+$$
+a_s^{(\mathrm{nc})}=
+\frac{(2I_p)^{5/4}}
+{\sqrt{2}\,E_z(t_s)[p_z+A_z(t_s)]}
+\exp\!\left[i\widetilde S_{\mathbf p}(t_s)\right]
+$$
+
+for the no-Coulomb sampled branches. The unweighted branch omits only $J_p$. The weighted branch multiplies this same contribution by $J_p$; neither branch may omit the saddle prefactor, sampling-cell measure or proposal-density correction appropriate to its estimator, or coherent phase.
+
+Choose and state a physically reasonable standard contour-deformation/steepest-descent and Stokes prescription. Completeness means the full contributing upper-half-plane set under that declared prescription within a demonstrated converged complex-time root domain. Count each distinct contribution once, apply the same saddle-selection and branch-continuation convention to the ordinary and time-sampled calculations, and report a root-count and stability audit as the domain is enlarged or refined. The root domain, seeds, root finder, sampling allocation, and branch-tracking implementation are your numerical choices.
+
+### Coulomb-including trajectories
+
+For the CCSFA branches, distinguish the real saddle/drift momentum parameter $\mathbf q=(q_x,0,q_z)$ from the asymptotic momentum $\mathbf p_\infty$ reached after propagation. The complex saddle relation is
+
+$$
+\frac{1}{2}[q_z+A_z(t_s)]^2+\frac{1}{2}q_x^2+I_p=0.
+$$
+
+Ordinary CCSFA samples $\mathbf q$ and solves this relation for the contributing saddles. Time-sampled CCSFA samples admissible $t_s$ and maps it to $\mathbf q$, with absolute area Jacobian
+
+$$
+J_q=\left|\det\frac{\partial(q_x,q_z)}{\partial(t_r,t_i)}\right|.
+$$
+
+Derive the expanded $\mathbf q$ map and $J_q$ from the saddle relation. Both branches then use the same nonadiabatic saddle launch at $t_r$. With $\sigma=\pm1$ for the two signed transverse branches,
+
+$$
+\mathbf r_0=\left(0,0,\operatorname{Re}\int_{t_s}^{t_r}A_z(\tau)\,d\tau\right),
+$$
+
+$$
+\mathbf v_0=\left(
+\sigma\sqrt{A_i^2(t_r,t_i)-2I_p},\,0,\,-A_r(t_r,t_i)+A_z(t_r)
+\right).
+$$
+
+Propagate after release with
+
+$$
+\frac{d\mathbf r}{dt}=\mathbf v,
+\qquad
+\frac{d\mathbf v}{dt}=-\mathbf E(t)-\frac{\mathbf r}{r^3}.
+$$
+
+After the pulse has ended, obtain each outgoing trajectory's $\mathbf p_\infty$ from its end-of-pulse phase-space coordinates using a stated standard analytic Coulomb/Kepler asymptotic mapping, or a demonstrably equivalent converged continuation. Include the corresponding finite regularized post-pulse Coulomb phase consistently in all three Coulomb-including branches. This fixes the asymptotic observable and coherent phase, but does not prescribe a propagation time, matching radius, integrator, or regularization algorithm.
+
+Use the under-barrier phase
+
+$$
+S_s=-\int_{t_s}^{t_r}d\tau
+\left\{\frac{[\mathbf q+\mathbf A(\tau)]^2}{2}+I_p\right\}
+$$
+
+and the retained post-release Coulomb action family
+
+$$
+S_C=-\int_{t_r}^{\infty}d\tau
+\left[\frac{\mathbf v^2(\tau)}{2}-\frac{2}{r(\tau)}+I_p\right].
+$$
+
+Only relative phases within a final-momentum cell affect its coherent yield. Give the infinite-limit expression a finite numerical meaning either by matching phases to a representative momentum for each finite cell or by using a trajectory-specific regularized action, with physically equivalent converged variants accepted. Apply one declared asymptotic-map and phase convention to all three Coulomb-including branches and jointly demonstrate stability as both its tail parameters and the final-momentum cell width are refined. No particular matching radius, cutoff, quadrature, regularization, or tolerance is prescribed.
+
+For each CCSFA trajectory, combine the saddle prefactor with the phase $S_s+S_C$ (using your converged representative of $S_C$); in the time-sampled branch also apply $J_q$. Propagate both CCSFA branches and coherently bin them by the reached $\mathbf p_\infty$. The ordinary branch is not an asymptotic-momentum shooting or boundary-value calculation, and no $\mathbf q\!\to\!\mathbf p_\infty$ change-of-variables Jacobian is introduced. For QTMC, use the amplitude magnitude implied by the stated standard launch distribution and the retained post-release action as its coherent phase. These statements fix the physical combination, not an integration or binning algorithm.
+
+All three Coulomb PMDs use an $x$-$z$ planar model with $y=v_y=p_y=0$. For the QTMC branch, choose and state a standard ADK ionization rate and the corresponding one-component signed transverse-$p_x$ launch distribution together with a standard Landau static tunnel exit. Do not substitute a cylindrical radial transverse distribution or a $p_y$-marginal for this planar model. The QTMC adiabatic launch is not to be replaced by the nonadiabatic CCSFA launch above. Use the same post-release equations, retained Coulomb action family, tail convention, final-momentum binning, and coherent-yield definition used for the CCSFA comparison.
+
+In the ordinary CCSFA branch, sample $\mathbf q$ and solve for the contributing saddles. In the time-sampled CCSFA branch, sample admissible complex times and map them to $\mathbf q$. Apart from this reversal of sampling direction and the required $J_q$ factor, the two branches must share the same physical launch, saddle set, propagation, action, tail, $\mathbf p_\infty$ binning, and phase conventions.
+
+## Output construction and plotting
+
+For every sampled or propagated branch, coherently add the complex contributions that reach the same final-momentum cell and then form
+
+$$
+P_b=\left|\sum_{j\in b} a_j\right|^2.
+$$
+
+Here $a_j$ contains the branch-appropriate initial magnitude, phase, absolute area Jacobian when required, and estimator weights. Use the same momentum-cell definition within each comparison group. Label every saved raw complex array as either a cell-integrated accumulation or an amplitude density/cell average. Record deterministic quadrature-cell measures or Monte Carlo proposal-density corrections separately from $J_p$ or $J_q$. If momentum-cell areas are unequal or change under refinement, convert the arrays to one consistently declared density convention before quantitative comparison. Report that complex array and the corresponding nonnegative $P_b$ array. Absolute normalization is not specified; state any one momentum-independent factor used for each branch. For display, unit-maximum normalization and either a linear or declared logarithmic color transform are acceptable. Absolute magnitude is not graded.
+
+Use $p_z$ as the horizontal axis and $p_x$ as the vertical axis, both in atomic units. The following are reference display windows, not mandatory computation domains:
+
+- no-Coulomb comparison: $-1\le p_z\le1$ and $-1\le p_x\le1$;
+- Coulomb-including comparison: $-2\le p_z\le2$ and $-1.5\le p_x\le2.5$.
+
+Submit the six PMDs with consistent orientation and readable scales. For the no-Coulomb group, also show quantitative slices or another data-derived comparison from the same arrays sufficient to assess agreement and sampling artifacts. For the Coulomb group, include a common data-derived comparison sufficient to assess global support, envelope, and resolved major ring or ridge positions; matched local regions or slices may be used where their structures are demonstrably resolved. Original annotations, colors, boxes, crops, or exact display ranges are not required.
+
+## Numerical choices and evidence
+
+You choose the momentum/time grids, sampling allocation, root solver, differentiation method, trajectory integrator, action quadrature and tail realization, threshold/caustic treatment, tolerances, refinement order, optimization, and parallelization. Document these choices and provide convergence or stability evidence for every conclusion that depends on them, including threshold/caustic and cell-width refinement where material. Claims about global support, envelope, or resolved major structures must remain stable at the resolution used for those claims. Finer structure that exceeds the resolution needed for a stated conclusion need not satisfy pointwise convergence; do not use an unresolved feature as evidence for a physical conclusion. Sampling branches should report random seeds, proposal/sample counts, propagated-root or trajectory counts, outgoing counts, and final per-cell coverage; deterministic branches should report grid and quadrature coverage. Use `not applicable` where a statistic does not belong to a branch.
+
+Resource limits are supplied exclusively by the accompanying `resource_limits.json`. Its fixed CPU allocation, candidate-active wall time, network boundary are binding. No separate aggregate CPU-hour limit applies. Greater computational expense receives no additional credit.
+
+If independent replicas are used, combine compatible complex estimators before forming $P_b$; duplicate random seeds are not independent physical samples. Report the resources actually used.
+
+## Reference and integrity policy
+
+This examination is conducted without network access or live literature
+retrieval. You may rely on your existing general scientific knowledge and, if any are
+explicitly supplied with the examination, on those offline materials or
+software documentation. Record every such source actually consulted. For formulas,
+methods, constants, or conventions used from general knowledge rather than a
+consulted source, state enough of the method basis, definition, value, units,
+and convention to make the calculation auditable; do not invent a citation.
+You are not required to identify or prove a publication date or to retrieve
+literature during the examination.
+
+The hidden target article and its identifying metadata, figures or captions,
+supplementary material, author code or data, target-specific reproduction
+code, solution or scoring material, online solutions, and worked
+reproductions of this case must not be used. All submitted scientific figures
+and numerical data must be generated by your own implementation of the stated
+problem.
+
+## Analysis questions
+
+1. Using the three no-Coulomb PMDs and your quantitative comparisons, determine whether complex-time sampling reproduces the direct SFA benchmark and under what numerical conditions. Connect your derived mapping and change of measure to identifiable signals in the computed arrays. Distinguish a physical difference from a sampling, binning, or convergence artifact, and state the evidential basis and supported scope of your conclusion.
+
+2. First determine whether the ordinary and time-sampled CCSFA calculations represent the same computed distribution within your demonstrated numerical accuracy. Then compare the QTMC result with the CCSFA family. Identify the specific global or local signals that distinguish the model families, interpret those signals using the stated differences in their initialization or contributing trajectories, and state the evidential basis and supported scope of each conclusion. Do not infer a mechanism from a feature that is not resolved in your submitted data.
+
+## Submission requirements
+
+Submit:
+
+Include a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge.
+
+- the derivation from the stated relations to the computable time-to-momentum map and change-of-variables factor;
+- the six figures and the underlying numerical arrays, including the complex accumulations needed to reconstruct each PMD;
+- code and exact production/plotting commands;
+- branch-appropriate run metadata, numerical settings, normalization/display conventions, and resource use;
+- convergence or stability evidence and the quantitative comparisons used in the analysis; and
+- answers to both analysis questions, with references for any formula or convention actually taken from supplied offline material.
+
+Report failed or superseded runs only when they materially affected parameter selection, convergence, numerical validity, or physical interpretation. No fixed directory tree is required, but the submitted material must be sufficient for an examiner to reconstruct every plotted result.
+
+See [submission requirements](../../submission_requirements.md) for the common submission entry points.

cases/case04/grading_rubric.json

@@ -0,0 +1,648 @@
+{
+  "case_id": "Case04",
+  "title": "Case04 — Quantum Optical Description of Radiation by a Two-Level System in Strong Laser Fields",
+  "atoms": [
+    {
+      "criterion_id": "F1",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.",
+      "award_conditions": [
+        "The specified nonperturbatively driven TLS, initial ground emitter/vacuum, pulse and units form one consistent model."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article pp.053301-1,3, Eqs.(1),(2),(11): driven TLS, vacuum initial radiation, nonperturbative classical pulse and three specified strengths."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F2",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.",
+      "award_conditions": [
+        "Complex first-order emission amplitudes resolve both final bare emitter states and retain correct final-time propagation and phase."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.)",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-2, Eqs.(3)-(5): first-order emitted-field perturbation with forward initial-state and backward endpoint propagation for each final bare emitter channel."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F3",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.",
+      "award_conditions": [
+        "The candidate derives coherent/incoherent amplitudes as an endpoint-unitary resolution of the same emission state; the complete-space one-projection/complement route is accepted under its stated conditions."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.); F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.)",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-2, Eqs.(7)-(10): coherent/incoherent amplitudes and endpoint unitary transformation. Frequencywise norm conservation and a complete-space one-projection/orthogonal-complement realization follow by unitary linear algebra; intensity subtraction alone is not that derivation."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F4",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.",
+      "award_conditions": [
+        "All graded spectra use the same squared first-order amplitude object before frequency-dependent radiation or detector prefactors, with consistent constant normalization."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.)",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-2, Eqs.(6),(9), contrasted with p.053301-3 Fig.1(b,c) caption: plotted Fourier amplitude squares precede hbar*omega*g(omega)^2. The task explicitly grades the pre-prefactor object."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "O1",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present reconstructible state dynamics/endpoint populations for all three drives, distinguishing substantial excitation in A, near-ground return in B and near-excited endpoint in C.",
+      "award_conditions": [
+        "Reconstructible state/endpoint evidence distinguishes substantial A excitation, near-ground B return and near-excited C endpoint.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.)",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article pp.053301-3-4, Figs.1(a),2(a),3(a): substantial residual excitation A, near-ground return B, near-excited endpoint C."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O2",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present reconstructible complex radiation data and spectral evidence for both Case-A final-state channels over a domain sufficient to examine low-order and broad high-order response separately; the corresponding signal identifications are independently assessed.",
+      "award_conditions": [
+        "Case-A final-state complex spectral evidence covers a claim-sufficient low and broad high response; equivalent declared bands/integrals/ratios are accepted, but populations alone are insufficient.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)",
+        "Preserve independently valid work in O1, O3, O4, I3, I4, M5, M6, M7, M8. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-3, Fig.1(b,c), low-order insets and adjacent Rayleigh/Raman paragraph: state-preserving harmonics, shifted state-changing structures and broad high-order ground-final dominance with nontrivial coherence mixing. Functional spectral equivalents remain accepted, not a compulsory author window."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O3",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present A/B/C coherent/incoherent complex radiation data and spectral evidence with frequency coverage, dynamic range and reconstructible presentation sufficient to examine each case's channel redistribution. Frequency-by-frequency cross-consistency is assessed only by O4.",
+      "award_conditions": [
+        "A/B/C coherent/incoherent spectral objects are reconstructible and sufficiently exposed under common frequency-domain and normalization rules; a valid endpoint-projection/complement representation is accepted.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)",
+        "Preserve independently valid work in O1, O2, O4, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-4, Fig.2(a,b), Eq.(10) discussion: near-ground endpoint realizes coherent ground-final and incoherent excited-final channels. For O3 the same object also covers A via Fig.1(c) and C via Fig.3(b)."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "M8",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Compare the independently established B and C control branches to explain how drive-induced endpoint-unitary changes reverse channel realization and coherent/incoherent dominance; this does not duplicate credit for either branch separately.",
+      "award_conditions": [
+        "Candidate-presented B/C radiation evidence under common object, frequency and weighting rules closes the drive-to-endpoint-to-remixing-to-reversal chain; an alternate material spectral domain can qualify."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: M5 (Use Case B's near-ground endpoint and radiation evidence to explain its endpoint-channel realization of coherent dominance.); M6 (Use Case C's near-excited endpoint and radiation evidence to explain the endpoint-channel reversal relative to B and incoherent dominance.); M7 (Explain how the drive changes the endpoint unitary matrix and coherently remixes final-state amplitudes into coherent/incoherent content; field labels or endpoint populations alone do not establish control.)",
+        "Preserve independently valid work in I2, I3, I4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article pp.053301-2-4, Eq.(10), Figs.2-3 and final-transition sensitivity discussion: drive controls endpoint-unitary remixing. Cross-case explanation requires candidate radiation evidence, not endpoint populations alone."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I2",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify from the submitted Case-A final-state and coherence-resolved evidence the dominant broad high-order final-state channel and substantial coherent/incoherent mixing, independently of low-order identification.",
+      "award_conditions": [
+        "The candidate identifies Case-A ground-final high-order dominance and material coherence mixing, or its accepted quantitative spectral equivalent, from their presented frequency-resolved evidence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)",
+        "Preserve independently valid work in I3, I4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-3, Fig.1(b,c), low-order insets and adjacent Rayleigh/Raman paragraph: state-preserving harmonics, shifted state-changing structures and broad high-order ground-final dominance with nontrivial coherence mixing. Functional spectral equivalents remain accepted, not a compulsory author window."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I3",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify from the submitted Case-B endpoint and coherence-resolved spectrum the near-ground endpoint realization and coherent dominance, without requiring Case C to succeed.",
+      "award_conditions": [
+        "The candidate identifies B's near-ground endpoint and coherent channel realization/dominance from their own common-rule radiation evidence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)",
+        "Preserve independently valid work in I2, I4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-4, Fig.2(a,b), Eq.(10) discussion: near-ground endpoint realizes coherent ground-final and incoherent excited-final channels. For O3 the same object also covers A via Fig.1(c) and C via Fig.3(b)."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M1",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain the two resolutions as endpoint-unitary decompositions of the same emitted state, why their total squared norms agree at each frequency, and why this is not a fixed channel-by-channel correspondence.",
+      "award_conditions": [
+        "The candidate explains same-state endpoint basis change, frequencywise norm conservation and the absence of fixed channel correspondence; an intensity identity alone is insufficient."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.)",
+        "Preserve independently valid work in M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-2, Eqs.(7)-(10): coherent/incoherent amplitudes and endpoint unitary transformation. Frequencywise norm conservation and a complete-space one-projection/orthogonal-complement realization follow by unitary linear algebra; intensity subtraction alone is not that derivation."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "O4",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present a frequency-by-frequency cross-check of equal summed intensity in the final-state and coherence resolutions under the same pre-prefactor object and normalization. A weak or locally incomplete cross-check does not erase independently valid coherence-resolved spectra.",
+      "award_conditions": [
+        "The candidate presents frequencywise equal summed intensity for the two resolutions under the same pre-prefactor object; a weak cross-check does not erase independently valid spectra.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)",
+        "Preserve independently valid work in O1, O2, O3, I2, I3, I4, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-2, Eqs.(7)-(10): coherent/incoherent amplitudes and endpoint unitary transformation. Frequencywise norm conservation and a complete-space one-projection/orthogonal-complement realization follow by unitary linear algebra; intensity subtraction alone is not that derivation."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "M3",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Identify odd-harmonic, displaced satellite or dip-type low-order structures in the submitted Case-A final-state spectrum and explain state-preserving/state-changing content and nontrivial mixing; identification and explanation together form this branch-local mechanism core.",
+      "award_conditions": [
+        "Identified Case-A low-order structures, or an accepted quantitative spectral equivalent, support state-preserving/state-changing content and nontrivial mixing in a branch-local explanation."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O2 (Present reconstructible complex radiation data and spectral evidence for both Case-A final-state channels over a domain sufficient to examine low-order and broad high-order response separately; the corresponding signal identifications are independently assessed.)",
+        "Preserve independently valid work in M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-3, Fig.1(b,c), low-order insets and adjacent Rayleigh/Raman paragraph: state-preserving harmonics, shifted state-changing structures and broad high-order ground-final dominance with nontrivial coherence mixing. Functional spectral equivalents remain accepted, not a compulsory author window."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M4",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain Case A's nontrivial two-resolution mixing using its dominant high-order final-state channel and substantial coherent and incoherent components.",
+      "award_conditions": [
+        "Case-A final-state and coherent/incoherent radiation evidence supports the candidate's explanation of nontrivial mixing, not merely equal spectral totals."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I2 (Identify from the submitted Case-A final-state and coherence-resolved evidence the dominant broad high-order final-state channel and substantial coherent/incoherent mixing, independently of low-order identification.)",
+        "Preserve independently valid work in M3, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-3, Fig.1(b,c), low-order insets and adjacent Rayleigh/Raman paragraph: state-preserving harmonics, shifted state-changing structures and broad high-order ground-final dominance with nontrivial coherence mixing. Functional spectral equivalents remain accepted, not a compulsory author window."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M5",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use Case B's near-ground endpoint and radiation evidence to explain its endpoint-channel realization of coherent dominance.",
+      "award_conditions": [
+        "Case-B radiation and near-ground endpoint mapping jointly explain coherent channel realization and dominance; endpoint populations or field labels alone are insufficient."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I3 (Identify from the submitted Case-B endpoint and coherence-resolved spectrum the near-ground endpoint realization and coherent dominance, without requiring Case C to succeed.)",
+        "Preserve independently valid work in M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-4, Fig.2(a,b), Eq.(10) discussion: near-ground endpoint realizes coherent ground-final and incoherent excited-final channels. For O3 the same object also covers A via Fig.1(c) and C via Fig.3(b)."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M6",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use Case C's near-excited endpoint and radiation evidence to explain the endpoint-channel reversal relative to B and incoherent dominance.",
+      "award_conditions": [
+        "Case-C radiation and near-excited endpoint mapping jointly explain reversed channel realization and relative incoherent dominance under the same spectral rules used for B."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I4 (Identify from the submitted Case-C endpoint and coherence-resolved spectrum the near-excited endpoint, reversed channel realization and incoherent dominance, without requiring Case B to succeed.)",
+        "Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-4, Fig.3(a,b): near-excited endpoint reverses channel realization and canonical high-order coherent/incoherent balance relative to Fig.2. Another genuinely discriminating common spectral domain is accepted."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M7",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain how the drive changes the endpoint unitary matrix and coherently remixes final-state amplitudes into coherent/incoherent content; field labels or endpoint populations alone do not establish control.",
+      "award_conditions": [
+        "The candidate connects drive-induced endpoint-unitary coefficients to coherent remixing of final-state complex amplitudes and spectral redistribution."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: M1 (Explain the two resolutions as endpoint-unitary decompositions of the same emitted state, why their total squared norms agree at each frequency, and why this is not a fixed channel-by-channel correspondence.); M5 (Use Case B's near-ground endpoint and radiation evidence to explain its endpoint-channel realization of coherent dominance.); M6 (Use Case C's near-excited endpoint and radiation evidence to explain the endpoint-channel reversal relative to B and incoherent dominance.)",
+        "Preserve independently valid work in O4, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article pp.053301-2-4, Eq.(10), Figs.2-3 and final-transition sensitivity discussion: drive controls endpoint-unitary remixing. Cross-case explanation requires candidate radiation evidence, not endpoint populations alone."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I4",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify from the submitted Case-C endpoint and coherence-resolved spectrum the near-excited endpoint, reversed channel realization and incoherent dominance, without requiring Case B to succeed.",
+      "award_conditions": [
+        "The candidate identifies C's near-excited endpoint, reversed channel realization and incoherent dominance, or a genuine accepted common-domain equivalent, independently of B success."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)",
+        "Preserve independently valid work in I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article p.053301-4, Fig.3(a,b): near-excited endpoint reverses channel realization and canonical high-order coherent/incoherent balance relative to Fig.2. Another genuinely discriminating common spectral domain is accepted."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V1",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Only when the submitted method, data, anomaly or claim exposes a concrete material alternative, exclude it with discriminating evidence or narrow the threatened conclusion.",
+      "award_conditions": [
+        "A concrete conclusion-threatening alternative is excluded by discriminating evidence or the claim is narrowed; if no material risk is triggered this item remains N/A."
+      ],
+      "applicability_and_na": [
+        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
+        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article pp.053301-1-2, first-order emitted-field coupling discussion and Eqs.(3)-(10); task pre-prefactor and three-drive domain. Alternative tests are risk-triggered task/evaluation duties, not source-specific plotting requirements."
+      ],
+      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V2",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Positively identify the actual domain: the specified TLS, three pulse cases, first-order emitted-field coupling and pre-prefactor spectral object.",
+      "award_conditions": [
+        "The actual TLS, three pulse cases, first-order emitted-field approximation and pre-prefactor spectrum domain are positively stated."
+      ],
+      "applicability_and_na": [
+        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.",
+        "In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.",
+        "The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.",
+        "Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.",
+        "B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.",
+        "Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing."
+      ],
+      "source_support": [
+        "Peng et al. (2023), article pp.053301-1-2, first-order emitted-field coupling discussion and Eqs.(3)-(10); task pre-prefactor and three-drive domain. Alternative tests are risk-triggered task/evaluation duties, not source-specific plotting requirements."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    }
+  ],
+  "case_scientific_rules": [
+    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
+    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
+    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
+    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
+    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
+    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
+    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
+    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
+    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
+    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
+    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
+    "A linear plot dominated by the fundamental with no numerical supplement, case-dependent weights, or endpoint populations without frequency-resolved radiation is not equivalent spectral evidence. Examiner reconstruction cannot supply omitted presentation, identification or branch comparison.",
+    "The source high-order reversal is a canonical material anchor, not the sole accepted control evidence. Low-order suppression in C is supporting detail, not compulsory, because it depends on band and display conventions.",
+    "A physical intensity with frequency-dependent prefactors may be secondary evidence, but cannot replace the fixed pre-prefactor graded object. Independent normalization cannot manufacture channel correspondence.",
+    "The one-projection/complement representation does not itself earn mechanism credit: the candidate must explain the same-state endpoint basis change, total-norm invariant, non-fixed channel correspondence and drive-dependent remixing.",
+    "Let $U_a(t,s)$ be the propagator of the standard driven two-level Hamiltonian. For $\\phi\\in\\{g,e\\}$, a final-state-resolved first-order amplitude is",
+    "$$\n\\bar d_{\\phi g}(\\omega)=\\int_0^{t_f}\n\\langle\\phi|U_a(t_f,t)f(t)\\hat dU_a(t,0)|g\\rangle e^{i\\omega t}\\,dt,\n$$",
+    "where $f(t)$ is the supplied sine-squared envelope. In the interaction picture,",
+    "$$\nd_{\\phi g}(\\omega)=\\int_0^{t_f}\n\\langle\\phi|U_a^\\dagger(t,0)f(t)\\hat dU_a(t,0)|g\\rangle e^{i\\omega t}\\,dt.\n$$",
+    "The first pair resolves the emitter's final bare state. The second pair gives the coherent dipole-expectation amplitude and the fluctuation-associated incoherent amplitude. With $|\\phi(t_f)\\rangle=U_a(t_f,0)|\\phi\\rangle$,",
+    "$$\n\\begin{pmatrix}d_{gg}\\\\ d_{eg}\\end{pmatrix}\n=\n\\begin{pmatrix}\n\\langle g(t_f)|g\\rangle & \\langle g(t_f)|e\\rangle\\\\\n\\langle e(t_f)|g\\rangle & \\langle e(t_f)|e\\rangle\n\\end{pmatrix}\n\\begin{pmatrix}\\bar d_{gg}\\\\ \\bar d_{eg}\\end{pmatrix}.\n$$",
+    "The transformation is unitary, so the summed amplitude squares agree at each frequency. Students may derive or compute these objects by an equivalent forward/backward, interaction-picture, correlation-function or explicitly unitary route.",
+    "Case A ends with substantial excitation, approximately $P_e(t_f)=0.524$. Both final-state channels are present. Low orders show odd-harmonic and displaced satellite/dip structure; the ground-final channel dominates the broad high-order response. The coherent and incoherent components are both substantial.",
+    "Case B returns close to the ground state. Its high-order coherent response is stronger than its incoherent response, with the corresponding endpoint channel assignment.",
+    "Case C ends close to the excited state. The endpoint-channel realization is reversed relative to Case B, and the high-order incoherent response is stronger. The source's low-order suppression is supporting detail, not a mandatory full-credit anchor because its strength is sensitive to the resolved band and display convention.",
+    "The physical conclusion is not merely that the two sums are equal. The end-of-pulse unitary controls how the final-state channel amplitudes mix into coherent and incoherent radiation, so changing the pulse can redistribute their channel content.",
+    "For F2-F4/M1/M7-M8, article p.053301-2, Eqs.(5),(8),(10), let $\\bar{\\mathbf d}=(\\bar d_{gg},\\bar d_{eg})^T$ be the final-bare-state amplitudes and $U_f=U_a(t_f,0)$. Then\n$$\\mathbf d=U_f^\\dagger\\bar{\\mathbf d},\\qquad\nS_{\\rm tot}=\\|\\bar{\\mathbf d}\\|^2=|d_{\\rm coh}|^2+|d_{\\rm inc}|^2.$$\nIf $r$ is the normalized coherent projection row of $U_f^\\dagger$, then $d_{\\rm coh}=r\\bar{\\mathbf d}$ and $S_{\\rm inc}=\\|\\bar{\\mathbf d}\\|^2-|r\\bar{\\mathbf d}|^2\\ge0$. This is an equivalent representation only when common final-state complex amplitudes, complete two-dimensional endpoint space, normalized projection and frequencywise common object are established; a stored second complex row is not compulsory. The same algebra does not supply candidate identification or drive-control reasoning. Canonical broad high-order B/C reversal is not the sole acceptable spectral domain, but a claim about the full strong-field spectrum cannot evade material high-order response by selecting a fundamental-dominated display."
+  ],
+  "closure_requirements": {
+    "RC0": [
+      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
+      "Required indispensable claim CL0, central physical object: all of: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC1": [
+      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
+      "Required indispensable claim CL0, indispensable material component: all of: F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL1, indispensable material component: all of: O1 (Present reconstructible state dynamics/endpoint populations for all three drives, distinguishing substantial excitation in A, near-ground return in B and near-excited endpoint in C.); O2 (Present reconstructible complex radiation data and spectral evidence for both Case-A final-state channels over a domain sufficient to examine low-order and broad high-order response separately; the corresponding signal identifications are independently assessed.); O3 (Present A/B/C coherent/incoherent complex radiation data and spectral evidence with frequency coverage, dynamic range and reconstructible presentation sufficient to examine each case's channel redistribution. Frequency-by-frequency cross-consistency is assessed only by O4.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC2": [
+      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
+      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M1 (Explain the two resolutions as endpoint-unitary decompositions of the same emitted state, why their total squared norms agree at each frequency, and why this is not a fixed channel-by-channel correspondence.); M5 (Use Case B's near-ground endpoint and radiation evidence to explain its endpoint-channel realization of coherent dominance.); M6 (Use Case C's near-excited endpoint and radiation evidence to explain the endpoint-channel reversal relative to B and incoherent dominance.); M7 (Explain how the drive changes the endpoint unitary matrix and coherently remixes final-state amplitudes into coherent/incoherent content; field labels or endpoint populations alone do not establish control.); M8 (Compare the independently established B and C control branches to explain how drive-induced endpoint-unitary changes reverse channel realization and coherent/incoherent dominance; this does not duplicate credit for either branch separately.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC3": [
+      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
+      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
+      "Required co primary claim CL3, material validation/scope: V1 (Only when the submitted method, data, anomaly or claim exposes a concrete material alternative, exclude it with discriminating evidence or narrow the threatened conclusion.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC4": [
+      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
+      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
+      "Close CL0 central physical object: all of: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.).",
+      "Close CL0 indispensable material component: all of: F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.).",
+      "Close CL1 indispensable material component: all of: O1 (Present reconstructible state dynamics/endpoint populations for all three drives, distinguishing substantial excitation in A, near-ground return in B and near-excited endpoint in C.); O2 (Present reconstructible complex radiation data and spectral evidence for both Case-A final-state channels over a domain sufficient to examine low-order and broad high-order response separately; the corresponding signal identifications are independently assessed.); O3 (Present A/B/C coherent/incoherent complex radiation data and spectral evidence with frequency coverage, dynamic range and reconstructible presentation sufficient to examine each case's channel redistribution. Frequency-by-frequency cross-consistency is assessed only by O4.).",
+      "Close CL2 principal mechanism or commissioned conclusion: all of: M1 (Explain the two resolutions as endpoint-unitary decompositions of the same emitted state, why their total squared norms agree at each frequency, and why this is not a fixed channel-by-channel correspondence.); M5 (Use Case B's near-ground endpoint and radiation evidence to explain its endpoint-channel realization of coherent dominance.); M6 (Use Case C's near-excited endpoint and radiation evidence to explain the endpoint-channel reversal relative to B and incoherent dominance.); M7 (Explain how the drive changes the endpoint unitary matrix and coherently remixes final-state amplitudes into coherent/incoherent content; field labels or endpoint populations alone do not establish control.); M8 (Compare the independently established B and C control branches to explain how drive-induced endpoint-unitary changes reverse channel realization and coherent/incoherent dominance; this does not duplicate credit for either branch separately.).",
+      "Close CL3 material validation/scope: V1 (Only when the submitted method, data, anomaly or claim exposes a concrete material alternative, exclude it with discriminating evidence or narrow the threatened conclusion.)."
+    ]
+  },
+  "references": [
+    {
+      "citation": "Zhaoyang Peng, Huayu Hu, Zengxiu Zhao, and Jianmin Yuan. 2023. *Quantum Optical Description of Radiation by a Two-Level System in Strong Laser Fields*. *Chinese Physics Letters*, 40, 053301.",
+      "url": "https://doi.org/10.1088/0256-307X/40/5/053301",
+      "scientific_scope": "Quantum Optical Description of Radiation by a Two-Level System in Strong Laser Fields",
+      "anchors": [
+        "Peng et al. (2023), article pp.053301-1,3, Eqs.(1),(2),(11): driven TLS, vacuum initial radiation, nonperturbative classical pulse and three specified strengths.",
+        "Peng et al. (2023), article p.053301-2, Eqs.(3)-(5): first-order emitted-field perturbation with forward initial-state and backward endpoint propagation for each final bare emitter channel.",
+        "Peng et al. (2023), article p.053301-2, Eqs.(7)-(10): coherent/incoherent amplitudes and endpoint unitary transformation. Frequencywise norm conservation and a complete-space one-projection/orthogonal-complement realization follow by unitary linear algebra; intensity subtraction alone is not that derivation.",
+        "Peng et al. (2023), article p.053301-2, Eqs.(6),(9), contrasted with p.053301-3 Fig.1(b,c) caption: plotted Fourier amplitude squares precede hbar*omega*g(omega)^2. The task explicitly grades the pre-prefactor object.",
+        "Peng et al. (2023), article pp.053301-3-4, Figs.1(a),2(a),3(a): substantial residual excitation A, near-ground return B, near-excited endpoint C.",
+        "Peng et al. (2023), article p.053301-3, Fig.1(b,c), low-order insets and adjacent Rayleigh/Raman paragraph: state-preserving harmonics, shifted state-changing structures and broad high-order ground-final dominance with nontrivial coherence mixing. Functional spectral equivalents remain accepted, not a compulsory author window.",
+        "Peng et al. (2023), article p.053301-4, Fig.2(a,b), Eq.(10) discussion: near-ground endpoint realizes coherent ground-final and incoherent excited-final channels. For O3 the same object also covers A via Fig.1(c) and C via Fig.3(b).",
+        "Peng et al. (2023), article p.053301-4, Fig.3(a,b): near-excited endpoint reverses channel realization and canonical high-order coherent/incoherent balance relative to Fig.2. Another genuinely discriminating common spectral domain is accepted.",
+        "Peng et al. (2023), article pp.053301-2-4, Eq.(10), Figs.2-3 and final-transition sensitivity discussion: drive controls endpoint-unitary remixing. Cross-case explanation requires candidate radiation evidence, not endpoint populations alone.",
+        "Peng et al. (2023), article pp.053301-1-2, first-order emitted-field coupling discussion and Eqs.(3)-(10); task pre-prefactor and three-drive domain. Alternative tests are risk-triggered task/evaluation duties, not source-specific plotting requirements."
+      ]
+    }
+  ]
+}

cases/case04/grading_rubric.md

@@ -0,0 +1,976 @@
+# Grading Rubric — Case04
+
+Case04 — Quantum Optical Description of Radiation by a Two-Level System in Strong Laser Fields
+
+## Atomic Scoring Criteria
+
+Each criterion awards 0 or 0.5 points, for a maximum of 10. Explicit N/A rules apply where stated.
+
+### F1 — F — 0.5 points
+
+**Scientific requirement**
+
+Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.
+
+**Conditions for credit**
+
+- The specified nonperturbatively driven TLS, initial ground emitter/vacuum, pulse and units form one consistent model.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article pp.053301-1,3, Eqs.(1),(2),(11): driven TLS, vacuum initial radiation, nonperturbative classical pulse and three specified strengths.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F2 — F — 0.5 points
+
+**Scientific requirement**
+
+Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.
+
+**Conditions for credit**
+
+- Complex first-order emission amplitudes resolve both final bare emitter states and retain correct final-time propagation and phase.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.)
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-2, Eqs.(3)-(5): first-order emitted-field perturbation with forward initial-state and backward endpoint propagation for each final bare emitter channel.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F3 — F — 0.5 points
+
+**Scientific requirement**
+
+Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.
+
+**Conditions for credit**
+
+- The candidate derives coherent/incoherent amplitudes as an endpoint-unitary resolution of the same emission state; the complete-space one-projection/complement route is accepted under its stated conditions.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.); F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.)
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-2, Eqs.(7)-(10): coherent/incoherent amplitudes and endpoint unitary transformation. Frequencywise norm conservation and a complete-space one-projection/orthogonal-complement realization follow by unitary linear algebra; intensity subtraction alone is not that derivation.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F4 — F — 0.5 points
+
+**Scientific requirement**
+
+Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.
+
+**Conditions for credit**
+
+- All graded spectra use the same squared first-order amplitude object before frequency-dependent radiation or detector prefactors, with consistent constant normalization.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.)
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-2, Eqs.(6),(9), contrasted with p.053301-3 Fig.1(b,c) caption: plotted Fourier amplitude squares precede hbar*omega*g(omega)^2. The task explicitly grades the pre-prefactor object.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### O1 — O — 0.5 points
+
+**Scientific requirement**
+
+Present reconstructible state dynamics/endpoint populations for all three drives, distinguishing substantial excitation in A, near-ground return in B and near-excited endpoint in C.
+
+**Conditions for credit**
+
+- Reconstructible state/endpoint evidence distinguishes substantial A excitation, near-ground B return and near-excited C endpoint.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.)
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article pp.053301-3-4, Figs.1(a),2(a),3(a): substantial residual excitation A, near-ground return B, near-excited endpoint C.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O2 — O — 0.5 points
+
+**Scientific requirement**
+
+Present reconstructible complex radiation data and spectral evidence for both Case-A final-state channels over a domain sufficient to examine low-order and broad high-order response separately; the corresponding signal identifications are independently assessed.
+
+**Conditions for credit**
+
+- Case-A final-state complex spectral evidence covers a claim-sufficient low and broad high response; equivalent declared bands/integrals/ratios are accepted, but populations alone are insufficient.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)
+
+- Preserve independently valid work in O1, O3, O4, I3, I4, M5, M6, M7, M8. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-3, Fig.1(b,c), low-order insets and adjacent Rayleigh/Raman paragraph: state-preserving harmonics, shifted state-changing structures and broad high-order ground-final dominance with nontrivial coherence mixing. Functional spectral equivalents remain accepted, not a compulsory author window.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O3 — O — 0.5 points
+
+**Scientific requirement**
+
+Present A/B/C coherent/incoherent complex radiation data and spectral evidence with frequency coverage, dynamic range and reconstructible presentation sufficient to examine each case's channel redistribution. Frequency-by-frequency cross-consistency is assessed only by O4.
+
+**Conditions for credit**
+
+- A/B/C coherent/incoherent spectral objects are reconstructible and sufficiently exposed under common frequency-domain and normalization rules; a valid endpoint-projection/complement representation is accepted.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)
+
+- Preserve independently valid work in O1, O2, O4, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-4, Fig.2(a,b), Eq.(10) discussion: near-ground endpoint realizes coherent ground-final and incoherent excited-final channels. For O3 the same object also covers A via Fig.1(c) and C via Fig.3(b).
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### M8 — M — 0.5 points
+
+**Scientific requirement**
+
+Compare the independently established B and C control branches to explain how drive-induced endpoint-unitary changes reverse channel realization and coherent/incoherent dominance; this does not duplicate credit for either branch separately.
+
+**Conditions for credit**
+
+- Candidate-presented B/C radiation evidence under common object, frequency and weighting rules closes the drive-to-endpoint-to-remixing-to-reversal chain; an alternate material spectral domain can qualify.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: M5 (Use Case B's near-ground endpoint and radiation evidence to explain its endpoint-channel realization of coherent dominance.); M6 (Use Case C's near-excited endpoint and radiation evidence to explain the endpoint-channel reversal relative to B and incoherent dominance.); M7 (Explain how the drive changes the endpoint unitary matrix and coherently remixes final-state amplitudes into coherent/incoherent content; field labels or endpoint populations alone do not establish control.)
+
+- Preserve independently valid work in I2, I3, I4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article pp.053301-2-4, Eq.(10), Figs.2-3 and final-transition sensitivity discussion: drive controls endpoint-unitary remixing. Cross-case explanation requires candidate radiation evidence, not endpoint populations alone.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I2 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify from the submitted Case-A final-state and coherence-resolved evidence the dominant broad high-order final-state channel and substantial coherent/incoherent mixing, independently of low-order identification.
+
+**Conditions for credit**
+
+- The candidate identifies Case-A ground-final high-order dominance and material coherence mixing, or its accepted quantitative spectral equivalent, from their presented frequency-resolved evidence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)
+
+- Preserve independently valid work in I3, I4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-3, Fig.1(b,c), low-order insets and adjacent Rayleigh/Raman paragraph: state-preserving harmonics, shifted state-changing structures and broad high-order ground-final dominance with nontrivial coherence mixing. Functional spectral equivalents remain accepted, not a compulsory author window.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I3 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify from the submitted Case-B endpoint and coherence-resolved spectrum the near-ground endpoint realization and coherent dominance, without requiring Case C to succeed.
+
+**Conditions for credit**
+
+- The candidate identifies B's near-ground endpoint and coherent channel realization/dominance from their own common-rule radiation evidence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)
+
+- Preserve independently valid work in I2, I4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-4, Fig.2(a,b), Eq.(10) discussion: near-ground endpoint realizes coherent ground-final and incoherent excited-final channels. For O3 the same object also covers A via Fig.1(c) and C via Fig.3(b).
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M1 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain the two resolutions as endpoint-unitary decompositions of the same emitted state, why their total squared norms agree at each frequency, and why this is not a fixed channel-by-channel correspondence.
+
+**Conditions for credit**
+
+- The candidate explains same-state endpoint basis change, frequencywise norm conservation and the absence of fixed channel correspondence; an intensity identity alone is insufficient.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.)
+
+- Preserve independently valid work in M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-2, Eqs.(7)-(10): coherent/incoherent amplitudes and endpoint unitary transformation. Frequencywise norm conservation and a complete-space one-projection/orthogonal-complement realization follow by unitary linear algebra; intensity subtraction alone is not that derivation.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### O4 — O — 0.5 points
+
+**Scientific requirement**
+
+Present a frequency-by-frequency cross-check of equal summed intensity in the final-state and coherence resolutions under the same pre-prefactor object and normalization. A weak or locally incomplete cross-check does not erase independently valid coherence-resolved spectra.
+
+**Conditions for credit**
+
+- The candidate presents frequencywise equal summed intensity for the two resolutions under the same pre-prefactor object; a weak cross-check does not erase independently valid spectra.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)
+
+- Preserve independently valid work in O1, O2, O3, I2, I3, I4, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-2, Eqs.(7)-(10): coherent/incoherent amplitudes and endpoint unitary transformation. Frequencywise norm conservation and a complete-space one-projection/orthogonal-complement realization follow by unitary linear algebra; intensity subtraction alone is not that derivation.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### M3 — M — 0.5 points
+
+**Scientific requirement**
+
+Identify odd-harmonic, displaced satellite or dip-type low-order structures in the submitted Case-A final-state spectrum and explain state-preserving/state-changing content and nontrivial mixing; identification and explanation together form this branch-local mechanism core.
+
+**Conditions for credit**
+
+- Identified Case-A low-order structures, or an accepted quantitative spectral equivalent, support state-preserving/state-changing content and nontrivial mixing in a branch-local explanation.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O2 (Present reconstructible complex radiation data and spectral evidence for both Case-A final-state channels over a domain sufficient to examine low-order and broad high-order response separately; the corresponding signal identifications are independently assessed.)
+
+- Preserve independently valid work in M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-3, Fig.1(b,c), low-order insets and adjacent Rayleigh/Raman paragraph: state-preserving harmonics, shifted state-changing structures and broad high-order ground-final dominance with nontrivial coherence mixing. Functional spectral equivalents remain accepted, not a compulsory author window.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M4 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain Case A's nontrivial two-resolution mixing using its dominant high-order final-state channel and substantial coherent and incoherent components.
+
+**Conditions for credit**
+
+- Case-A final-state and coherent/incoherent radiation evidence supports the candidate's explanation of nontrivial mixing, not merely equal spectral totals.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I2 (Identify from the submitted Case-A final-state and coherence-resolved evidence the dominant broad high-order final-state channel and substantial coherent/incoherent mixing, independently of low-order identification.)
+
+- Preserve independently valid work in M3, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-3, Fig.1(b,c), low-order insets and adjacent Rayleigh/Raman paragraph: state-preserving harmonics, shifted state-changing structures and broad high-order ground-final dominance with nontrivial coherence mixing. Functional spectral equivalents remain accepted, not a compulsory author window.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M5 — M — 0.5 points
+
+**Scientific requirement**
+
+Use Case B's near-ground endpoint and radiation evidence to explain its endpoint-channel realization of coherent dominance.
+
+**Conditions for credit**
+
+- Case-B radiation and near-ground endpoint mapping jointly explain coherent channel realization and dominance; endpoint populations or field labels alone are insufficient.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I3 (Identify from the submitted Case-B endpoint and coherence-resolved spectrum the near-ground endpoint realization and coherent dominance, without requiring Case C to succeed.)
+
+- Preserve independently valid work in M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-4, Fig.2(a,b), Eq.(10) discussion: near-ground endpoint realizes coherent ground-final and incoherent excited-final channels. For O3 the same object also covers A via Fig.1(c) and C via Fig.3(b).
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M6 — M — 0.5 points
+
+**Scientific requirement**
+
+Use Case C's near-excited endpoint and radiation evidence to explain the endpoint-channel reversal relative to B and incoherent dominance.
+
+**Conditions for credit**
+
+- Case-C radiation and near-excited endpoint mapping jointly explain reversed channel realization and relative incoherent dominance under the same spectral rules used for B.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I4 (Identify from the submitted Case-C endpoint and coherence-resolved spectrum the near-excited endpoint, reversed channel realization and incoherent dominance, without requiring Case B to succeed.)
+
+- Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-4, Fig.3(a,b): near-excited endpoint reverses channel realization and canonical high-order coherent/incoherent balance relative to Fig.2. Another genuinely discriminating common spectral domain is accepted.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M7 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain how the drive changes the endpoint unitary matrix and coherently remixes final-state amplitudes into coherent/incoherent content; field labels or endpoint populations alone do not establish control.
+
+**Conditions for credit**
+
+- The candidate connects drive-induced endpoint-unitary coefficients to coherent remixing of final-state complex amplitudes and spectral redistribution.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: M1 (Explain the two resolutions as endpoint-unitary decompositions of the same emitted state, why their total squared norms agree at each frequency, and why this is not a fixed channel-by-channel correspondence.); M5 (Use Case B's near-ground endpoint and radiation evidence to explain its endpoint-channel realization of coherent dominance.); M6 (Use Case C's near-excited endpoint and radiation evidence to explain the endpoint-channel reversal relative to B and incoherent dominance.)
+
+- Preserve independently valid work in O4, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article pp.053301-2-4, Eq.(10), Figs.2-3 and final-transition sensitivity discussion: drive controls endpoint-unitary remixing. Cross-case explanation requires candidate radiation evidence, not endpoint populations alone.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I4 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify from the submitted Case-C endpoint and coherence-resolved spectrum the near-excited endpoint, reversed channel realization and incoherent dominance, without requiring Case B to succeed.
+
+**Conditions for credit**
+
+- The candidate identifies C's near-excited endpoint, reversed channel realization and incoherent dominance, or a genuine accepted common-domain equivalent, independently of B success.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.)
+
+- Preserve independently valid work in I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article p.053301-4, Fig.3(a,b): near-excited endpoint reverses channel realization and canonical high-order coherent/incoherent balance relative to Fig.2. Another genuinely discriminating common spectral domain is accepted.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V1 — V — 0.5 points
+
+**Scientific requirement**
+
+Only when the submitted method, data, anomaly or claim exposes a concrete material alternative, exclude it with discriminating evidence or narrow the threatened conclusion.
+
+**Conditions for credit**
+
+- A concrete conclusion-threatening alternative is excluded by discriminating evidence or the claim is narrowed; if no material risk is triggered this item remains N/A.
+
+**Applicability and N/A**
+
+- Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.
+
+- If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article pp.053301-1-2, first-order emitted-field coupling discussion and Eqs.(3)-(10); task pre-prefactor and three-drive domain. Alternative tests are risk-triggered task/evaluation duties, not source-specific plotting requirements.
+
+**Research Closure relation**
+
+Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V2 — V — 0.5 points
+
+**Scientific requirement**
+
+Positively identify the actual domain: the specified TLS, three pulse cases, first-order emitted-field coupling and pre-prefactor spectral object.
+
+**Conditions for credit**
+
+- The actual TLS, three pulse cases, first-order emitted-field approximation and pre-prefactor spectrum domain are positively stated.
+
+**Applicability and N/A**
+
+- This positive scientific scope/evidence duty is unconditional; N/A is not permitted.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent basis phases, Fourier signs and constant normalization are accepted. Forward/backward propagation, interaction-picture, correlation-function and explicitly unitary formulations are accepted when they preserve the same emitted state and both resolutions.
+
+- In the complete two-dimensional final-state space, one normalized endpoint projection of the final-state complex amplitude pair plus its orthogonal spectral complement is equivalent to an explicit 2x2 unitary transformation. The second complex row need not be printed or stored if completeness, endpoint unitarity, per-frequency norm conservation and the incoherent physical identity are established.
+
+- The incoherent spectrum may be obtained by subtracting the coherent spectrum from the same pre-prefactor total spectrum at each frequency, provided the final-state complex amplitudes, normalized endpoint projection, common frequency/normalization rule and complementary result are reconstructible. A bare intensity remainder without those identities is insufficient.
+
+- Candidate-defined common frequency bands, consistent band integrals, ratios or reconstructible tables may replace fixed low/high-order windows or six panels if they expose the same material channel relation and the candidate identifies and explains it.
+
+- B/C control reversal need not use a fixed high-order window: another materially informative spectral domain, logarithmic/local display, common band integral, ratio or table is equivalent when it closes drive change -> endpoint unitary -> coherent amplitude remixing -> B/C radiation-channel reversal. A claim about the full strong-field spectrum must still examine any high-order response capable of changing that conclusion.
+
+- Equivalent Case-A evidence may use quantitative spectral structures or consistently defined bands/ratios instead of the canonical odd/satellite/dip combination, but must preserve both resolutions and distinguish state-preserving/state-changing content and nontrivial mixing.
+
+**Scientific source locations**
+
+- Peng et al. (2023), article pp.053301-1-2, first-order emitted-field coupling discussion and Eqs.(3)-(10); task pre-prefactor and three-drive domain. Alternative tests are risk-triggered task/evaluation duties, not source-specific plotting requirements.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+## Research Closure Requirements
+
+### RC0
+
+- The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.
+
+- Required indispensable claim CL0, central physical object: all of: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC1
+
+- With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.
+
+- Required indispensable claim CL0, indispensable material component: all of: F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL1, indispensable material component: all of: O1 (Present reconstructible state dynamics/endpoint populations for all three drives, distinguishing substantial excitation in A, near-ground return in B and near-excited endpoint in C.); O2 (Present reconstructible complex radiation data and spectral evidence for both Case-A final-state channels over a domain sufficient to examine low-order and broad high-order response separately; the corresponding signal identifications are independently assessed.); O3 (Present A/B/C coherent/incoherent complex radiation data and spectral evidence with frequency coverage, dynamic range and reconstructible presentation sufficient to examine each case's channel redistribution. Frequency-by-frequency cross-consistency is assessed only by O4.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC2
+
+- With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.
+
+- Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M1 (Explain the two resolutions as endpoint-unitary decompositions of the same emitted state, why their total squared norms agree at each frequency, and why this is not a fixed channel-by-channel correspondence.); M5 (Use Case B's near-ground endpoint and radiation evidence to explain its endpoint-channel realization of coherent dominance.); M6 (Use Case C's near-excited endpoint and radiation evidence to explain the endpoint-channel reversal relative to B and incoherent dominance.); M7 (Explain how the drive changes the endpoint unitary matrix and coherently remixes final-state amplitudes into coherent/incoherent content; field labels or endpoint populations alone do not establish control.); M8 (Compare the independently established B and C control branches to explain how drive-induced endpoint-unitary changes reverse channel realization and coherent/incoherent dominance; this does not duplicate credit for either branch separately.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC3
+
+- With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.
+
+- Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.
+
+- Required co primary claim CL3, material validation/scope: V1 (Only when the submitted method, data, anomaly or claim exposes a concrete material alternative, exclude it with discriminating evidence or narrow the threatened conclusion.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC4
+
+- All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.
+
+- Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.
+
+- Close CL0 central physical object: all of: F1 (Establish the specified driven two-level Hamiltonian, nonperturbative classical drive, initial emitter/vacuum state, pulse and consistent units/phases.); F4 (Use squared first-order emission amplitudes before any frequency-dependent radiation, density-of-states or detector prefactor, with consistent constant normalization.).
+
+- Close CL0 indispensable material component: all of: F2 (Derive complex first-order one-photon emission amplitudes resolved by final bare emitter state, retaining the correct endpoint propagation and phase conventions.); F3 (Derive the coherent/incoherent radiation resolution and endpoint unitary transformation from the final-state amplitude pair, rather than merely labelling curves.).
+
+- Close CL1 indispensable material component: all of: O1 (Present reconstructible state dynamics/endpoint populations for all three drives, distinguishing substantial excitation in A, near-ground return in B and near-excited endpoint in C.); O2 (Present reconstructible complex radiation data and spectral evidence for both Case-A final-state channels over a domain sufficient to examine low-order and broad high-order response separately; the corresponding signal identifications are independently assessed.); O3 (Present A/B/C coherent/incoherent complex radiation data and spectral evidence with frequency coverage, dynamic range and reconstructible presentation sufficient to examine each case's channel redistribution. Frequency-by-frequency cross-consistency is assessed only by O4.).
+
+- Close CL2 principal mechanism or commissioned conclusion: all of: M1 (Explain the two resolutions as endpoint-unitary decompositions of the same emitted state, why their total squared norms agree at each frequency, and why this is not a fixed channel-by-channel correspondence.); M5 (Use Case B's near-ground endpoint and radiation evidence to explain its endpoint-channel realization of coherent dominance.); M6 (Use Case C's near-excited endpoint and radiation evidence to explain the endpoint-channel reversal relative to B and incoherent dominance.); M7 (Explain how the drive changes the endpoint unitary matrix and coherently remixes final-state amplitudes into coherent/incoherent content; field labels or endpoint populations alone do not establish control.); M8 (Compare the independently established B and C control branches to explain how drive-induced endpoint-unitary changes reverse channel realization and coherent/incoherent dominance; this does not duplicate credit for either branch separately.).
+
+- Close CL3 material validation/scope: V1 (Only when the submitted method, data, anomaly or claim exposes a concrete material alternative, exclude it with discriminating evidence or narrow the threatened conclusion.).
+
+## Applicability and Equivalent Evidence
+
+- Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.
+
+- Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.
+
+- For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.
+
+- Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.
+
+- Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.
+
+- Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.
+
+- Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.
+
+- Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.
+
+- Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.
+
+- Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.
+
+- A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.
+
+- A linear plot dominated by the fundamental with no numerical supplement, case-dependent weights, or endpoint populations without frequency-resolved radiation is not equivalent spectral evidence. Examiner reconstruction cannot supply omitted presentation, identification or branch comparison.
+
+- The source high-order reversal is a canonical material anchor, not the sole accepted control evidence. Low-order suppression in C is supporting detail, not compulsory, because it depends on band and display conventions.
+
+- A physical intensity with frequency-dependent prefactors may be secondary evidence, but cannot replace the fixed pre-prefactor graded object. Independent normalization cannot manufacture channel correspondence.
+
+- The one-projection/complement representation does not itself earn mechanism credit: the candidate must explain the same-state endpoint basis change, total-norm invariant, non-fixed channel correspondence and drive-dependent remixing.
+
+- Let $U_a(t,s)$ be the propagator of the standard driven two-level Hamiltonian. For $\phi\in\{g,e\}$, a final-state-resolved first-order amplitude is
+
+$$
+\bar d_{\phi g}(\omega)=\int_0^{t_f}
+\langle\phi|U_a(t_f,t)f(t)\hat dU_a(t,0)|g\rangle e^{i\omega t}\,dt,
+$$
+
+- where $f(t)$ is the supplied sine-squared envelope. In the interaction picture,
+
+$$
+d_{\phi g}(\omega)=\int_0^{t_f}
+\langle\phi|U_a^\dagger(t,0)f(t)\hat dU_a(t,0)|g\rangle e^{i\omega t}\,dt.
+$$
+
+- The first pair resolves the emitter's final bare state. The second pair gives the coherent dipole-expectation amplitude and the fluctuation-associated incoherent amplitude. With $|\phi(t_f)\rangle=U_a(t_f,0)|\phi\rangle$,
+
+$$
+\begin{pmatrix}d_{gg}\\ d_{eg}\end{pmatrix}
+=
+\begin{pmatrix}
+\langle g(t_f)|g\rangle & \langle g(t_f)|e\rangle\\
+\langle e(t_f)|g\rangle & \langle e(t_f)|e\rangle
+\end{pmatrix}
+\begin{pmatrix}\bar d_{gg}\\ \bar d_{eg}\end{pmatrix}.
+$$
+
+- The transformation is unitary, so the summed amplitude squares agree at each frequency. Students may derive or compute these objects by an equivalent forward/backward, interaction-picture, correlation-function or explicitly unitary route.
+
+- Case A ends with substantial excitation, approximately $P_e(t_f)=0.524$. Both final-state channels are present. Low orders show odd-harmonic and displaced satellite/dip structure; the ground-final channel dominates the broad high-order response. The coherent and incoherent components are both substantial.
+
+- Case B returns close to the ground state. Its high-order coherent response is stronger than its incoherent response, with the corresponding endpoint channel assignment.
+
+- Case C ends close to the excited state. The endpoint-channel realization is reversed relative to Case B, and the high-order incoherent response is stronger. The source's low-order suppression is supporting detail, not a mandatory full-credit anchor because its strength is sensitive to the resolved band and display convention.
+
+- The physical conclusion is not merely that the two sums are equal. The end-of-pulse unitary controls how the final-state channel amplitudes mix into coherent and incoherent radiation, so changing the pulse can redistribute their channel content.
+
+For F2-F4/M1/M7-M8, article p.053301-2, Eqs.(5),(8),(10), let $\bar{\mathbf d}=(\bar d_{gg},\bar d_{eg})^T$ be the final-bare-state amplitudes and $U_f=U_a(t_f,0)$. Then
+$$\mathbf d=U_f^\dagger\bar{\mathbf d},\qquad
+S_{\rm tot}=\|\bar{\mathbf d}\|^2=|d_{\rm coh}|^2+|d_{\rm inc}|^2.$$
+If $r$ is the normalized coherent projection row of $U_f^\dagger$, then $d_{\rm coh}=r\bar{\mathbf d}$ and $S_{\rm inc}=\|\bar{\mathbf d}\|^2-|r\bar{\mathbf d}|^2\ge0$. This is an equivalent representation only when common final-state complex amplitudes, complete two-dimensional endpoint space, normalized projection and frequencywise common object are established; a stored second complex row is not compulsory. The same algebra does not supply candidate identification or drive-control reasoning. Canonical broad high-order B/C reversal is not the sole acceptable spectral domain, but a claim about the full strong-field spectrum cannot evade material high-order response by selecting a fundamental-dominated display.

cases/case04/resource_limits.json

@@ -0,0 +1,8 @@
+{
+  "cpu_cores": 8,
+  "nodes": 1,
+  "time_limit_minutes": 30,
+  "network_access": "disabled",
+  "temporary_storage_gib": 64,
+  "memory_policy": "No separate task-specific RAM limit is specified."
+}

cases/case04/sources.md

@@ -0,0 +1,35 @@
+# Scientific Sources — Case04
+
+## References
+
+Zhaoyang Peng, Huayu Hu, Zengxiu Zhao, and Jianmin Yuan. 2023. *Quantum Optical Description of Radiation by a Two-Level System in Strong Laser Fields*. *Chinese Physics Letters*, 40, 053301. [Source](https://doi.org/10.1088/0256-307X/40/5/053301)
+
+Quantum Optical Description of Radiation by a Two-Level System in Strong Laser Fields
+
+## Criterion-to-source crosswalk
+
+Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.
+
+| Criteria | Source locations, scientific use and limits |
+|---|---|
+| F1 | Peng et al. (2023), article pp.053301-1,3, Eqs.(1),(2),(11): driven TLS, vacuum initial radiation, nonperturbative classical pulse and three specified strengths. |
+| F2 | Peng et al. (2023), article p.053301-2, Eqs.(3)-(5): first-order emitted-field perturbation with forward initial-state and backward endpoint propagation for each final bare emitter channel. |
+| F3, M1, O4 | Peng et al. (2023), article p.053301-2, Eqs.(7)-(10): coherent/incoherent amplitudes and endpoint unitary transformation. Frequencywise norm conservation and a complete-space one-projection/orthogonal-complement realization follow by unitary linear algebra; intensity subtraction alone is not that derivation. |
+| F4 | Peng et al. (2023), article p.053301-2, Eqs.(6),(9), contrasted with p.053301-3 Fig.1(b,c) caption: plotted Fourier amplitude squares precede hbar*omega*g(omega)^2. The task explicitly grades the pre-prefactor object. |
+| O1 | Peng et al. (2023), article pp.053301-3-4, Figs.1(a),2(a),3(a): substantial residual excitation A, near-ground return B, near-excited endpoint C. |
+| O2, I2, M3, M4 | Peng et al. (2023), article p.053301-3, Fig.1(b,c), low-order insets and adjacent Rayleigh/Raman paragraph: state-preserving harmonics, shifted state-changing structures and broad high-order ground-final dominance with nontrivial coherence mixing. Functional spectral equivalents remain accepted, not a compulsory author window. |
+| O3, I3, M5 | Peng et al. (2023), article p.053301-4, Fig.2(a,b), Eq.(10) discussion: near-ground endpoint realizes coherent ground-final and incoherent excited-final channels. For O3 the same object also covers A via Fig.1(c) and C via Fig.3(b). |
+| I4, M6 | Peng et al. (2023), article p.053301-4, Fig.3(a,b): near-excited endpoint reverses channel realization and canonical high-order coherent/incoherent balance relative to Fig.2. Another genuinely discriminating common spectral domain is accepted. |
+| M7, M8 | Peng et al. (2023), article pp.053301-2-4, Eq.(10), Figs.2-3 and final-transition sensitivity discussion: drive controls endpoint-unitary remixing. Cross-case explanation requires candidate radiation evidence, not endpoint populations alone. |
+| V1, V2 | Peng et al. (2023), article pp.053301-1-2, first-order emitted-field coupling discussion and Eqs.(3)-(10); task pre-prefactor and three-drive domain. Alternative tests are risk-triggered task/evaluation duties, not source-specific plotting requirements. |
+
+## Formula and convention notes
+
+For F2-F4/M1/M7-M8, article p.053301-2, Eqs.(5),(8),(10), let $\bar{\mathbf d}=(\bar d_{gg},\bar d_{eg})^T$ be the final-bare-state amplitudes and $U_f=U_a(t_f,0)$. Then
+$$\mathbf d=U_f^\dagger\bar{\mathbf d},\qquad
+S_{\rm tot}=\|\bar{\mathbf d}\|^2=|d_{\rm coh}|^2+|d_{\rm inc}|^2.$$
+If $r$ is the normalized coherent projection row of $U_f^\dagger$, then $d_{\rm coh}=r\bar{\mathbf d}$ and $S_{\rm inc}=\|\bar{\mathbf d}\|^2-|r\bar{\mathbf d}|^2\ge0$. This is an equivalent representation only when common final-state complex amplitudes, complete two-dimensional endpoint space, normalized projection and frequencywise common object are established; a stored second complex row is not compulsory. The same algebra does not supply candidate identification or drive-control reasoning. Canonical broad high-order B/C reversal is not the sole acceptable spectral domain, but a claim about the full strong-field spectrum cannot evade material high-order response by selecting a fundamental-dominated display.
+
+## Scope of the source anchors
+
+The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.

cases/case04/task.md

@@ -0,0 +1,113 @@
+# Quantum radiation from a strongly driven two-level system
+
+## Background
+
+A strongly driven two-level emitter can radiate while ending in either of its
+bare states. The same radiation may also be discussed in terms of the part
+that is phase coherent across an ensemble of identical emitters and the part
+associated with quantum fluctuations. These are different physical
+resolutions of one emitted state. Their relation under strong driving is the
+object of this task.
+
+## Research problem
+
+Develop a quantum-optical calculation that resolves the radiation from the
+driven two-level system both by the emitter's final state and by radiation
+coherence. Determine how the two descriptions are related and whether, and if
+so how, their relationship can be controlled by changing the driving strength.
+
+The derivation, numerical construction, choice of scientific evidence and
+organization of the argument are yours. Establish the conclusion from your
+calculation rather than assuming a fixed correspondence between the two
+descriptions.
+
+## Physical inputs
+
+The emitter has bare states $|g\rangle$ and $|e\rangle$, energy separation
+$\hbar\omega_a$, and only the off-diagonal electric-dipole matrix element
+$\Omega=\langle e|\hat d|g\rangle$ (with its conjugate). It starts in
+$|g\rangle$. The quantized radiation modes start in vacuum.
+
+Treat the classical drive nonperturbatively. Its electric field is
+
+$$
+E_L(t)=E_0\sin^2\!\left(\frac{\omega_0t}{2N_c}\right)
+\sin(\omega_0t),
+\qquad 0\le t\le \frac{2\pi N_c}{\omega_0},
+$$
+
+and is zero outside this interval. Use the same sine-squared envelope as the
+turn-on and turn-off factor in the coupling to the quantized radiation modes.
+Treat that coupling to first order; reabsorption and higher orders in the
+emitted field are outside the task.
+
+Use
+
+$$
+\omega_0=\frac{\omega_a}{7},\qquad N_c=20,
+$$
+
+and the following cases:
+
+| Case | $E_0|\Omega|/\omega_0$ |
+|---|---:|
+| A | 11.23 |
+| B | 13.21 |
+| C | 13.87 |
+
+You may set $\hbar=\omega_a=|\Omega|=1$ or use another consistent unit
+system. State all phase, Fourier and basis conventions.
+
+The graded spectral object is the squared modulus of the first-order emission
+amplitude before any optional frequency-dependent radiative,
+density-of-modes or detector prefactor. Declare any constant normalization
+used in a comparison; absolute spectral magnitude is not a grading target.
+
+## Method boundary
+
+Use standard two-level dynamics and first-order quantum-optical emission
+theory. You must derive the task-specific quantities used to resolve the two
+descriptions and their relationship. No particular propagator, quadrature,
+grid, transform implementation, plotting layout or validation procedure is
+prescribed.
+
+You are responsible for checking that the computed evidence is sufficiently
+reliable and reproducible for the claims made. A state or spectral comparison
+must be backed by reconstructible numerical data from the corresponding case.
+
+## Submission
+
+Submit one self-contained scientific report and an offline reproduction
+package containing the derivation, executable code, numerical data underlying
+the reported emitter-state and radiation-coherence evidence, references
+actually used, and concise run and environment information. The choice and
+number of figures are yours. No fixed file tree, filename scheme, exploratory
+history or examiner-selected validation sequence is required.
+
+Include a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge.
+
+The active examination resources and limits are defined in the companion
+`resource_limits.json`. All retained production calculations must run
+within that fixed allocation and active wall time. More expensive modelling
+does not receive additional credit.
+
+## Reference and integrity policy
+
+This examination is conducted without network access or live literature
+retrieval. You may rely on your existing general scientific knowledge and, if any are
+explicitly supplied with the examination, on those offline materials or
+software documentation. Record every such source actually consulted. For formulas,
+methods, constants, or conventions used from general knowledge rather than a
+consulted source, state enough of the method basis, definition, value, units,
+and convention to make the calculation auditable; do not invent a citation.
+You are not required to identify or prove a publication date or to retrieve
+literature during the examination.
+
+The hidden target article and its identifying metadata, figures or captions,
+supplementary material, author code or data, target-specific reproduction
+code, solution or scoring material, online solutions, and worked
+reproductions of this case must not be used. All submitted scientific figures
+and numerical data must be generated by your own implementation of the stated
+problem.
+
+See [submission requirements](../../submission_requirements.md) for the common submission entry points.

cases/case05/grading_rubric.json

@@ -0,0 +1,597 @@
+{
+  "case_id": "Case05",
+  "title": "Case05 — High-Harmonic Generation in Solids with and without Topological Edge States",
+  "atoms": [
+    {
+      "criterion_id": "F1",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Establish the specified N=100, soft-core, spin-neutral continuous-space x-only LSD model and fixed M/D+/D- geometries; an SSH/tight-binding replacement is not equivalent.",
+      "award_conditions": [
+        "The model is the N=100 spin-neutral continuous-space soft-core x-only LSD chain at the fixed M/D+/D- geometries, not SSH/tight binding."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F2, F3, F4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article p.177401-2, Eqs.(1)-(6): soft-core continuous-space x-only LSD chain, spin-neutral occupation and fixed dimerized geometries; not a tight-binding replacement."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F2",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Construct finite-chain stationary analysis capable of distinguishing metal, insulating manifolds and edge-localized states from the continuous-space calculation rather than assigning labels from the sign of delta.",
+      "award_conditions": [
+        "The finite-chain stationary calculation can distinguish metallic/insulating manifolds and localize edge states without assigning physics solely from the sign of distortion."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F1, O1, I1, M1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-2-3, Fig.1(b-d), Eq.(6) and edge-state paragraph: half-filled metal, dimerized insulators and an in-gap edge pair with only its lower member occupied. Fig.1(a) exact energy minima are not compulsory targets."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F3",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Construct the specified driven dynamics from the corresponding occupied stationary orbitals and the spin-summed total-dipole spectrum. A current/acceleration representation requires its relation and frequency weighting to that object.",
+      "award_conditions": [
+        "Driven dynamics starts from the appropriate occupied stationary orbitals and yields the coherent spin-summed total-dipole spectrum; derivative forms explicitly account for frequency weights."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F1, F4, O2, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article p.177401-3, Eqs.(7),(8): driven KS orbitals, spin-summed coherent total dipole and squared Fourier modulus; current/acceleration variants require omega^2/omega^4 weighting."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F4",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Consistently use units, specified field, Fourier convention, orbital occupation and one common constant spectral scale across M/D+/D- and dynamical comparisons.",
+      "award_conditions": [
+        "Field, units, Fourier convention, occupation and one common constant spectral scale remain consistent across all phase and dynamical comparisons."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F3, O2, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article p.177401-3, Eqs.(7),(8): driven KS orbitals, spin-summed coherent total dipole and squared Fourier modulus; current/acceleration variants require omega^2/omega^4 weighting."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "O1",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present reconstructible stationary evidence distinguishing M from both insulators and establishing D-'s in-gap pair, occupation and edge localization relative to D+.",
+      "award_conditions": [
+        "Reconstructible stationary evidence distinguishes metal and insulators and establishes the D- in-gap pair, its occupation and edge localization relative to D+.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F1, F2, I1, M1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-2-3, Fig.1(b-d), Eq.(6) and edge-state paragraph: half-filled metal, dimerized insulators and an in-gap edge pair with only its lower member occupied. Fig.1(a) exact energy minima are not compulsory targets."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O2",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present correct common-scale spin-summed total-dipole HHG spectra for M, D+ and D-, making sub-gap relative strength and case ordering assessable.",
+      "award_conditions": [
+        "Common-scale total-dipole spectra for M/D+/D- expose correct material sub-gap ordering and the large insulating contrast.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F3 (Construct the specified driven dynamics from the corresponding occupied stationary orbitals and the spin-summed total-dipole spectrum. A current/acceleration representation requires its relation and frequency weighting to that object.)",
+        "Preserve independently valid work in F4, O3, I2, M2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and sub-gap discussion: large D- (source phase B) / D+ (source phase A) contrast on common scale; exact 14-order magnitude or colors are not targets."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O3",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present a valid comparison/intervention showing that evolving internal Kohn-Sham potential does not generate the D-/D+ sub-gap contrast and that M is more sensitive to that dynamics; full/frozen propagation is accepted but not mandatory.",
+      "award_conditions": [
+        "A valid causal comparison establishes robust insulating contrast and stronger metal sensitivity to evolving internal KS potential; a named full/frozen plot is not mandatory.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F3 (Construct the specified driven dynamics from the corresponding occupied stationary orbitals and the spin-summed total-dipole spectrum. A current/acceleration representation requires its relation and frequency weighting to that object.)",
+        "Preserve independently valid work in O2, O4, I3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and frozen-KS/screening paragraphs: insulating contrast survives frozen internal potential, while metal is much more sensitive. A functionally equivalent intervention is accepted."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O4",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present a candidate-designed calculation/control distinguishing edge occupation/incomplete coherent cancellation from gap-only, distortion-only or generic edge-state-presence explanations; no named canonical control is mandatory.",
+      "award_conditions": [
+        "A candidate-designed intervention distinguishes occupation/incomplete cancellation from at least one gap-only, distortion-only or generic edge-presence alternative.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in O2, O3, I4, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning \"The key question\": incoherent orbital powers versus coherent total distinguish cancellation. The same page, \"Topological vs other edge states\", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "I1",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify from the submitted stationary evidence metallic M, insulating D+/D-, and the occupied in-gap edge-state pair and end localization in D-.",
+      "award_conditions": [
+        "The candidate identifies metallic M, insulating D+/D- and D- occupied edge-pair/end localization in their stationary evidence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O1 (Present reconstructible stationary evidence distinguishing M from both insulators and establishing D-'s in-gap pair, occupation and edge localization relative to D+.)",
+        "Preserve independently valid work in F2, M1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-2-3, Fig.1(b-d), Eq.(6) and edge-state paragraph: half-filled metal, dimerized insulators and an in-gap edge pair with only its lower member occupied. Fig.1(a) exact energy minima are not compulsory targets."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I2",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify the correct common-scale sub-gap HHG case ordering and large D-/D+ contrast, without relying on absolute scale.",
+      "award_conditions": [
+        "The candidate identifies common-scale sub-gap case ordering and large D-/D+ contrast without relying on absolute yield."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O2 (Present correct common-scale spin-summed total-dipole HHG spectra for M, D+ and D-, making sub-gap relative strength and case ordering assessable.)",
+        "Preserve independently valid work in F4, M2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and sub-gap discussion: large D- (source phase B) / D+ (source phase A) contrast on common scale; exact 14-order magnitude or colors are not targets."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I3",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify from the causal comparison the robustness of the insulating contrast and stronger M sensitivity to the evolving self-consistent potential.",
+      "award_conditions": [
+        "The candidate identifies the robust insulating contrast and larger metal response to the evolving-potential intervention."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O3 (Present a valid comparison/intervention showing that evolving internal Kohn-Sham potential does not generate the D-/D+ sub-gap contrast and that M is more sensitive to that dynamics; full/frozen propagation is accepted but not mandatory.)",
+        "Preserve independently valid work in I2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and frozen-KS/screening paragraphs: insulating contrast survives frozen internal potential, while metal is much more sensitive. A functionally equivalent intervention is accepted."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I4",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify a concrete discriminating signal consistent with edge occupation and incomplete coherent cancellation and capable of distinguishing at least one alternative.",
+      "award_conditions": [
+        "The candidate identifies the actual discriminating control signal and the alternative it distinguishes."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O4 (Present a candidate-designed calculation/control distinguishing edge occupation/incomplete coherent cancellation from gap-only, distortion-only or generic edge-state-presence explanations; no named canonical control is mandatory.)",
+        "Preserve independently valid work in M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning \"The key question\": incoherent orbital powers versus coherent total distinguish cancellation. The same page, \"Topological vs other edge states\", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M1",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain finite-chain phase identities and the finite-chain/topological character of D- edge states using continuous-space evidence, not generic detached SSH language.",
+      "award_conditions": [
+        "Continuous-space finite-chain evidence supports phase/topological edge assignments; detached SSH terminology is insufficient."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (Construct finite-chain stationary analysis capable of distinguishing metal, insulating manifolds and edge-localized states from the continuous-space calculation rather than assigning labels from the sign of delta.); I1 (Identify from the submitted stationary evidence metallic M, insulating D+/D-, and the occupied in-gap edge-state pair and end localization in D-.)",
+        "Preserve independently valid work in F1, O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-2-3, Fig.1(b-d), Eq.(6) and edge-state paragraph: half-filled metal, dimerized insulators and an in-gap edge pair with only its lower member occupied. Fig.1(a) exact energy minima are not compulsory targets."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M2",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Infer how topology is encoded in the low-energy HHG response from the identified common-scale sub-gap ordering, limiting the conclusion to supported relative rather than absolute strength.",
+      "award_conditions": [
+        "The identified relative sub-gap HHG ordering supports the stated topology-sensitive inference without claiming absolute strength."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I2 (Identify the correct common-scale sub-gap HHG case ordering and large D-/D+ contrast, without relying on absolute scale.)",
+        "Preserve independently valid work in O2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and sub-gap discussion: large D- (source phase B) / D+ (source phase A) contrast on common scale; exact 14-order magnitude or colors are not targets."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M3",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use discriminating evidence to explain near-cancellation of strong individual-orbital radiation in the coherent fully occupied D+ valence total and incomplete cancellation in D-.",
+      "award_conditions": [
+        "Causal evidence connects strong individual orbital emission to near-cancellation in the filled D+ valence total and incomplete cancellation in D-."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I4 (Identify a concrete discriminating signal consistent with edge occupation and incomplete coherent cancellation and capable of distinguishing at least one alternative.)",
+        "Preserve independently valid work in M4, M5, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning \"The key question\": incoherent orbital powers versus coherent total distinguish cancellation. The same page, \"Topological vs other edge states\", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M4",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Connect half occupation of the D- in-gap edge pair to incomplete coherent cancellation and explain why an in-gap eigenvalue alone does not establish the mechanism.",
+      "award_conditions": [
+        "The half-occupied D- in-gap pair explains incomplete coherent cancellation; an in-gap eigenvalue alone is insufficient."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I4 (Identify a concrete discriminating signal consistent with edge occupation and incomplete coherent cancellation and capable of distinguishing at least one alternative.)",
+        "Preserve independently valid work in M3, M5, I1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning \"The key question\": incoherent orbital powers versus coherent total distinguish cancellation. The same page, \"Topological vs other edge states\", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M5",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explicitly reject at least one plausible gap-only, distortion-only or edge-state-presence-only alternative using the causal discriminating evidence.",
+      "award_conditions": [
+        "The candidate explicitly rejects at least one plausible alternative using their discriminating calculation rather than association alone."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I4 (Identify a concrete discriminating signal consistent with edge occupation and incomplete coherent cancellation and capable of distinguishing at least one alternative.)",
+        "Preserve independently valid work in M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning \"The key question\": incoherent orbital powers versus coherent total distinguish cancellation. The same page, \"Topological vs other edge states\", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M6",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use the identified ordering and intervention sensitivity to distinguish robust D-/D+ insulating contrast from stronger M sensitivity to the evolving self-consistent potential.",
+      "award_conditions": [
+        "The causal comparison separates the robust insulating contrast from stronger metallic sensitivity to time-dependent screening/internal potential."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I2 (Identify the correct common-scale sub-gap HHG case ordering and large D-/D+ contrast, without relying on absolute scale.); I3 (Identify from the causal comparison the robustness of the insulating contrast and stronger M sensitivity to the evolving self-consistent potential.)",
+        "Preserve independently valid work in O2, O3, M2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and frozen-KS/screening paragraphs: insulating contrast survives frozen internal potential, while metal is much more sensitive. A functionally equivalent intervention is accepted."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M7",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Bound the conclusion to the specified finite-chain continuous-space x-only LSD model, honestly handling known energy-curve differences or unresolved numerical features without manufacturing certainty or demanding exact source-curve reproduction.",
+      "award_conditions": [
+        "The conclusion remains within the specified finite-chain x-only LSD model and handles energy-curve uncertainty honestly without demanding exact source minima."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in M1, M2, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-2-4, model equations and conclusion delimit finite-chain mean-field scope. Exact Fig.1(a) energy-curve reproduction is excluded by the task/effective rubric because its printed-functional reproduction remains unresolved; risk validation is task-defined."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V1",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Only when the model, transform/rescaling, occupation control or claim creates a concrete material risk to the central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.",
+      "award_conditions": [
+        "Only a concrete material risk in the model, transform, occupation intervention or claim requires discriminating validation; otherwise N/A."
+      ],
+      "applicability_and_na": [
+        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
+        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F1, F2, F3, F4, O1, O2, O3, O4, I1, I2, I3, I4, M1, M2, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.",
+        "Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.",
+        "A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations."
+      ],
+      "source_support": [
+        "Bauer and Hansen (2018), article pp.177401-2-4, model equations and conclusion delimit finite-chain mean-field scope. Exact Fig.1(a) energy-curve reproduction is excluded by the task/effective rubric because its printed-functional reproduction remains unresolved; risk validation is task-defined."
+      ],
+      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    }
+  ],
+  "case_scientific_rules": [
+    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
+    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
+    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
+    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
+    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
+    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
+    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
+    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
+    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
+    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
+    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
+    "Use the source-stated +0.265 and -0.165 geometries for driven/stationary comparisons. An optional energy scan may establish converged dimerization-lowered two-basin structure and undistorted instability, but exact minima, well depths, barrier, curvature and pixels are excluded anchors.",
+    "The unresolved published energy-curve detail does not invalidate the source-fixed-geometry driven analysis and does not determine RC. Do not tune unconverged conventions to imitate it.",
+    "Changing occupation can redefine the physical target. Mere edge-state presence, a gap or a stationary association does not establish the causal occupation/interference explanation.",
+    "For the stated continuous-space x-only LSD model, the undimerized finite chain is a half-filled metal. Both nonzero shifts dimerize the chain and open an insulating gap. D- has an almost-degenerate in-gap edge-state pair with only the lower state occupied; the occupied edge state is localized near the chain ends and broad in momentum. D+ lacks this half-occupied in-gap pair.",
+    "The Hanning-windowed total-dipole spectra support these central anchors:",
+    "below the D+ valence-to-first-conduction gap, D- emits many orders of magnitude more strongly than D+; D+ retains chiefly low odd harmonics;",
+    "the large D-/D+ contrast persists when the internal KS potential is frozen, so it is not created by the time dependence of the mean-field potential;",
+    "the metallic M case changes much more between full and frozen propagation, consistent with screening by the time-dependent metallic density;",
+    "individual occupied orbitals emit strongly in the sub-gap range, but their coherent total nearly cancels for the fully occupied D+ valence manifold. The half-occupied edge-state pair in D- makes the cancellation incomplete.",
+    "The source's canonical discriminating evidence is the comparison between the true coherent total spectrum and an incoherent sum of individual-orbital spectra. Supplemental controls using nontopological impurity edge states and a virtual electron occupying the second D- edge state support the same occupation/interference mechanism. Students need not reproduce a named control, but high mechanism credit requires evidence with equivalent causal discrimination; the presence of an edge-state eigenvalue alone is insufficient.",
+    "the task fixes $+0.265$ and $-0.165$ only as source-stated geometries for the stationary and driven comparison;",
+    "an energy scan is optional supporting evidence, not a hidden required output;",
+    "if submitted, grade only a converged dimerization-lowered two-basin structure and the instability of the undistorted case;",
+    "never grade the exact source minima, relative well depth, central maximum, curvature or pixel similarity;",
+    "do not tune an unconverged numerical convention to imitate the published curve.",
+    "The task fixes the physical chain, geometries and total-dipole spectral class, not full/frozen branches, a particular window, a ground-state plot list or one mechanism diagnostic. Accept momentum-resolved stationary maps, real-space edge-state localization, projectors, spectral functions or equivalent stationary evidence by function. Accept the canonical full/frozen comparison or another intervention only when it genuinely tests the role of the evolving internal potential. Accept an incoherent-sum comparison, controlled edge occupation, impurity control, orbital-removal test or another intervention for the cancellation evidence/mechanism only when it genuinely distinguishes the competing physical explanations.",
+    "Do not accept an SSH result as equivalent to the specified interacting continuous-space model. Do not grade source colours, crops, arrows, exact energy-curve shape, absolute HHG magnitude or a fixed number of figures. Charge an upstream numerical defect first to the physical output evidence it damages; A dependent scientific inference loses credit only when the same defect makes the inference false or unsupported.",
+    "For F1/F3-F4/M3-M4, article pp.177401-2-4, Eqs.(3),(4),(8) and Fig.3, the spin densities and internal potential obey\n$$n_\\sigma(x,t)=\\sum_{i\\in\\mathrm{occ}}|\\varphi_{\\sigma i}(x,t)|^2,\\quad\nu[n](x,t)=\\int\\frac{n(x',t)dx'}{\\sqrt{(x-x')^2+1}},\\quad\nv_{x,\\sigma}=-[6n_\\sigma/\\pi]^{1/3}.$$\nThe coherent observable is\n$$X(t)=\\sum_{i,\\sigma}\\int x|\\varphi_{\\sigma i}(x,t)|^2dx,\\qquad\nS_D(\\Omega)\\propto|\\mathcal F[wX](\\Omega)|^2,$$\nnot $\\sum_{i,\\sigma}|\\mathcal F[wx_{\\sigma i}]|^2$. The latter is an optional cancellation diagnostic. Derivative-form spectra differ by $\\Omega^2$ or $\\Omega^4$ when transform/window boundary terms are controlled. Frozen-KS comparison freezes the internal Hartree/exchange potential at its stationary value, not the external laser coupling.\n\nThe continuous-space orbital equation is $i\\partial_t\\varphi_{\\sigma i}=[-\\partial_x^2/2+v_{\\rm ion}(x)-iA(t)\\partial_x+u[n]+v_{x,\\sigma}]\\varphi_{\\sigma i}$, with $v_{\\rm ion}(x)=-\\sum_j[(x-x_j)^2+1]^{-1/2}$ and $x_j=(j-(N+1)/2)a-(-1)^j\\delta$. This is the x-only LSD velocity-gauge convention of source Eqs.(1)-(6); a common time-dependent scalar A-squared phase does not change the graded density/dipole."
+  ],
+  "closure_requirements": {
+    "RC0": [
+      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
+      "Required indispensable claim CL1, central physical object: all of: F1 (Establish the specified N=100, soft-core, spin-neutral continuous-space x-only LSD model and fixed M/D+/D- geometries; an SSH/tight-binding replacement is not equivalent.); F2 (Construct finite-chain stationary analysis capable of distinguishing metal, insulating manifolds and edge-localized states from the continuous-space calculation rather than assigning labels from the sign of delta.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required indispensable claim CL2, central physical object: all of: F3 (Construct the specified driven dynamics from the corresponding occupied stationary orbitals and the spin-summed total-dipole spectrum. A current/acceleration representation requires its relation and frequency weighting to that object.); F4 (Consistently use units, specified field, Fourier convention, orbital occupation and one common constant spectral scale across M/D+/D- and dynamical comparisons.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC1": [
+      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
+      "Required indispensable claim CL1, indispensable material component: O1 (Present reconstructible stationary evidence distinguishing M from both insulators and establishing D-'s in-gap pair, occupation and edge localization relative to D+.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required indispensable claim CL2, indispensable material component: all of: O2 (Present correct common-scale spin-summed total-dipole HHG spectra for M, D+ and D-, making sub-gap relative strength and case ordering assessable.); O3 (Present a valid comparison/intervention showing that evolving internal Kohn-Sham potential does not generate the D-/D+ sub-gap contrast and that M is more sensitive to that dynamics; full/frozen propagation is accepted but not mandatory.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL3, indispensable material component: O4 (Present a candidate-designed calculation/control distinguishing edge occupation/incomplete coherent cancellation from gap-only, distortion-only or generic edge-state-presence explanations; no named canonical control is mandatory.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC2": [
+      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
+      "Required indispensable claim CL1, principal mechanism or commissioned conclusion: M1 (Explain finite-chain phase identities and the finite-chain/topological character of D- edge states using continuous-space evidence, not generic detached SSH language.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required indispensable claim CL2, principal mechanism or commissioned conclusion: all of: M2 (Infer how topology is encoded in the low-energy HHG response from the identified common-scale sub-gap ordering, limiting the conclusion to supported relative rather than absolute strength.); M6 (Use the identified ordering and intervention sensitivity to distinguish robust D-/D+ insulating contrast from stronger M sensitivity to the evolving self-consistent potential.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL3, principal mechanism or commissioned conclusion: all of: M3 (Use discriminating evidence to explain near-cancellation of strong individual-orbital radiation in the coherent fully occupied D+ valence total and incomplete cancellation in D-.); M4 (Connect half occupation of the D- in-gap edge pair to incomplete coherent cancellation and explain why an in-gap eigenvalue alone does not establish the mechanism.); M5 (Explicitly reject at least one plausible gap-only, distortion-only or edge-state-presence-only alternative using the causal discriminating evidence.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL4, principal mechanism or commissioned conclusion: M7 (Bound the conclusion to the specified finite-chain continuous-space x-only LSD model, honestly handling known energy-curve differences or unresolved numerical features without manufacturing certainty or demanding exact source-curve reproduction.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC3": [
+      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
+      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
+      "Required co primary claim CL3, material validation/scope: V1 (Only when the model, transform/rescaling, occupation control or claim creates a concrete material risk to the central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC4": [
+      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
+      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
+      "Close CL1 central physical object: all of: F1 (Establish the specified N=100, soft-core, spin-neutral continuous-space x-only LSD model and fixed M/D+/D- geometries; an SSH/tight-binding replacement is not equivalent.); F2 (Construct finite-chain stationary analysis capable of distinguishing metal, insulating manifolds and edge-localized states from the continuous-space calculation rather than assigning labels from the sign of delta.).",
+      "Close CL1 indispensable material component: O1 (Present reconstructible stationary evidence distinguishing M from both insulators and establishing D-'s in-gap pair, occupation and edge localization relative to D+.).",
+      "Close CL1 principal mechanism or commissioned conclusion: M1 (Explain finite-chain phase identities and the finite-chain/topological character of D- edge states using continuous-space evidence, not generic detached SSH language.).",
+      "Close CL2 central physical object: all of: F3 (Construct the specified driven dynamics from the corresponding occupied stationary orbitals and the spin-summed total-dipole spectrum. A current/acceleration representation requires its relation and frequency weighting to that object.); F4 (Consistently use units, specified field, Fourier convention, orbital occupation and one common constant spectral scale across M/D+/D- and dynamical comparisons.).",
+      "Close CL2 indispensable material component: all of: O2 (Present correct common-scale spin-summed total-dipole HHG spectra for M, D+ and D-, making sub-gap relative strength and case ordering assessable.); O3 (Present a valid comparison/intervention showing that evolving internal Kohn-Sham potential does not generate the D-/D+ sub-gap contrast and that M is more sensitive to that dynamics; full/frozen propagation is accepted but not mandatory.).",
+      "Close CL2 principal mechanism or commissioned conclusion: all of: M2 (Infer how topology is encoded in the low-energy HHG response from the identified common-scale sub-gap ordering, limiting the conclusion to supported relative rather than absolute strength.); M6 (Use the identified ordering and intervention sensitivity to distinguish robust D-/D+ insulating contrast from stronger M sensitivity to the evolving self-consistent potential.).",
+      "Close CL3 indispensable material component: O4 (Present a candidate-designed calculation/control distinguishing edge occupation/incomplete coherent cancellation from gap-only, distortion-only or generic edge-state-presence explanations; no named canonical control is mandatory.).",
+      "Close CL3 principal mechanism or commissioned conclusion: all of: M3 (Use discriminating evidence to explain near-cancellation of strong individual-orbital radiation in the coherent fully occupied D+ valence total and incomplete cancellation in D-.); M4 (Connect half occupation of the D- in-gap edge pair to incomplete coherent cancellation and explain why an in-gap eigenvalue alone does not establish the mechanism.); M5 (Explicitly reject at least one plausible gap-only, distortion-only or edge-state-presence-only alternative using the causal discriminating evidence.).",
+      "Close CL3 material validation/scope: V1 (Only when the model, transform/rescaling, occupation control or claim creates a concrete material risk to the central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.).",
+      "Close CL4 principal mechanism or commissioned conclusion: M7 (Bound the conclusion to the specified finite-chain continuous-space x-only LSD model, honestly handling known energy-curve differences or unresolved numerical features without manufacturing certainty or demanding exact source-curve reproduction.)."
+    ]
+  },
+  "references": [
+    {
+      "citation": "Dieter Bauer and Kenneth K. Hansen. 2018. *High-Harmonic Generation in Solids with and without Topological Edge States*. *Physical Review Letters*, 120, 177401.",
+      "url": "https://doi.org/10.1103/PhysRevLett.120.177401",
+      "scientific_scope": "High-Harmonic Generation in Solids with and without Topological Edge States",
+      "anchors": [
+        "Bauer and Hansen (2018), article p.177401-2, Eqs.(1)-(6): soft-core continuous-space x-only LSD chain, spin-neutral occupation and fixed dimerized geometries; not a tight-binding replacement.",
+        "Bauer and Hansen (2018), article pp.177401-2-3, Fig.1(b-d), Eq.(6) and edge-state paragraph: half-filled metal, dimerized insulators and an in-gap edge pair with only its lower member occupied. Fig.1(a) exact energy minima are not compulsory targets.",
+        "Bauer and Hansen (2018), article p.177401-3, Eqs.(7),(8): driven KS orbitals, spin-summed coherent total dipole and squared Fourier modulus; current/acceleration variants require omega^2/omega^4 weighting.",
+        "Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and sub-gap discussion: large D- (source phase B) / D+ (source phase A) contrast on common scale; exact 14-order magnitude or colors are not targets.",
+        "Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and frozen-KS/screening paragraphs: insulating contrast survives frozen internal potential, while metal is much more sensitive. A functionally equivalent intervention is accepted.",
+        "Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning \"The key question\": incoherent orbital powers versus coherent total distinguish cancellation. The same page, \"Topological vs other edge states\", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples.",
+        "Bauer and Hansen (2018), article pp.177401-2-4, model equations and conclusion delimit finite-chain mean-field scope. Exact Fig.1(a) energy-curve reproduction is excluded by the task/effective rubric because its printed-functional reproduction remains unresolved; risk validation is task-defined."
+      ]
+    }
+  ]
+}

cases/case05/grading_rubric.md

@@ -0,0 +1,872 @@
+# Grading Rubric — Case05
+
+Case05 — High-Harmonic Generation in Solids with and without Topological Edge States
+
+## Atomic Scoring Criteria
+
+Each criterion awards 0 or 0.5 points, for a maximum of 10. Explicit N/A rules apply where stated.
+
+### F1 — F — 0.5 points
+
+**Scientific requirement**
+
+Establish the specified N=100, soft-core, spin-neutral continuous-space x-only LSD model and fixed M/D+/D- geometries; an SSH/tight-binding replacement is not equivalent.
+
+**Conditions for credit**
+
+- The model is the N=100 spin-neutral continuous-space soft-core x-only LSD chain at the fixed M/D+/D- geometries, not SSH/tight binding.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F2, F3, F4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article p.177401-2, Eqs.(1)-(6): soft-core continuous-space x-only LSD chain, spin-neutral occupation and fixed dimerized geometries; not a tight-binding replacement.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F2 — F — 0.5 points
+
+**Scientific requirement**
+
+Construct finite-chain stationary analysis capable of distinguishing metal, insulating manifolds and edge-localized states from the continuous-space calculation rather than assigning labels from the sign of delta.
+
+**Conditions for credit**
+
+- The finite-chain stationary calculation can distinguish metallic/insulating manifolds and localize edge states without assigning physics solely from the sign of distortion.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F1, O1, I1, M1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-2-3, Fig.1(b-d), Eq.(6) and edge-state paragraph: half-filled metal, dimerized insulators and an in-gap edge pair with only its lower member occupied. Fig.1(a) exact energy minima are not compulsory targets.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F3 — F — 0.5 points
+
+**Scientific requirement**
+
+Construct the specified driven dynamics from the corresponding occupied stationary orbitals and the spin-summed total-dipole spectrum. A current/acceleration representation requires its relation and frequency weighting to that object.
+
+**Conditions for credit**
+
+- Driven dynamics starts from the appropriate occupied stationary orbitals and yields the coherent spin-summed total-dipole spectrum; derivative forms explicitly account for frequency weights.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F1, F4, O2, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article p.177401-3, Eqs.(7),(8): driven KS orbitals, spin-summed coherent total dipole and squared Fourier modulus; current/acceleration variants require omega^2/omega^4 weighting.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F4 — F — 0.5 points
+
+**Scientific requirement**
+
+Consistently use units, specified field, Fourier convention, orbital occupation and one common constant spectral scale across M/D+/D- and dynamical comparisons.
+
+**Conditions for credit**
+
+- Field, units, Fourier convention, occupation and one common constant spectral scale remain consistent across all phase and dynamical comparisons.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F3, O2, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article p.177401-3, Eqs.(7),(8): driven KS orbitals, spin-summed coherent total dipole and squared Fourier modulus; current/acceleration variants require omega^2/omega^4 weighting.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### O1 — O — 0.5 points
+
+**Scientific requirement**
+
+Present reconstructible stationary evidence distinguishing M from both insulators and establishing D-'s in-gap pair, occupation and edge localization relative to D+.
+
+**Conditions for credit**
+
+- Reconstructible stationary evidence distinguishes metal and insulators and establishes the D- in-gap pair, its occupation and edge localization relative to D+.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F1, F2, I1, M1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-2-3, Fig.1(b-d), Eq.(6) and edge-state paragraph: half-filled metal, dimerized insulators and an in-gap edge pair with only its lower member occupied. Fig.1(a) exact energy minima are not compulsory targets.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O2 — O — 0.5 points
+
+**Scientific requirement**
+
+Present correct common-scale spin-summed total-dipole HHG spectra for M, D+ and D-, making sub-gap relative strength and case ordering assessable.
+
+**Conditions for credit**
+
+- Common-scale total-dipole spectra for M/D+/D- expose correct material sub-gap ordering and the large insulating contrast.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F3 (Construct the specified driven dynamics from the corresponding occupied stationary orbitals and the spin-summed total-dipole spectrum. A current/acceleration representation requires its relation and frequency weighting to that object.)
+
+- Preserve independently valid work in F4, O3, I2, M2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and sub-gap discussion: large D- (source phase B) / D+ (source phase A) contrast on common scale; exact 14-order magnitude or colors are not targets.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O3 — O — 0.5 points
+
+**Scientific requirement**
+
+Present a valid comparison/intervention showing that evolving internal Kohn-Sham potential does not generate the D-/D+ sub-gap contrast and that M is more sensitive to that dynamics; full/frozen propagation is accepted but not mandatory.
+
+**Conditions for credit**
+
+- A valid causal comparison establishes robust insulating contrast and stronger metal sensitivity to evolving internal KS potential; a named full/frozen plot is not mandatory.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F3 (Construct the specified driven dynamics from the corresponding occupied stationary orbitals and the spin-summed total-dipole spectrum. A current/acceleration representation requires its relation and frequency weighting to that object.)
+
+- Preserve independently valid work in O2, O4, I3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and frozen-KS/screening paragraphs: insulating contrast survives frozen internal potential, while metal is much more sensitive. A functionally equivalent intervention is accepted.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O4 — O — 0.5 points
+
+**Scientific requirement**
+
+Present a candidate-designed calculation/control distinguishing edge occupation/incomplete coherent cancellation from gap-only, distortion-only or generic edge-state-presence explanations; no named canonical control is mandatory.
+
+**Conditions for credit**
+
+- A candidate-designed intervention distinguishes occupation/incomplete cancellation from at least one gap-only, distortion-only or generic edge-presence alternative.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in O2, O3, I4, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning "The key question": incoherent orbital powers versus coherent total distinguish cancellation. The same page, "Topological vs other edge states", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### I1 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify from the submitted stationary evidence metallic M, insulating D+/D-, and the occupied in-gap edge-state pair and end localization in D-.
+
+**Conditions for credit**
+
+- The candidate identifies metallic M, insulating D+/D- and D- occupied edge-pair/end localization in their stationary evidence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O1 (Present reconstructible stationary evidence distinguishing M from both insulators and establishing D-'s in-gap pair, occupation and edge localization relative to D+.)
+
+- Preserve independently valid work in F2, M1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-2-3, Fig.1(b-d), Eq.(6) and edge-state paragraph: half-filled metal, dimerized insulators and an in-gap edge pair with only its lower member occupied. Fig.1(a) exact energy minima are not compulsory targets.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I2 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify the correct common-scale sub-gap HHG case ordering and large D-/D+ contrast, without relying on absolute scale.
+
+**Conditions for credit**
+
+- The candidate identifies common-scale sub-gap case ordering and large D-/D+ contrast without relying on absolute yield.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O2 (Present correct common-scale spin-summed total-dipole HHG spectra for M, D+ and D-, making sub-gap relative strength and case ordering assessable.)
+
+- Preserve independently valid work in F4, M2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and sub-gap discussion: large D- (source phase B) / D+ (source phase A) contrast on common scale; exact 14-order magnitude or colors are not targets.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I3 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify from the causal comparison the robustness of the insulating contrast and stronger M sensitivity to the evolving self-consistent potential.
+
+**Conditions for credit**
+
+- The candidate identifies the robust insulating contrast and larger metal response to the evolving-potential intervention.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O3 (Present a valid comparison/intervention showing that evolving internal Kohn-Sham potential does not generate the D-/D+ sub-gap contrast and that M is more sensitive to that dynamics; full/frozen propagation is accepted but not mandatory.)
+
+- Preserve independently valid work in I2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and frozen-KS/screening paragraphs: insulating contrast survives frozen internal potential, while metal is much more sensitive. A functionally equivalent intervention is accepted.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I4 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify a concrete discriminating signal consistent with edge occupation and incomplete coherent cancellation and capable of distinguishing at least one alternative.
+
+**Conditions for credit**
+
+- The candidate identifies the actual discriminating control signal and the alternative it distinguishes.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O4 (Present a candidate-designed calculation/control distinguishing edge occupation/incomplete coherent cancellation from gap-only, distortion-only or generic edge-state-presence explanations; no named canonical control is mandatory.)
+
+- Preserve independently valid work in M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning "The key question": incoherent orbital powers versus coherent total distinguish cancellation. The same page, "Topological vs other edge states", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M1 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain finite-chain phase identities and the finite-chain/topological character of D- edge states using continuous-space evidence, not generic detached SSH language.
+
+**Conditions for credit**
+
+- Continuous-space finite-chain evidence supports phase/topological edge assignments; detached SSH terminology is insufficient.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (Construct finite-chain stationary analysis capable of distinguishing metal, insulating manifolds and edge-localized states from the continuous-space calculation rather than assigning labels from the sign of delta.); I1 (Identify from the submitted stationary evidence metallic M, insulating D+/D-, and the occupied in-gap edge-state pair and end localization in D-.)
+
+- Preserve independently valid work in F1, O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-2-3, Fig.1(b-d), Eq.(6) and edge-state paragraph: half-filled metal, dimerized insulators and an in-gap edge pair with only its lower member occupied. Fig.1(a) exact energy minima are not compulsory targets.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M2 — M — 0.5 points
+
+**Scientific requirement**
+
+Infer how topology is encoded in the low-energy HHG response from the identified common-scale sub-gap ordering, limiting the conclusion to supported relative rather than absolute strength.
+
+**Conditions for credit**
+
+- The identified relative sub-gap HHG ordering supports the stated topology-sensitive inference without claiming absolute strength.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I2 (Identify the correct common-scale sub-gap HHG case ordering and large D-/D+ contrast, without relying on absolute scale.)
+
+- Preserve independently valid work in O2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and sub-gap discussion: large D- (source phase B) / D+ (source phase A) contrast on common scale; exact 14-order magnitude or colors are not targets.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M3 — M — 0.5 points
+
+**Scientific requirement**
+
+Use discriminating evidence to explain near-cancellation of strong individual-orbital radiation in the coherent fully occupied D+ valence total and incomplete cancellation in D-.
+
+**Conditions for credit**
+
+- Causal evidence connects strong individual orbital emission to near-cancellation in the filled D+ valence total and incomplete cancellation in D-.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I4 (Identify a concrete discriminating signal consistent with edge occupation and incomplete coherent cancellation and capable of distinguishing at least one alternative.)
+
+- Preserve independently valid work in M4, M5, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning "The key question": incoherent orbital powers versus coherent total distinguish cancellation. The same page, "Topological vs other edge states", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M4 — M — 0.5 points
+
+**Scientific requirement**
+
+Connect half occupation of the D- in-gap edge pair to incomplete coherent cancellation and explain why an in-gap eigenvalue alone does not establish the mechanism.
+
+**Conditions for credit**
+
+- The half-occupied D- in-gap pair explains incomplete coherent cancellation; an in-gap eigenvalue alone is insufficient.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I4 (Identify a concrete discriminating signal consistent with edge occupation and incomplete coherent cancellation and capable of distinguishing at least one alternative.)
+
+- Preserve independently valid work in M3, M5, I1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning "The key question": incoherent orbital powers versus coherent total distinguish cancellation. The same page, "Topological vs other edge states", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M5 — M — 0.5 points
+
+**Scientific requirement**
+
+Explicitly reject at least one plausible gap-only, distortion-only or edge-state-presence-only alternative using the causal discriminating evidence.
+
+**Conditions for credit**
+
+- The candidate explicitly rejects at least one plausible alternative using their discriminating calculation rather than association alone.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I4 (Identify a concrete discriminating signal consistent with edge occupation and incomplete coherent cancellation and capable of distinguishing at least one alternative.)
+
+- Preserve independently valid work in M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning "The key question": incoherent orbital powers versus coherent total distinguish cancellation. The same page, "Topological vs other edge states", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M6 — M — 0.5 points
+
+**Scientific requirement**
+
+Use the identified ordering and intervention sensitivity to distinguish robust D-/D+ insulating contrast from stronger M sensitivity to the evolving self-consistent potential.
+
+**Conditions for credit**
+
+- The causal comparison separates the robust insulating contrast from stronger metallic sensitivity to time-dependent screening/internal potential.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: I2 (Identify the correct common-scale sub-gap HHG case ordering and large D-/D+ contrast, without relying on absolute scale.); I3 (Identify from the causal comparison the robustness of the insulating contrast and stronger M sensitivity to the evolving self-consistent potential.)
+
+- Preserve independently valid work in O2, O3, M2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and frozen-KS/screening paragraphs: insulating contrast survives frozen internal potential, while metal is much more sensitive. A functionally equivalent intervention is accepted.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M7 — M — 0.5 points
+
+**Scientific requirement**
+
+Bound the conclusion to the specified finite-chain continuous-space x-only LSD model, honestly handling known energy-curve differences or unresolved numerical features without manufacturing certainty or demanding exact source-curve reproduction.
+
+**Conditions for credit**
+
+- The conclusion remains within the specified finite-chain x-only LSD model and handles energy-curve uncertainty honestly without demanding exact source minima.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in M1, M2, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-2-4, model equations and conclusion delimit finite-chain mean-field scope. Exact Fig.1(a) energy-curve reproduction is excluded by the task/effective rubric because its printed-functional reproduction remains unresolved; risk validation is task-defined.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V1 — V — 0.5 points
+
+**Scientific requirement**
+
+Only when the model, transform/rescaling, occupation control or claim creates a concrete material risk to the central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.
+
+**Conditions for credit**
+
+- Only a concrete material risk in the model, transform, occupation intervention or claim requires discriminating validation; otherwise N/A.
+
+**Applicability and N/A**
+
+- Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.
+
+- If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F1, F2, F3, F4, O1, O2, O3, O4, I1, I2, I3, I4, M1, M2, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global orbital phases, momentum signs, Fourier conventions and one common constant spectrum scale are accepted after alignment. Current/acceleration spectra require a demonstrated relation and treatment of frequency weighting.
+
+- Stationary momentum maps, real-space localization, projectors, spectral functions or equivalent evidence are accepted by their ability to establish state and occupation identity.
+
+- A full/frozen comparison or any genuinely isolating intervention may test evolving internal potential. Incoherent-orbital-sum, controlled occupation, impurity, orbital-removal or equivalent interventions may test cancellation only when they distinguish the competing explanations.
+
+**Scientific source locations**
+
+- Bauer and Hansen (2018), article pp.177401-2-4, model equations and conclusion delimit finite-chain mean-field scope. Exact Fig.1(a) energy-curve reproduction is excluded by the task/effective rubric because its printed-functional reproduction remains unresolved; risk validation is task-defined.
+
+**Research Closure relation**
+
+Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+## Research Closure Requirements
+
+### RC0
+
+- The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.
+
+- Required indispensable claim CL1, central physical object: all of: F1 (Establish the specified N=100, soft-core, spin-neutral continuous-space x-only LSD model and fixed M/D+/D- geometries; an SSH/tight-binding replacement is not equivalent.); F2 (Construct finite-chain stationary analysis capable of distinguishing metal, insulating manifolds and edge-localized states from the continuous-space calculation rather than assigning labels from the sign of delta.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required indispensable claim CL2, central physical object: all of: F3 (Construct the specified driven dynamics from the corresponding occupied stationary orbitals and the spin-summed total-dipole spectrum. A current/acceleration representation requires its relation and frequency weighting to that object.); F4 (Consistently use units, specified field, Fourier convention, orbital occupation and one common constant spectral scale across M/D+/D- and dynamical comparisons.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC1
+
+- With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.
+
+- Required indispensable claim CL1, indispensable material component: O1 (Present reconstructible stationary evidence distinguishing M from both insulators and establishing D-'s in-gap pair, occupation and edge localization relative to D+.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required indispensable claim CL2, indispensable material component: all of: O2 (Present correct common-scale spin-summed total-dipole HHG spectra for M, D+ and D-, making sub-gap relative strength and case ordering assessable.); O3 (Present a valid comparison/intervention showing that evolving internal Kohn-Sham potential does not generate the D-/D+ sub-gap contrast and that M is more sensitive to that dynamics; full/frozen propagation is accepted but not mandatory.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL3, indispensable material component: O4 (Present a candidate-designed calculation/control distinguishing edge occupation/incomplete coherent cancellation from gap-only, distortion-only or generic edge-state-presence explanations; no named canonical control is mandatory.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC2
+
+- With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.
+
+- Required indispensable claim CL1, principal mechanism or commissioned conclusion: M1 (Explain finite-chain phase identities and the finite-chain/topological character of D- edge states using continuous-space evidence, not generic detached SSH language.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required indispensable claim CL2, principal mechanism or commissioned conclusion: all of: M2 (Infer how topology is encoded in the low-energy HHG response from the identified common-scale sub-gap ordering, limiting the conclusion to supported relative rather than absolute strength.); M6 (Use the identified ordering and intervention sensitivity to distinguish robust D-/D+ insulating contrast from stronger M sensitivity to the evolving self-consistent potential.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL3, principal mechanism or commissioned conclusion: all of: M3 (Use discriminating evidence to explain near-cancellation of strong individual-orbital radiation in the coherent fully occupied D+ valence total and incomplete cancellation in D-.); M4 (Connect half occupation of the D- in-gap edge pair to incomplete coherent cancellation and explain why an in-gap eigenvalue alone does not establish the mechanism.); M5 (Explicitly reject at least one plausible gap-only, distortion-only or edge-state-presence-only alternative using the causal discriminating evidence.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL4, principal mechanism or commissioned conclusion: M7 (Bound the conclusion to the specified finite-chain continuous-space x-only LSD model, honestly handling known energy-curve differences or unresolved numerical features without manufacturing certainty or demanding exact source-curve reproduction.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC3
+
+- With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.
+
+- Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.
+
+- Required co primary claim CL3, material validation/scope: V1 (Only when the model, transform/rescaling, occupation control or claim creates a concrete material risk to the central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC4
+
+- All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.
+
+- Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.
+
+- Close CL1 central physical object: all of: F1 (Establish the specified N=100, soft-core, spin-neutral continuous-space x-only LSD model and fixed M/D+/D- geometries; an SSH/tight-binding replacement is not equivalent.); F2 (Construct finite-chain stationary analysis capable of distinguishing metal, insulating manifolds and edge-localized states from the continuous-space calculation rather than assigning labels from the sign of delta.).
+
+- Close CL1 indispensable material component: O1 (Present reconstructible stationary evidence distinguishing M from both insulators and establishing D-'s in-gap pair, occupation and edge localization relative to D+.).
+
+- Close CL1 principal mechanism or commissioned conclusion: M1 (Explain finite-chain phase identities and the finite-chain/topological character of D- edge states using continuous-space evidence, not generic detached SSH language.).
+
+- Close CL2 central physical object: all of: F3 (Construct the specified driven dynamics from the corresponding occupied stationary orbitals and the spin-summed total-dipole spectrum. A current/acceleration representation requires its relation and frequency weighting to that object.); F4 (Consistently use units, specified field, Fourier convention, orbital occupation and one common constant spectral scale across M/D+/D- and dynamical comparisons.).
+
+- Close CL2 indispensable material component: all of: O2 (Present correct common-scale spin-summed total-dipole HHG spectra for M, D+ and D-, making sub-gap relative strength and case ordering assessable.); O3 (Present a valid comparison/intervention showing that evolving internal Kohn-Sham potential does not generate the D-/D+ sub-gap contrast and that M is more sensitive to that dynamics; full/frozen propagation is accepted but not mandatory.).
+
+- Close CL2 principal mechanism or commissioned conclusion: all of: M2 (Infer how topology is encoded in the low-energy HHG response from the identified common-scale sub-gap ordering, limiting the conclusion to supported relative rather than absolute strength.); M6 (Use the identified ordering and intervention sensitivity to distinguish robust D-/D+ insulating contrast from stronger M sensitivity to the evolving self-consistent potential.).
+
+- Close CL3 indispensable material component: O4 (Present a candidate-designed calculation/control distinguishing edge occupation/incomplete coherent cancellation from gap-only, distortion-only or generic edge-state-presence explanations; no named canonical control is mandatory.).
+
+- Close CL3 principal mechanism or commissioned conclusion: all of: M3 (Use discriminating evidence to explain near-cancellation of strong individual-orbital radiation in the coherent fully occupied D+ valence total and incomplete cancellation in D-.); M4 (Connect half occupation of the D- in-gap edge pair to incomplete coherent cancellation and explain why an in-gap eigenvalue alone does not establish the mechanism.); M5 (Explicitly reject at least one plausible gap-only, distortion-only or edge-state-presence-only alternative using the causal discriminating evidence.).
+
+- Close CL3 material validation/scope: V1 (Only when the model, transform/rescaling, occupation control or claim creates a concrete material risk to the central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.).
+
+- Close CL4 principal mechanism or commissioned conclusion: M7 (Bound the conclusion to the specified finite-chain continuous-space x-only LSD model, honestly handling known energy-curve differences or unresolved numerical features without manufacturing certainty or demanding exact source-curve reproduction.).
+
+## Applicability and Equivalent Evidence
+
+- Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.
+
+- Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.
+
+- For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.
+
+- Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.
+
+- Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.
+
+- Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.
+
+- Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.
+
+- Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.
+
+- Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.
+
+- Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.
+
+- A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.
+
+- Use the source-stated +0.265 and -0.165 geometries for driven/stationary comparisons. An optional energy scan may establish converged dimerization-lowered two-basin structure and undistorted instability, but exact minima, well depths, barrier, curvature and pixels are excluded anchors.
+
+- The unresolved published energy-curve detail does not invalidate the source-fixed-geometry driven analysis and does not determine RC. Do not tune unconverged conventions to imitate it.
+
+- Changing occupation can redefine the physical target. Mere edge-state presence, a gap or a stationary association does not establish the causal occupation/interference explanation.
+
+- For the stated continuous-space x-only LSD model, the undimerized finite chain is a half-filled metal. Both nonzero shifts dimerize the chain and open an insulating gap. D- has an almost-degenerate in-gap edge-state pair with only the lower state occupied; the occupied edge state is localized near the chain ends and broad in momentum. D+ lacks this half-occupied in-gap pair.
+
+- The Hanning-windowed total-dipole spectra support these central anchors:
+
+- below the D+ valence-to-first-conduction gap, D- emits many orders of magnitude more strongly than D+; D+ retains chiefly low odd harmonics;
+
+- the large D-/D+ contrast persists when the internal KS potential is frozen, so it is not created by the time dependence of the mean-field potential;
+
+- the metallic M case changes much more between full and frozen propagation, consistent with screening by the time-dependent metallic density;
+
+- individual occupied orbitals emit strongly in the sub-gap range, but their coherent total nearly cancels for the fully occupied D+ valence manifold. The half-occupied edge-state pair in D- makes the cancellation incomplete.
+
+- The source's canonical discriminating evidence is the comparison between the true coherent total spectrum and an incoherent sum of individual-orbital spectra. Supplemental controls using nontopological impurity edge states and a virtual electron occupying the second D- edge state support the same occupation/interference mechanism. Students need not reproduce a named control, but high mechanism credit requires evidence with equivalent causal discrimination; the presence of an edge-state eigenvalue alone is insufficient.
+
+- the task fixes $+0.265$ and $-0.165$ only as source-stated geometries for the stationary and driven comparison;
+
+- an energy scan is optional supporting evidence, not a hidden required output;
+
+- if submitted, grade only a converged dimerization-lowered two-basin structure and the instability of the undistorted case;
+
+- never grade the exact source minima, relative well depth, central maximum, curvature or pixel similarity;
+
+- do not tune an unconverged numerical convention to imitate the published curve.
+
+- The task fixes the physical chain, geometries and total-dipole spectral class, not full/frozen branches, a particular window, a ground-state plot list or one mechanism diagnostic. Accept momentum-resolved stationary maps, real-space edge-state localization, projectors, spectral functions or equivalent stationary evidence by function. Accept the canonical full/frozen comparison or another intervention only when it genuinely tests the role of the evolving internal potential. Accept an incoherent-sum comparison, controlled edge occupation, impurity control, orbital-removal test or another intervention for the cancellation evidence/mechanism only when it genuinely distinguishes the competing physical explanations.
+
+- Do not accept an SSH result as equivalent to the specified interacting continuous-space model. Do not grade source colours, crops, arrows, exact energy-curve shape, absolute HHG magnitude or a fixed number of figures. Charge an upstream numerical defect first to the physical output evidence it damages; A dependent scientific inference loses credit only when the same defect makes the inference false or unsupported.
+
+For F1/F3-F4/M3-M4, article pp.177401-2-4, Eqs.(3),(4),(8) and Fig.3, the spin densities and internal potential obey
+$$n_\sigma(x,t)=\sum_{i\in\mathrm{occ}}|\varphi_{\sigma i}(x,t)|^2,\quad
+u[n](x,t)=\int\frac{n(x',t)dx'}{\sqrt{(x-x')^2+1}},\quad
+v_{x,\sigma}=-[6n_\sigma/\pi]^{1/3}.$$
+The coherent observable is
+$$X(t)=\sum_{i,\sigma}\int x|\varphi_{\sigma i}(x,t)|^2dx,\qquad
+S_D(\Omega)\propto|\mathcal F[wX](\Omega)|^2,$$
+not $\sum_{i,\sigma}|\mathcal F[wx_{\sigma i}]|^2$. The latter is an optional cancellation diagnostic. Derivative-form spectra differ by $\Omega^2$ or $\Omega^4$ when transform/window boundary terms are controlled. Frozen-KS comparison freezes the internal Hartree/exchange potential at its stationary value, not the external laser coupling.
+
+The continuous-space orbital equation is $i\partial_t\varphi_{\sigma i}=[-\partial_x^2/2+v_{\rm ion}(x)-iA(t)\partial_x+u[n]+v_{x,\sigma}]\varphi_{\sigma i}$, with $v_{\rm ion}(x)=-\sum_j[(x-x_j)^2+1]^{-1/2}$ and $x_j=(j-(N+1)/2)a-(-1)^j\delta$. This is the x-only LSD velocity-gauge convention of source Eqs.(1)-(6); a common time-dependent scalar A-squared phase does not change the graded density/dipole.

cases/case05/resource_limits.json

@@ -0,0 +1,8 @@
+{
+  "cpu_cores": 32,
+  "nodes": 1,
+  "time_limit_minutes": 45,
+  "network_access": "disabled",
+  "temporary_storage_gib": 128,
+  "memory_policy": "No separate task-specific RAM limit is specified."
+}

cases/case05/sources.md

@@ -0,0 +1,38 @@
+# Scientific Sources — Case05
+
+## References
+
+Dieter Bauer and Kenneth K. Hansen. 2018. *High-Harmonic Generation in Solids with and without Topological Edge States*. *Physical Review Letters*, 120, 177401. [Source](https://doi.org/10.1103/PhysRevLett.120.177401)
+
+High-Harmonic Generation in Solids with and without Topological Edge States
+
+## Criterion-to-source crosswalk
+
+Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.
+
+| Criteria | Source locations, scientific use and limits |
+|---|---|
+| F1 | Bauer and Hansen (2018), article p.177401-2, Eqs.(1)-(6): soft-core continuous-space x-only LSD chain, spin-neutral occupation and fixed dimerized geometries; not a tight-binding replacement. |
+| F2, O1, I1, M1 | Bauer and Hansen (2018), article pp.177401-2-3, Fig.1(b-d), Eq.(6) and edge-state paragraph: half-filled metal, dimerized insulators and an in-gap edge pair with only its lower member occupied. Fig.1(a) exact energy minima are not compulsory targets. |
+| F3, F4 | Bauer and Hansen (2018), article p.177401-3, Eqs.(7),(8): driven KS orbitals, spin-summed coherent total dipole and squared Fourier modulus; current/acceleration variants require omega^2/omega^4 weighting. |
+| O2, I2, M2 | Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and sub-gap discussion: large D- (source phase B) / D+ (source phase A) contrast on common scale; exact 14-order magnitude or colors are not targets. |
+| O3, I3, M6 | Bauer and Hansen (2018), article pp.177401-3-4, Fig.2(a,b) and frozen-KS/screening paragraphs: insulating contrast survives frozen internal potential, while metal is much more sensitive. A functionally equivalent intervention is accepted. |
+| O4, I4, M3, M4, M5 | Bauer and Hansen (2018), article p.177401-4, Fig.3 and paragraph beginning "The key question": incoherent orbital powers versus coherent total distinguish cancellation. The same page, "Topological vs other edge states", describes impurity/occupation controls and a virtual extra electron filling the vacant edge state; these are optional canonical causal examples. |
+| M7, V1 | Bauer and Hansen (2018), article pp.177401-2-4, model equations and conclusion delimit finite-chain mean-field scope. Exact Fig.1(a) energy-curve reproduction is excluded by the task/effective rubric because its printed-functional reproduction remains unresolved; risk validation is task-defined. |
+
+## Formula and convention notes
+
+For F1/F3-F4/M3-M4, article pp.177401-2-4, Eqs.(3),(4),(8) and Fig.3, the spin densities and internal potential obey
+$$n_\sigma(x,t)=\sum_{i\in\mathrm{occ}}|\varphi_{\sigma i}(x,t)|^2,\quad
+u[n](x,t)=\int\frac{n(x',t)dx'}{\sqrt{(x-x')^2+1}},\quad
+v_{x,\sigma}=-[6n_\sigma/\pi]^{1/3}.$$
+The coherent observable is
+$$X(t)=\sum_{i,\sigma}\int x|\varphi_{\sigma i}(x,t)|^2dx,\qquad
+S_D(\Omega)\propto|\mathcal F[wX](\Omega)|^2,$$
+not $\sum_{i,\sigma}|\mathcal F[wx_{\sigma i}]|^2$. The latter is an optional cancellation diagnostic. Derivative-form spectra differ by $\Omega^2$ or $\Omega^4$ when transform/window boundary terms are controlled. Frozen-KS comparison freezes the internal Hartree/exchange potential at its stationary value, not the external laser coupling.
+
+The continuous-space orbital equation is $i\partial_t\varphi_{\sigma i}=[-\partial_x^2/2+v_{\rm ion}(x)-iA(t)\partial_x+u[n]+v_{x,\sigma}]\varphi_{\sigma i}$, with $v_{\rm ion}(x)=-\sum_j[(x-x_j)^2+1]^{-1/2}$ and $x_j=(j-(N+1)/2)a-(-1)^j\delta$. This is the x-only LSD velocity-gauge convention of source Eqs.(1)-(6); a common time-dependent scalar A-squared phase does not change the graded density/dipole.
+
+## Scope of the source anchors
+
+The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.

cases/case05/task.md

@@ -0,0 +1,140 @@
+# Topological edge states in finite-chain high-harmonic generation
+
+## Background
+
+In a finite dimerized chain, opposite structural phases can have different
+edge-state content even when both are insulating. High-harmonic emission is a
+coherent many-electron observable, so an edge state need not influence the
+total radiation in the same way that it changes a one-electron spectrum.
+
+## Research problem
+
+Using the continuous-space finite-chain model below, determine whether and how
+the chain's dimerization topology is encoded in its low-energy high-harmonic
+response. Establish what role is played by edge-state occupation, and
+distinguish it from an explanation based only on the static gap, the structural
+distortion, or the time dependence of the self-consistent Kohn-Sham potential.
+
+The derivation, numerical construction, choice of discriminating evidence and
+organization of the argument are yours. Establish the mechanism from your
+calculation rather than assuming that the presence of an in-gap state is by
+itself sufficient.
+
+## Physical inputs
+
+Use atomic units. The chain contains $N=100$ fixed singly charged ions and
+$N=100$ electrons in the spin-neutral configuration
+$N_\uparrow=N_\downarrow=50$. With $a=2$, define
+
+$$
+x_i=\left(i-\frac{N+1}{2}\right)a,
+\qquad
+x_i'(\delta)=x_i-(-1)^i\delta,
+\qquad i=1,\ldots,N,
+$$
+
+and
+
+$$
+v_{\mathrm{ion}}(x)=-\sum_{i=1}^{N}
+\frac{1}{\sqrt{[x-x_i'(\delta)]^2+1}}.
+$$
+
+Use the continuous-space, self-consistent x-only local-spin-density model with
+the same soft-core interaction in the Hartree and ion-ion terms and
+
+$$
+v_{\mathrm{xc},\sigma}(x,t)=-
+\left[\frac{6}{\pi}n_\sigma(x,t)\right]^{1/3}.
+$$
+
+Correlation is neglected. An SSH or other tight-binding Hamiltonian is not a
+substitute for this physical model.
+
+Investigate the following fixed geometries:
+
+| Task label | Dimerization shift |
+|---|---:|
+| M | $\delta=0$ |
+| D+ | $\delta=0.265$ |
+| D- | $\delta=-0.165$ |
+
+These shifts are prescribed structural inputs for the comparison; they are
+not stated here as numerical minima of a student-computed energy curve.
+
+Drive each geometry with
+
+$$
+A(t)=A_0\sin^2\!\left(\frac{\omega t}{2n_{\mathrm{cyc}}}\right)
+\sin(\omega t),
+\qquad 0<t<\frac{2\pi n_{\mathrm{cyc}}}{\omega},
+$$
+
+and $A(t)=0$ otherwise, using
+
+$$
+A_0=0.1,
+\qquad \omega=0.0075,
+\qquad n_{\mathrm{cyc}}=5.
+$$
+
+The field is polarized along the chain. Construct the graded radiation
+observable consistently from the spin-summed total dipole and report it
+against harmonic order. Declare the spectral transform and any window used.
+Use one common constant display factor across every case or dynamical
+comparison for which relative magnitude is scientific evidence. Absolute
+magnitude is not a grading target.
+
+## Method boundary
+
+Use standard stationary and time-dependent Kohn-Sham methods for the stated
+continuous-space functional. Initialize the driven dynamics from the
+corresponding stationary occupied orbitals. The comparison or intervention
+used to distinguish static structure from the effect of the evolving
+self-consistent Kohn-Sham potential is yours.
+
+All task-specific analytical, numerical and evidential constructions are
+yours. No spatial or temporal grid, box, boundary treatment, eigensolver,
+propagator, number of displayed orbitals, spectral floor, plotting range,
+diagnostic order or validation sequence is prescribed. You are responsible
+for checking that the reported evidence is sufficiently reliable and
+reproducible for the conclusions made. Numerical reliability has no separate
+score and is reflected in the correctness and quality of the physical
+evidence.
+
+## Submission
+
+Submit one self-contained scientific report and an offline reproduction
+package containing the derivation, executable code, reconstructible numerical
+data underlying every central structural and radiation claim, references
+actually used, and concise run and environment information. The organization
+and number of figures are yours. No fixed file tree, filename scheme,
+complete exploratory history or examiner-selected control is required.
+
+Include a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge.
+
+The active examination resources and limits are defined in the companion
+`resource_limits.json`. All retained production calculations must run
+within that fixed allocation and active wall time. More expensive modelling
+does not receive additional credit.
+
+## Reference and integrity policy
+
+This examination is conducted without network access or live literature
+retrieval. You may rely on your existing general scientific knowledge and, if any are
+explicitly supplied with the examination, on those offline materials or
+software documentation. Record every such source actually consulted. For formulas,
+methods, constants, or conventions used from general knowledge rather than a
+consulted source, state enough of the method basis, definition, value, units,
+and convention to make the calculation auditable; do not invent a citation.
+You are not required to identify or prove a publication date or to retrieve
+literature during the examination.
+
+The hidden target article and its identifying metadata, figures or captions,
+supplementary material, author code or data, target-specific reproduction
+code, solution or scoring material, online solutions, and worked
+reproductions of this case must not be used. All submitted scientific figures
+and numerical data must be generated by your own implementation of the stated
+problem.
+
+See [submission requirements](../../submission_requirements.md) for the common submission entry points.

cases/case06/grading_rubric.json

@@ -0,0 +1,614 @@
+{
+  "case_id": "Case06",
+  "title": "Case06 — Theory of dipole moment reconstruction by attosecond transient absorption spectroscopy",
+  "atoms": [
+    {
+      "criterion_id": "F1",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.",
+      "award_conditions": [
+        "The initial state, three-level TDSE and allowed XUV g-a/IR a-f couplings yield a real physical dipole under consistent phases and signs."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article p.063121-3, Eq.(11) and coupling paragraph: three-level g-a-f topology, energy gaps and transition moments; coherent physical dipole follows the stated basis convention."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F2",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.",
+      "award_conditions": [
+        "Positive-frequency absorption determines a real causal response which is convolved with the actual finite XUV waveform; equivalent KK/transform routes preserve that chain."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article pp.063121-1-2, Eqs.(1)-(4), p.063121-3 Eq.(12) and p.063121-5 Appendix A Eqs.(A1)-(A5): absorption, even frequency extension and real causal response."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F3",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Apply the specified 50 fs decay to the real physical dipole after propagation and before transformation, avoiding Hamiltonian, amplitude or population damping and any extra Fourier window.",
+      "award_conditions": [
+        "The stipulated 50 fs decay acts on the real physical dipole after propagation and before transformation, with no Hamiltonian/population damping or extra Fourier window."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article p.063121-4, Fig.2 caption specifies 50 fs decoherence scale. Applying it to the real dipole after propagation and using no extra Fourier window are explicit task conventions, not an added Hamiltonian relaxation law."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "O4",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present reconstructible computational evidence distinguishing full finite-XUV convolution from impulse-response-only interpretation, exposing at least one material early/late-time difference and its direction across 100/300/500 as; common figures, differences/residuals, interventions and functionally equivalent organizations are accepted.",
+      "award_conditions": [
+        "A valid computational comparison distinguishes convolution from impulse-only interpretation and exposes at least one material early/late difference and its direction across durations.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in O1, O2, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article pp.063121-2-4, Eqs.(2),(7),(10), Fig.3(b-d): finite waveform convolution differs from the impulse response and the distinction grows with probe duration. Eq.(7) is an explanatory approximation, not a substitute for the stated reconstruction."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O1",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 100 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.",
+      "award_conditions": [
+        "Direct and absorption-derived finite-waveform reconstructed dipoles at 100 as are reconstructible and expose short and claim-sufficient long times with correct duration binding.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.); F2 (Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.); F3 (Apply the specified 50 fs decay to the real physical dipole after propagation and before transformation, avoiding Hamiltonian, amplitude or population damping and any extra Fourier window.)",
+        "Preserve independently valid work in O2, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article p.063121-4, Fig.3(b), caption and adjacent onset/long-time discussion: 100 as direct and convolved dipoles versus impulse response."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O2",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 300 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.",
+      "award_conditions": [
+        "The 300 as direct and reconstructed dipoles are valid and exposed over claim-sufficient long records, not prematurely erased by transform truncation.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.); F2 (Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.); F3 (Apply the specified 50 fs decay to the real physical dipole after propagation and before transformation, avoiding Hamiltonian, amplitude or population damping and any extra Fourier window.)",
+        "Preserve independently valid work in O1, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article p.063121-4, Fig.2(b,c) for the 300 as case and Fig.3(c): persistent long-time direct/reconstructed agreement; record-truncation rejection follows the task numerical-evidence boundary."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O3",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 500 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.",
+      "award_conditions": [
+        "The 500 as direct/reconstructed signals expose timing, phase, envelope and long-time motion with correct finite-probe identity.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.); F2 (Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.); F3 (Apply the specified 50 fs decay to the real physical dipole after propagation and before transformation, avoiding Hamiltonian, amplitude or population damping and any extra Fourier window.)",
+        "Preserve independently valid work in O1, O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article p.063121-4, Fig.3(d): 500 as finite-probe difference from impulse response, including late-time structure; full convolution remains faithful."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "I1",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify in the submitted 100 as output onset timing, phase, envelope and long-lived oscillation agreement and local differences between direct and reconstructed dipoles.",
+      "award_conditions": [
+        "The candidate identifies onset, phase, envelope and long-lived agreement or actual local differences in the 100 as evidence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O1 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 100 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.)",
+        "Preserve independently valid work in I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article p.063121-4, Fig.3(b), caption and adjacent onset/long-time discussion: 100 as direct and convolved dipoles versus impulse response."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I2",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify short-time agreement and persistent long-time phase/envelope agreement or actual differences in the 300 as output; premature disappearance is not a physical result.",
+      "award_conditions": [
+        "The candidate identifies 300 as short-time and persistent long-time behavior, not a spurious disappearing trace."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O2 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 300 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.)",
+        "Preserve independently valid work in I1, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article p.063121-4, Fig.2(b,c) for the 300 as case and Fig.3(c): persistent long-time direct/reconstructed agreement; record-truncation rejection follows the task numerical-evidence boundary."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I3",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify timing, phase, envelope and more visible finite-pulse departures in the 500 as output, including their long-time visibility.",
+      "award_conditions": [
+        "The candidate identifies timing, phase/envelope and more visible finite-probe departures in the 500 as evidence, including late times."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O3 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 500 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.)",
+        "Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article p.063121-4, Fig.3(d): 500 as finite-probe difference from impulse response, including late-time structure; full convolution remains faithful."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I4",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Explicitly distinguish impulse response from the finite-waveform reconstructed dipole in the submitted calculation and identify the increasing difference with probe duration.",
+      "award_conditions": [
+        "The candidate distinguishes the impulse response from the finite-waveform reconstructed dipole and identifies increasing difference with probe duration."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O4 (Present reconstructible computational evidence distinguishing full finite-XUV convolution from impulse-response-only interpretation, exposing at least one material early/late-time difference and its direction across 100/300/500 as; common figures, differences/residuals, interventions and functionally equivalent organizations are accepted.)",
+        "Preserve independently valid work in I1, I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article pp.063121-2-4, Eqs.(2),(7),(10), Fig.3(b-d): finite waveform convolution differs from the impulse response and the distinction grows with probe duration. Eq.(7) is an explanatory approximation, not a substitute for the stated reconstruction."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M1",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain from derivation and submitted evidence how positive-frequency absorption retains the information required for a real causal time-domain response, not merely reciting Kramers-Kronig relations.",
+      "award_conditions": [
+        "The derivation and evidence explain why absorption plus causality retain the information needed for a real time-domain response."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article pp.063121-1-2, Eqs.(1)-(4), p.063121-3 Eq.(12) and p.063121-5 Appendix A Eqs.(A1)-(A5): absorption, even frequency extension and real causal response."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M2",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain why convolution of a finite XUV waveform with the causal response differs from the impulse response and connect that explanation to the identified signal.",
+      "award_conditions": [
+        "Finite-waveform convolution, rather than an impulse-only picture, explains the identified temporal difference."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I4 (Explicitly distinguish impulse response from the finite-waveform reconstructed dipole in the submitted calculation and identify the increasing difference with probe duration.)",
+        "Preserve independently valid work in M1, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article pp.063121-2-4, Eqs.(2),(7),(10), Fig.3(b-d): finite waveform convolution differs from the impulse response and the distinction grows with probe duration. Eq.(7) is an explanatory approximation, not a substitute for the stated reconstruction."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M3",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain the finite-probe dependence across 100/300/500 as using feature-level evidence from all three calculations and the correct direction.",
+      "award_conditions": [
+        "Feature-level evidence from all three calculations supports the correct finite-probe-duration trend."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I4 (Explicitly distinguish impulse response from the finite-waveform reconstructed dipole in the submitted calculation and identify the increasing difference with probe duration.)",
+        "Preserve independently valid work in M2, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article pp.063121-2-4, Eqs.(2),(7),(10), Fig.3(b-d): finite waveform convolution differs from the impulse response and the distinction grows with probe duration. Eq.(7) is an explanatory approximation, not a substitute for the stated reconstruction."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M4",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Determine the fidelity supported at all three durations by synthesizing timing, phase, envelope, short/long-time motion and finite-probe differences, with claim strength commensurate with evidence.",
+      "award_conditions": [
+        "The candidate synthesizes onset, phase, envelope and early/late behavior to assess supported reconstruction fidelity at every duration."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I1 (Identify in the submitted 100 as output onset timing, phase, envelope and long-lived oscillation agreement and local differences between direct and reconstructed dipoles.); I2 (Identify short-time agreement and persistent long-time phase/envelope agreement or actual differences in the 300 as output; premature disappearance is not a physical result.); I3 (Identify timing, phase, envelope and more visible finite-pulse departures in the 500 as output, including their long-time visibility.); I4 (Explicitly distinguish impulse response from the finite-waveform reconstructed dipole in the submitted calculation and identify the increasing difference with probe duration.)",
+        "Preserve independently valid work in M1, M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article pp.063121-4-5, Fig.4, Eq.(13) and Sec.IV: linear-response/probe-duration fidelity boundary. Actual long-record evidence, processing safeguards and triggered alternative tests are task-defined; no exact correlation value is required."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M5",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain near-probe-centre onset timing and phase/envelope agreement from the 100 as signal rather than a context-free similarity metric.",
+      "award_conditions": [
+        "The 100 as evidence grounds the near-centre onset and phase/envelope explanation rather than an isolated similarity metric."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I1 (Identify in the submitted 100 as output onset timing, phase, envelope and long-lived oscillation agreement and local differences between direct and reconstructed dipoles.)",
+        "Preserve independently valid work in M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article p.063121-4, Fig.3(b), caption and adjacent onset/long-time discussion: 100 as direct and convolved dipoles versus impulse response."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M6",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use the submitted 300 as long-time signal to assess continued reconstruction reliability and distinguish physical decay from premature record-truncation/transform disappearance.",
+      "award_conditions": [
+        "The 300 as long-time evidence distinguishes continued fidelity and physical decay from processing/truncation loss."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I2 (Identify short-time agreement and persistent long-time phase/envelope agreement or actual differences in the 300 as output; premature disappearance is not a physical result.)",
+        "Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article p.063121-4, Fig.2(b,c) for the 300 as case and Fig.3(c): persistent long-time direct/reconstructed agreement; record-truncation rejection follows the task numerical-evidence boundary."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M7",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Positively establish with actual long records, feature comparisons or equivalent evidence that claimed time-domain fidelity is not manufactured by truncation, transform processing or display selection; reconcile representations only where an actual disagreement exists.",
+      "award_conditions": [
+        "Actual long records and feature comparisons establish that fidelity is not manufactured by truncation, processing or selective display; actual conflicts are reconciled."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: at least one of: O1 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 100 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.); O2 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 300 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.); O3 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 500 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.)",
+        "Preserve independently valid work in M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article pp.063121-4-5, Fig.4, Eq.(13) and Sec.IV: linear-response/probe-duration fidelity boundary. Actual long-record evidence, processing safeguards and triggered alternative tests are task-defined; no exact correlation value is required."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V1",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Positively state that the conclusion concerns the specified weak-probe causal linear-response three-level model and the three calculated probe durations.",
+      "award_conditions": [
+        "The candidate positively limits the conclusion to the specified weak-probe causal linear-response three-level model and three probe durations."
+      ],
+      "applicability_and_na": [
+        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article pp.063121-4-5, Fig.4, Eq.(13) and Sec.IV: linear-response/probe-duration fidelity boundary. Actual long-record evidence, processing safeguards and triggered alternative tests are task-defined; no exact correlation value is required."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V2",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.",
+      "award_conditions": [
+        "A concrete triggered processing/model/claim risk is addressed with capable evidence or narrowed claims; otherwise the item is N/A."
+      ],
+      "applicability_and_na": [
+        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
+        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.",
+        "At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.",
+        "A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.",
+        "Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted."
+      ],
+      "source_support": [
+        "Wu et al. (2021), article pp.063121-4-5, Fig.4, Eq.(13) and Sec.IV: linear-response/probe-duration fidelity boundary. Actual long-record evidence, processing safeguards and triggered alternative tests are task-defined; no exact correlation value is required."
+      ],
+      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    }
+  ],
+  "case_scientific_rules": [
+    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
+    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
+    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
+    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
+    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
+    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
+    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
+    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
+    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
+    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
+    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
+    "The direct dipole begins slightly before probe-centred zero. Full finite-pulse reconstruction follows timing, phase, envelope and long-lived oscillation; the impulse response alone differs during the first hundreds of attoseconds, increasingly at longer probe duration.",
+    "For 300 as, long-time evidence can support persistent agreement over approximately 0-150 fs; a prematurely vanished reconstructed trace is an implementation failure, not a source-physical result. Exact correlation value or evaluation window is not required.",
+    "M7 can be established by any one actually used valid duration output with sufficient long-record/feature evidence; it is not hard-gated by success of every duration. Missing cases remain separately assessed.",
+    "No absolute vertical scale, fixed source crop, solver, extra Fourier window or named convergence check is a target.",
+    "For the interaction-picture state",
+    "$$\n|\\psi(t)\\rangle=\\sum_{j\\in\\{g,a,f\\}}C_j(t)e^{-iE_jt}|j\\rangle,\n$$",
+    "the standard three-level TDSE contains only the stated $g\\leftrightarrow a$ XUV and $a\\leftrightarrow f$ IR couplings. A canonical full allowed dipole is",
+    "$$\nd_0(t)=2\\operatorname{Re}\\!\\left[\n\\mu_{ga}C_g^*C_a e^{-i(E_a-E_g)t}\n+\\mu_{af}C_a^*C_f e^{-i(E_f-E_a)t}\n\\right].\n$$",
+    "At the stated weak-XUV parameters, a clearly justified $g$-$a$ readout is numerically equivalent for the graded absorption/reconstruction structures and is acceptable. Adding a $g$-$f$ transition or changing the coherent preparation is not equivalent.",
+    "The author decay is applied to the real physical dipole after propagation and before any transform. It is not a Hamiltonian, Lindblad, amplitude-damping or population-damping term. No additional Fourier window is permitted.",
+    "With a self-consistent Fourier convention, the canonical source route obtains the positive-frequency absorption from the physical dipole and XUV field, uses the physical even continuation of the cross section, recovers the causal IR-dressed response and folds that response with the finite XUV waveform. In the source convention,",
+    "$$\n\\sigma(\\omega)=-4\\pi\\alpha\\omega\\operatorname{Im}\n\\left[\\frac{\\widetilde d_{\\mathrm{phys}}(\\omega)}\n{\\widetilde E_X(\\omega)}\\right],\\qquad \\omega>0,\n$$",
+    "$$\n\\sigma(-\\omega)=\\sigma(\\omega),\\qquad\n\\chi_{\\mathrm{IR}}(t)=\\mathcal F^{-1}\\!\\left[\n-i\\frac{\\sigma(\\omega)}{2\\pi\\alpha\\omega}\\right](t),\\quad t>0,\n$$",
+    "$$\nd_{\\mathrm{rec}}(t)=\\frac{1}{\\sqrt{2\\pi}}\n\\int_0^\\infty\\chi_{\\mathrm{IR}}(s)E_X(t-s)\\,ds.\n$$",
+    "A mathematically equivalent Kramers-Kronig or transform implementation earns full credit. An arbitrary filter or fit that maps the known direct dipole onto itself is not an absorption-based reconstruction.",
+    "In all three finite-pulse cases, the directly calculated dipole begins slightly before the probe-centred plotted zero. The full finite-pulse reconstruction closely follows its timing, phase, envelope and long-lived oscillation.",
+    "The recovered impulse response alone is not identical to the finite-pulse dipole during the first few hundred attoseconds. The distinction grows with probe duration; for 500 as it is also visible in the later oscillation.",
+    "For the 300 as case, direct and reconstructed dipoles remain closely aligned over the long source interval of approximately 0-150 fs. A reconstructed trace that disappears partway through this interval is an implementation failure, not a physical source result.",
+    "A correlation coefficient may support the comparison but does not replace feature-level evidence. No exact value or evaluation window is required.",
+    "The conclusion is limited to the supplied weak-probe, causal linear-response three-level model and stated fields. The shown cases do not establish arbitrary probe duration, stronger nonlinear probes or general atomic structure.",
+    "The reconstruction formulas correspond to article pp.063121-2-3, Eqs.(2)-(4),(11),(12). With the source symmetric Fourier convention $\\widetilde f=(2\\pi)^{-1/2}\\int f(t)e^{-i\\omega t}dt$, the real-dipole identity requires $\\widetilde d(-\\omega)=\\widetilde d(\\omega)^*$ and the physical continuation $\\sigma(-\\omega)=\\sigma(\\omega)$. The causal inverse transform is retained only for $t>0$ before folding with the finite probe. A global convention change is accepted only when absorption sign, time direction, phases and normalization transform consistently. The 50 fs task decay is post-propagation readout processing, not a relaxation term in Eq.(11)."
+  ],
+  "closure_requirements": {
+    "RC0": [
+      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
+      "Required indispensable claim CL1, central physical object: all of: F1 (Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.); F2 (Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC1": [
+      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
+      "Required co primary claim CL2, indispensable material component: O1 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 100 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL3, indispensable material component: O2 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 300 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL4, indispensable material component: O3 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 500 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC2": [
+      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
+      "Required co primary claim CL5, principal mechanism or commissioned conclusion: all of: M2 (Explain why convolution of a finite XUV waveform with the causal response differs from the impulse response and connect that explanation to the identified signal.); M3 (Explain the finite-probe dependence across 100/300/500 as using feature-level evidence from all three calculations and the correct direction.); M4 (Determine the fidelity supported at all three durations by synthesizing timing, phase, envelope, short/long-time motion and finite-probe differences, with claim strength commensurate with evidence.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC3": [
+      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
+      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
+      "Required co primary claim CL5, material validation/scope: V2 (Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC4": [
+      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
+      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
+      "Close CL1 central physical object: all of: F1 (Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.); F2 (Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.).",
+      "Close CL2 indispensable material component: O1 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 100 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.).",
+      "Close CL3 indispensable material component: O2 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 300 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.).",
+      "Close CL4 indispensable material component: O3 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 500 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.).",
+      "Close CL5 principal mechanism or commissioned conclusion: all of: M2 (Explain why convolution of a finite XUV waveform with the causal response differs from the impulse response and connect that explanation to the identified signal.); M3 (Explain the finite-probe dependence across 100/300/500 as using feature-level evidence from all three calculations and the correct direction.); M4 (Determine the fidelity supported at all three durations by synthesizing timing, phase, envelope, short/long-time motion and finite-probe differences, with claim strength commensurate with evidence.).",
+      "Close CL5 material validation/scope: V2 (Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.).",
+      "Supporting claim CL6 is separately scored but does not determine overall closure: Positively state that the conclusion concerns the specified weak-probe causal linear-response three-level model and the three calculated probe durations."
+    ]
+  },
+  "references": [
+    {
+      "citation": "Xiaoxia Wu, Linxuan Zhang, Shaofeng Zhang, and Difa Ye. 2021. *Theory of dipole moment reconstruction by attosecond transient absorption spectroscopy*. *Physical Review A*, 104, 063121.",
+      "url": "https://doi.org/10.1103/PhysRevA.104.063121",
+      "scientific_scope": "Theory of dipole moment reconstruction by attosecond transient absorption spectroscopy",
+      "anchors": [
+        "Wu et al. (2021), article p.063121-3, Eq.(11) and coupling paragraph: three-level g-a-f topology, energy gaps and transition moments; coherent physical dipole follows the stated basis convention.",
+        "Wu et al. (2021), article pp.063121-1-2, Eqs.(1)-(4), p.063121-3 Eq.(12) and p.063121-5 Appendix A Eqs.(A1)-(A5): absorption, even frequency extension and real causal response.",
+        "Wu et al. (2021), article p.063121-4, Fig.2 caption specifies 50 fs decoherence scale. Applying it to the real dipole after propagation and using no extra Fourier window are explicit task conventions, not an added Hamiltonian relaxation law.",
+        "Wu et al. (2021), article p.063121-4, Fig.3(b), caption and adjacent onset/long-time discussion: 100 as direct and convolved dipoles versus impulse response.",
+        "Wu et al. (2021), article p.063121-4, Fig.2(b,c) for the 300 as case and Fig.3(c): persistent long-time direct/reconstructed agreement; record-truncation rejection follows the task numerical-evidence boundary.",
+        "Wu et al. (2021), article p.063121-4, Fig.3(d): 500 as finite-probe difference from impulse response, including late-time structure; full convolution remains faithful.",
+        "Wu et al. (2021), article pp.063121-2-4, Eqs.(2),(7),(10), Fig.3(b-d): finite waveform convolution differs from the impulse response and the distinction grows with probe duration. Eq.(7) is an explanatory approximation, not a substitute for the stated reconstruction.",
+        "Wu et al. (2021), article pp.063121-4-5, Fig.4, Eq.(13) and Sec.IV: linear-response/probe-duration fidelity boundary. Actual long-record evidence, processing safeguards and triggered alternative tests are task-defined; no exact correlation value is required."
+      ]
+    }
+  ]
+}

cases/case06/grading_rubric.md

@@ -0,0 +1,913 @@
+# Grading Rubric — Case06
+
+Case06 — Theory of dipole moment reconstruction by attosecond transient absorption spectroscopy
+
+## Atomic Scoring Criteria
+
+Each criterion awards 0 or 0.5 points, for a maximum of 10. Explicit N/A rules apply where stated.
+
+### F1 — F — 0.5 points
+
+**Scientific requirement**
+
+Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.
+
+**Conditions for credit**
+
+- The initial state, three-level TDSE and allowed XUV g-a/IR a-f couplings yield a real physical dipole under consistent phases and signs.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article p.063121-3, Eq.(11) and coupling paragraph: three-level g-a-f topology, energy gaps and transition moments; coherent physical dipole follows the stated basis convention.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F2 — F — 0.5 points
+
+**Scientific requirement**
+
+Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.
+
+**Conditions for credit**
+
+- Positive-frequency absorption determines a real causal response which is convolved with the actual finite XUV waveform; equivalent KK/transform routes preserve that chain.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article pp.063121-1-2, Eqs.(1)-(4), p.063121-3 Eq.(12) and p.063121-5 Appendix A Eqs.(A1)-(A5): absorption, even frequency extension and real causal response.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F3 — F — 0.5 points
+
+**Scientific requirement**
+
+Apply the specified 50 fs decay to the real physical dipole after propagation and before transformation, avoiding Hamiltonian, amplitude or population damping and any extra Fourier window.
+
+**Conditions for credit**
+
+- The stipulated 50 fs decay acts on the real physical dipole after propagation and before transformation, with no Hamiltonian/population damping or extra Fourier window.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article p.063121-4, Fig.2 caption specifies 50 fs decoherence scale. Applying it to the real dipole after propagation and using no extra Fourier window are explicit task conventions, not an added Hamiltonian relaxation law.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### O4 — O — 0.5 points
+
+**Scientific requirement**
+
+Present reconstructible computational evidence distinguishing full finite-XUV convolution from impulse-response-only interpretation, exposing at least one material early/late-time difference and its direction across 100/300/500 as; common figures, differences/residuals, interventions and functionally equivalent organizations are accepted.
+
+**Conditions for credit**
+
+- A valid computational comparison distinguishes convolution from impulse-only interpretation and exposes at least one material early/late difference and its direction across durations.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in O1, O2, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article pp.063121-2-4, Eqs.(2),(7),(10), Fig.3(b-d): finite waveform convolution differs from the impulse response and the distinction grows with probe duration. Eq.(7) is an explanatory approximation, not a substitute for the stated reconstruction.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O1 — O — 0.5 points
+
+**Scientific requirement**
+
+Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 100 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.
+
+**Conditions for credit**
+
+- Direct and absorption-derived finite-waveform reconstructed dipoles at 100 as are reconstructible and expose short and claim-sufficient long times with correct duration binding.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.); F2 (Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.); F3 (Apply the specified 50 fs decay to the real physical dipole after propagation and before transformation, avoiding Hamiltonian, amplitude or population damping and any extra Fourier window.)
+
+- Preserve independently valid work in O2, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article p.063121-4, Fig.3(b), caption and adjacent onset/long-time discussion: 100 as direct and convolved dipoles versus impulse response.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O2 — O — 0.5 points
+
+**Scientific requirement**
+
+Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 300 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.
+
+**Conditions for credit**
+
+- The 300 as direct and reconstructed dipoles are valid and exposed over claim-sufficient long records, not prematurely erased by transform truncation.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.); F2 (Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.); F3 (Apply the specified 50 fs decay to the real physical dipole after propagation and before transformation, avoiding Hamiltonian, amplitude or population damping and any extra Fourier window.)
+
+- Preserve independently valid work in O1, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article p.063121-4, Fig.2(b,c) for the 300 as case and Fig.3(c): persistent long-time direct/reconstructed agreement; record-truncation rejection follows the task numerical-evidence boundary.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O3 — O — 0.5 points
+
+**Scientific requirement**
+
+Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 500 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.
+
+**Conditions for credit**
+
+- The 500 as direct/reconstructed signals expose timing, phase, envelope and long-time motion with correct finite-probe identity.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.); F2 (Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.); F3 (Apply the specified 50 fs decay to the real physical dipole after propagation and before transformation, avoiding Hamiltonian, amplitude or population damping and any extra Fourier window.)
+
+- Preserve independently valid work in O1, O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article p.063121-4, Fig.3(d): 500 as finite-probe difference from impulse response, including late-time structure; full convolution remains faithful.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### I1 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify in the submitted 100 as output onset timing, phase, envelope and long-lived oscillation agreement and local differences between direct and reconstructed dipoles.
+
+**Conditions for credit**
+
+- The candidate identifies onset, phase, envelope and long-lived agreement or actual local differences in the 100 as evidence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O1 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 100 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.)
+
+- Preserve independently valid work in I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article p.063121-4, Fig.3(b), caption and adjacent onset/long-time discussion: 100 as direct and convolved dipoles versus impulse response.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I2 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify short-time agreement and persistent long-time phase/envelope agreement or actual differences in the 300 as output; premature disappearance is not a physical result.
+
+**Conditions for credit**
+
+- The candidate identifies 300 as short-time and persistent long-time behavior, not a spurious disappearing trace.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O2 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 300 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.)
+
+- Preserve independently valid work in I1, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article p.063121-4, Fig.2(b,c) for the 300 as case and Fig.3(c): persistent long-time direct/reconstructed agreement; record-truncation rejection follows the task numerical-evidence boundary.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I3 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify timing, phase, envelope and more visible finite-pulse departures in the 500 as output, including their long-time visibility.
+
+**Conditions for credit**
+
+- The candidate identifies timing, phase/envelope and more visible finite-probe departures in the 500 as evidence, including late times.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O3 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 500 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.)
+
+- Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article p.063121-4, Fig.3(d): 500 as finite-probe difference from impulse response, including late-time structure; full convolution remains faithful.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I4 — I — 0.5 points
+
+**Scientific requirement**
+
+Explicitly distinguish impulse response from the finite-waveform reconstructed dipole in the submitted calculation and identify the increasing difference with probe duration.
+
+**Conditions for credit**
+
+- The candidate distinguishes the impulse response from the finite-waveform reconstructed dipole and identifies increasing difference with probe duration.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O4 (Present reconstructible computational evidence distinguishing full finite-XUV convolution from impulse-response-only interpretation, exposing at least one material early/late-time difference and its direction across 100/300/500 as; common figures, differences/residuals, interventions and functionally equivalent organizations are accepted.)
+
+- Preserve independently valid work in I1, I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article pp.063121-2-4, Eqs.(2),(7),(10), Fig.3(b-d): finite waveform convolution differs from the impulse response and the distinction grows with probe duration. Eq.(7) is an explanatory approximation, not a substitute for the stated reconstruction.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M1 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain from derivation and submitted evidence how positive-frequency absorption retains the information required for a real causal time-domain response, not merely reciting Kramers-Kronig relations.
+
+**Conditions for credit**
+
+- The derivation and evidence explain why absorption plus causality retain the information needed for a real time-domain response.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article pp.063121-1-2, Eqs.(1)-(4), p.063121-3 Eq.(12) and p.063121-5 Appendix A Eqs.(A1)-(A5): absorption, even frequency extension and real causal response.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M2 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain why convolution of a finite XUV waveform with the causal response differs from the impulse response and connect that explanation to the identified signal.
+
+**Conditions for credit**
+
+- Finite-waveform convolution, rather than an impulse-only picture, explains the identified temporal difference.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I4 (Explicitly distinguish impulse response from the finite-waveform reconstructed dipole in the submitted calculation and identify the increasing difference with probe duration.)
+
+- Preserve independently valid work in M1, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article pp.063121-2-4, Eqs.(2),(7),(10), Fig.3(b-d): finite waveform convolution differs from the impulse response and the distinction grows with probe duration. Eq.(7) is an explanatory approximation, not a substitute for the stated reconstruction.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M3 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain the finite-probe dependence across 100/300/500 as using feature-level evidence from all three calculations and the correct direction.
+
+**Conditions for credit**
+
+- Feature-level evidence from all three calculations supports the correct finite-probe-duration trend.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I4 (Explicitly distinguish impulse response from the finite-waveform reconstructed dipole in the submitted calculation and identify the increasing difference with probe duration.)
+
+- Preserve independently valid work in M2, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article pp.063121-2-4, Eqs.(2),(7),(10), Fig.3(b-d): finite waveform convolution differs from the impulse response and the distinction grows with probe duration. Eq.(7) is an explanatory approximation, not a substitute for the stated reconstruction.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M4 — M — 0.5 points
+
+**Scientific requirement**
+
+Determine the fidelity supported at all three durations by synthesizing timing, phase, envelope, short/long-time motion and finite-probe differences, with claim strength commensurate with evidence.
+
+**Conditions for credit**
+
+- The candidate synthesizes onset, phase, envelope and early/late behavior to assess supported reconstruction fidelity at every duration.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: I1 (Identify in the submitted 100 as output onset timing, phase, envelope and long-lived oscillation agreement and local differences between direct and reconstructed dipoles.); I2 (Identify short-time agreement and persistent long-time phase/envelope agreement or actual differences in the 300 as output; premature disappearance is not a physical result.); I3 (Identify timing, phase, envelope and more visible finite-pulse departures in the 500 as output, including their long-time visibility.); I4 (Explicitly distinguish impulse response from the finite-waveform reconstructed dipole in the submitted calculation and identify the increasing difference with probe duration.)
+
+- Preserve independently valid work in M1, M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article pp.063121-4-5, Fig.4, Eq.(13) and Sec.IV: linear-response/probe-duration fidelity boundary. Actual long-record evidence, processing safeguards and triggered alternative tests are task-defined; no exact correlation value is required.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M5 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain near-probe-centre onset timing and phase/envelope agreement from the 100 as signal rather than a context-free similarity metric.
+
+**Conditions for credit**
+
+- The 100 as evidence grounds the near-centre onset and phase/envelope explanation rather than an isolated similarity metric.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I1 (Identify in the submitted 100 as output onset timing, phase, envelope and long-lived oscillation agreement and local differences between direct and reconstructed dipoles.)
+
+- Preserve independently valid work in M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article p.063121-4, Fig.3(b), caption and adjacent onset/long-time discussion: 100 as direct and convolved dipoles versus impulse response.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M6 — M — 0.5 points
+
+**Scientific requirement**
+
+Use the submitted 300 as long-time signal to assess continued reconstruction reliability and distinguish physical decay from premature record-truncation/transform disappearance.
+
+**Conditions for credit**
+
+- The 300 as long-time evidence distinguishes continued fidelity and physical decay from processing/truncation loss.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I2 (Identify short-time agreement and persistent long-time phase/envelope agreement or actual differences in the 300 as output; premature disappearance is not a physical result.)
+
+- Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article p.063121-4, Fig.2(b,c) for the 300 as case and Fig.3(c): persistent long-time direct/reconstructed agreement; record-truncation rejection follows the task numerical-evidence boundary.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M7 — M — 0.5 points
+
+**Scientific requirement**
+
+Positively establish with actual long records, feature comparisons or equivalent evidence that claimed time-domain fidelity is not manufactured by truncation, transform processing or display selection; reconcile representations only where an actual disagreement exists.
+
+**Conditions for credit**
+
+- Actual long records and feature comparisons establish that fidelity is not manufactured by truncation, processing or selective display; actual conflicts are reconciled.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: at least one of: O1 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 100 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.); O2 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 300 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.); O3 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 500 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.)
+
+- Preserve independently valid work in M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article pp.063121-4-5, Fig.4, Eq.(13) and Sec.IV: linear-response/probe-duration fidelity boundary. Actual long-record evidence, processing safeguards and triggered alternative tests are task-defined; no exact correlation value is required.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V1 — V — 0.5 points
+
+**Scientific requirement**
+
+Positively state that the conclusion concerns the specified weak-probe causal linear-response three-level model and the three calculated probe durations.
+
+**Conditions for credit**
+
+- The candidate positively limits the conclusion to the specified weak-probe causal linear-response three-level model and three probe durations.
+
+**Applicability and N/A**
+
+- This positive scientific scope/evidence duty is unconditional; N/A is not permitted.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article pp.063121-4-5, Fig.4, Eq.(13) and Sec.IV: linear-response/probe-duration fidelity boundary. Actual long-record evidence, processing safeguards and triggered alternative tests are task-defined; no exact correlation value is required.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V2 — V — 0.5 points
+
+**Scientific requirement**
+
+Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.
+
+**Conditions for credit**
+
+- A concrete triggered processing/model/claim risk is addressed with capable evidence or narrowed claims; otherwise the item is N/A.
+
+**Applicability and N/A**
+
+- Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.
+
+- If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Global Fourier, dipole-sign, time-origin and positive display-scale conventions are accepted after physical alignment.
+
+- At the stated weak-XUV parameters a clearly justified g-a-only readout is equivalent for the absorption/reconstruction structures; adding a g-f transition or changing coherent preparation is not.
+
+- A mathematically equivalent causal Kramers-Kronig or transform reconstruction is accepted. A filter or fit mapping the known direct dipole onto itself is not absorption-derived reconstruction.
+
+- Finite-probe/impulse discrimination need not be a separately named figure. Any submitted calculation with the same causal discriminating function is accepted.
+
+**Scientific source locations**
+
+- Wu et al. (2021), article pp.063121-4-5, Fig.4, Eq.(13) and Sec.IV: linear-response/probe-duration fidelity boundary. Actual long-record evidence, processing safeguards and triggered alternative tests are task-defined; no exact correlation value is required.
+
+**Research Closure relation**
+
+Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+## Research Closure Requirements
+
+### RC0
+
+- The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.
+
+- Required indispensable claim CL1, central physical object: all of: F1 (Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.); F2 (Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC1
+
+- With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.
+
+- Required co primary claim CL2, indispensable material component: O1 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 100 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL3, indispensable material component: O2 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 300 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL4, indispensable material component: O3 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 500 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC2
+
+- With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.
+
+- Required co primary claim CL5, principal mechanism or commissioned conclusion: all of: M2 (Explain why convolution of a finite XUV waveform with the causal response differs from the impulse response and connect that explanation to the identified signal.); M3 (Explain the finite-probe dependence across 100/300/500 as using feature-level evidence from all three calculations and the correct direction.); M4 (Determine the fidelity supported at all three durations by synthesizing timing, phase, envelope, short/long-time motion and finite-probe differences, with claim strength commensurate with evidence.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC3
+
+- With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.
+
+- Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.
+
+- Required co primary claim CL5, material validation/scope: V2 (Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC4
+
+- All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.
+
+- Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.
+
+- Close CL1 central physical object: all of: F1 (Establish the specified three-level TDSE, initial state, coupling topology and real physical dipole; equivalent representations require consistent phase/sign mapping.); F2 (Construct a computable positive-frequency-absorption -> real causal response -> finite-XUV-waveform convolution -> reconstructed-dipole chain; mathematically equivalent Kramers-Kronig/transform implementations are accepted.).
+
+- Close CL2 indispensable material component: O1 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 100 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.).
+
+- Close CL3 indispensable material component: O2 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 300 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.).
+
+- Close CL4 indispensable material component: O3 (Present valid, reconstructible, adequately exposed direct and absorption-derived finite-pulse reconstructed dipoles for 500 as, with short-time and claim-sufficient long-time motion auditable and correct duration binding.).
+
+- Close CL5 principal mechanism or commissioned conclusion: all of: M2 (Explain why convolution of a finite XUV waveform with the causal response differs from the impulse response and connect that explanation to the identified signal.); M3 (Explain the finite-probe dependence across 100/300/500 as using feature-level evidence from all three calculations and the correct direction.); M4 (Determine the fidelity supported at all three durations by synthesizing timing, phase, envelope, short/long-time motion and finite-probe differences, with claim strength commensurate with evidence.).
+
+- Close CL5 material validation/scope: V2 (Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.).
+
+- Supporting claim CL6 is separately scored but does not determine overall closure: Positively state that the conclusion concerns the specified weak-probe causal linear-response three-level model and the three calculated probe durations.
+
+## Applicability and Equivalent Evidence
+
+- Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.
+
+- Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.
+
+- For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.
+
+- Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.
+
+- Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.
+
+- Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.
+
+- Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.
+
+- Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.
+
+- Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.
+
+- Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.
+
+- A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.
+
+- The direct dipole begins slightly before probe-centred zero. Full finite-pulse reconstruction follows timing, phase, envelope and long-lived oscillation; the impulse response alone differs during the first hundreds of attoseconds, increasingly at longer probe duration.
+
+- For 300 as, long-time evidence can support persistent agreement over approximately 0-150 fs; a prematurely vanished reconstructed trace is an implementation failure, not a source-physical result. Exact correlation value or evaluation window is not required.
+
+- M7 can be established by any one actually used valid duration output with sufficient long-record/feature evidence; it is not hard-gated by success of every duration. Missing cases remain separately assessed.
+
+- No absolute vertical scale, fixed source crop, solver, extra Fourier window or named convergence check is a target.
+
+- For the interaction-picture state
+
+$$
+|\psi(t)\rangle=\sum_{j\in\{g,a,f\}}C_j(t)e^{-iE_jt}|j\rangle,
+$$
+
+- the standard three-level TDSE contains only the stated $g\leftrightarrow a$ XUV and $a\leftrightarrow f$ IR couplings. A canonical full allowed dipole is
+
+$$
+d_0(t)=2\operatorname{Re}\!\left[
+\mu_{ga}C_g^*C_a e^{-i(E_a-E_g)t}
++\mu_{af}C_a^*C_f e^{-i(E_f-E_a)t}
+\right].
+$$
+
+- At the stated weak-XUV parameters, a clearly justified $g$-$a$ readout is numerically equivalent for the graded absorption/reconstruction structures and is acceptable. Adding a $g$-$f$ transition or changing the coherent preparation is not equivalent.
+
+- The author decay is applied to the real physical dipole after propagation and before any transform. It is not a Hamiltonian, Lindblad, amplitude-damping or population-damping term. No additional Fourier window is permitted.
+
+- With a self-consistent Fourier convention, the canonical source route obtains the positive-frequency absorption from the physical dipole and XUV field, uses the physical even continuation of the cross section, recovers the causal IR-dressed response and folds that response with the finite XUV waveform. In the source convention,
+
+$$
+\sigma(\omega)=-4\pi\alpha\omega\operatorname{Im}
+\left[\frac{\widetilde d_{\mathrm{phys}}(\omega)}
+{\widetilde E_X(\omega)}\right],\qquad \omega>0,
+$$
+
+$$
+\sigma(-\omega)=\sigma(\omega),\qquad
+\chi_{\mathrm{IR}}(t)=\mathcal F^{-1}\!\left[
+-i\frac{\sigma(\omega)}{2\pi\alpha\omega}\right](t),\quad t>0,
+$$
+
+$$
+d_{\mathrm{rec}}(t)=\frac{1}{\sqrt{2\pi}}
+\int_0^\infty\chi_{\mathrm{IR}}(s)E_X(t-s)\,ds.
+$$
+
+- A mathematically equivalent Kramers-Kronig or transform implementation earns full credit. An arbitrary filter or fit that maps the known direct dipole onto itself is not an absorption-based reconstruction.
+
+- In all three finite-pulse cases, the directly calculated dipole begins slightly before the probe-centred plotted zero. The full finite-pulse reconstruction closely follows its timing, phase, envelope and long-lived oscillation.
+
+- The recovered impulse response alone is not identical to the finite-pulse dipole during the first few hundred attoseconds. The distinction grows with probe duration; for 500 as it is also visible in the later oscillation.
+
+- For the 300 as case, direct and reconstructed dipoles remain closely aligned over the long source interval of approximately 0-150 fs. A reconstructed trace that disappears partway through this interval is an implementation failure, not a physical source result.
+
+- A correlation coefficient may support the comparison but does not replace feature-level evidence. No exact value or evaluation window is required.
+
+- The conclusion is limited to the supplied weak-probe, causal linear-response three-level model and stated fields. The shown cases do not establish arbitrary probe duration, stronger nonlinear probes or general atomic structure.
+
+- The reconstruction formulas correspond to article pp.063121-2-3, Eqs.(2)-(4),(11),(12). With the source symmetric Fourier convention $\widetilde f=(2\pi)^{-1/2}\int f(t)e^{-i\omega t}dt$, the real-dipole identity requires $\widetilde d(-\omega)=\widetilde d(\omega)^*$ and the physical continuation $\sigma(-\omega)=\sigma(\omega)$. The causal inverse transform is retained only for $t>0$ before folding with the finite probe. A global convention change is accepted only when absorption sign, time direction, phases and normalization transform consistently. The 50 fs task decay is post-propagation readout processing, not a relaxation term in Eq.(11).

cases/case06/resource_limits.json

@@ -0,0 +1,8 @@
+{
+  "cpu_cores": 8,
+  "nodes": 1,
+  "time_limit_minutes": 45,
+  "network_access": "disabled",
+  "temporary_storage_gib": 64,
+  "memory_policy": "No separate task-specific RAM limit is specified."
+}

cases/case06/sources.md

@@ -0,0 +1,30 @@
+# Scientific Sources — Case06
+
+## References
+
+Xiaoxia Wu, Linxuan Zhang, Shaofeng Zhang, and Difa Ye. 2021. *Theory of dipole moment reconstruction by attosecond transient absorption spectroscopy*. *Physical Review A*, 104, 063121. [Source](https://doi.org/10.1103/PhysRevA.104.063121)
+
+Theory of dipole moment reconstruction by attosecond transient absorption spectroscopy
+
+## Criterion-to-source crosswalk
+
+Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.
+
+| Criteria | Source locations, scientific use and limits |
+|---|---|
+| F1 | Wu et al. (2021), article p.063121-3, Eq.(11) and coupling paragraph: three-level g-a-f topology, energy gaps and transition moments; coherent physical dipole follows the stated basis convention. |
+| F2, M1 | Wu et al. (2021), article pp.063121-1-2, Eqs.(1)-(4), p.063121-3 Eq.(12) and p.063121-5 Appendix A Eqs.(A1)-(A5): absorption, even frequency extension and real causal response. |
+| F3 | Wu et al. (2021), article p.063121-4, Fig.2 caption specifies 50 fs decoherence scale. Applying it to the real dipole after propagation and using no extra Fourier window are explicit task conventions, not an added Hamiltonian relaxation law. |
+| O1, I1, M5 | Wu et al. (2021), article p.063121-4, Fig.3(b), caption and adjacent onset/long-time discussion: 100 as direct and convolved dipoles versus impulse response. |
+| O2, I2, M6 | Wu et al. (2021), article p.063121-4, Fig.2(b,c) for the 300 as case and Fig.3(c): persistent long-time direct/reconstructed agreement; record-truncation rejection follows the task numerical-evidence boundary. |
+| O3, I3 | Wu et al. (2021), article p.063121-4, Fig.3(d): 500 as finite-probe difference from impulse response, including late-time structure; full convolution remains faithful. |
+| O4, I4, M2, M3 | Wu et al. (2021), article pp.063121-2-4, Eqs.(2),(7),(10), Fig.3(b-d): finite waveform convolution differs from the impulse response and the distinction grows with probe duration. Eq.(7) is an explanatory approximation, not a substitute for the stated reconstruction. |
+| M4, M7, V1, V2 | Wu et al. (2021), article pp.063121-4-5, Fig.4, Eq.(13) and Sec.IV: linear-response/probe-duration fidelity boundary. Actual long-record evidence, processing safeguards and triggered alternative tests are task-defined; no exact correlation value is required. |
+
+## Formula and convention notes
+
+The reconstruction formulas correspond to article pp.063121-2-3, Eqs.(2)-(4),(11),(12). With the source symmetric Fourier convention $\widetilde f=(2\pi)^{-1/2}\int f(t)e^{-i\omega t}dt$, the real-dipole identity requires $\widetilde d(-\omega)=\widetilde d(\omega)^*$ and the physical continuation $\sigma(-\omega)=\sigma(\omega)$. The causal inverse transform is retained only for $t>0$ before folding with the finite probe. A global convention change is accepted only when absorption sign, time direction, phases and normalization transform consistently. The 50 fs task decay is post-propagation readout processing, not a relaxation term in Eq.(11).
+
+## Scope of the source anchors
+
+The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.

cases/case06/task.md

@@ -0,0 +1,150 @@
+# Causal time-domain inference in a driven three-state system
+
+## Background
+
+Attosecond transient-absorption spectra can encode the causal electronic
+response of a laser-dressed system. Recovering the corresponding motion in the
+time domain would make the spectrum a direct probe of ultrafast dynamics, but
+an experimental attosecond probe has a finite duration rather than the ideal
+impulsive form often assumed in such an interpretation.
+
+## Research problem
+
+Develop and assess a reproducible procedure, within causal linear-response
+theory, for recovering the time-dependent dipole motion of the infrared-dressed
+system below from its transient-absorption signal. Determine how faithfully the
+relevant motion can be recovered for attosecond-probe durations of 100, 300 and
+500 as, why the finite probe matters, and what physical claim is supported by
+the calculated evidence.
+
+The derivation, numerical realization, signal processing, diagnostic design,
+choice of figures and structure of the scientific argument are yours. Assess
+the reconstruction from computed evidence rather than assuming that it works.
+
+## Physical inputs
+
+Use atomic units for the dynamical calculation. The model contains a ground
+state $|g\rangle$, a dipole-allowed excited state $|a\rangle$ and an
+infrared-coupled state $|f\rangle$. The only nonzero transition dipoles in the
+model are
+
+$$
+\mu_{ga}=0.34,\qquad \mu_{af}=2.72,
+$$
+
+with energy differences
+
+$$
+E_a-E_g=21.057\ \mathrm{eV},\qquad E_f-E_a=-0.82\ \mathrm{eV}.
+$$
+
+The system is initially in $|g\rangle$ before either field is appreciable.
+Use electric-dipole coupling and the following linearly polarized fields. The
+attosecond probe is
+
+$$
+E_X(t)=E_{X0}e^{-\lambda |t|}\cos(\omega_X t),
+\qquad \tau_X=\frac{2\ln 2}{\lambda},
+$$
+
+with photon energy $21\ \mathrm{eV}$, peak intensity
+$10^{10}\ \mathrm{W\,cm^{-2}}$, and $\tau_X=100$, 300 or 500 as. Define the
+probe centre as $t=0$.
+
+The infrared field is
+
+$$
+E_{\mathrm{IR}}(t,\tau)=E_0 A(t-\tau)
+\cos[\omega_{\mathrm{IR}}(t-\tau)],
+$$
+
+where
+
+$$
+A(u)=
+\begin{cases}
+\cos^2\!\left(\dfrac{\omega_{\mathrm{IR}}u}{2N}\right),
+& |u|\le N\pi/\omega_{\mathrm{IR}},\\[4pt]
+0,&\text{otherwise},
+\end{cases}
+$$
+
+$N=10$, $\hbar\omega_{\mathrm{IR}}=0.82\ \mathrm{eV}$ and the peak intensity
+is $5\ \mathrm{TW\,cm^{-2}}$. Set the infrared-pulse centre five infrared
+optical cycles after the probe centre. Obtain field amplitudes from a standard,
+consistently reported intensity conversion.
+
+For this task, the source-model decoherence is imposed by the following
+author-supplied policy. First solve the driven three-state problem and obtain
+its physical real dipole $d_0(t)$. Then define
+
+$$
+d_{\mathrm{phys}}(t)=
+\begin{cases}
+d_0(t),&t\le 0,\\
+d_0(t)e^{-t/(50\ \mathrm{fs})},&t>0.
+\end{cases}
+$$
+
+Apply this operation before constructing the absorption signal. Do not put it
+in the Hamiltonian, reinterpret it as population or amplitude damping, or
+apply an additional Fourier apodization window.
+
+State the time, frequency, Fourier-sign, dipole-sign and display conventions
+used in your work. Absolute arbitrary-unit vertical scale is not a grading
+target.
+
+## Method and scope
+
+Use the standard three-level time-dependent Schrödinger equation for the
+stated couplings and a causal linear-response or Kramers-Kronig reconstruction
+from the positive-frequency transient-absorption signal. You may choose and
+cite standard formulations consistent with these method families. Do not add
+levels, ionization channels or nonlinear probe response to the graded model.
+
+All numerical choices not fixed above are yours. Check that the reported
+signals are sufficiently reliable and reproducible to support your claim; no
+particular grid, record length, propagator, transform algorithm, regularizer,
+comparison metric or refinement sequence is prescribed.
+
+## Submission
+
+Submit one self-contained scientific report and an offline reproduction
+package. The report must answer the research question from your calculated
+time-dependent reconstruction and must contain enough quantitative evidence
+to audit every probe-duration-dependent claim. The selection and organization
+of that evidence are yours.
+
+Include a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge.
+
+Include the derivation actually used, source code, an executable command or
+script, machine-readable data underlying the reported evidence, plotting or
+analysis code, references, and concise run and environment information. No
+fixed file tree, filename scheme, complete exploratory history or
+examiner-selected intermediate plot is required.
+
+The active examination resources and limits are defined in the companion
+`resource_limits.json`. All retained production calculations must run
+within that fixed allocation and active wall time. More expensive modelling
+does not receive additional credit.
+
+## Reference and integrity policy
+
+This examination is conducted without network access or live literature
+retrieval. You may rely on your existing general scientific knowledge and, if any are
+explicitly supplied with the examination, on those offline materials or
+software documentation. Record every such source actually consulted. For formulas,
+methods, constants, or conventions used from general knowledge rather than a
+consulted source, state enough of the method basis, definition, value, units,
+and convention to make the calculation auditable; do not invent a citation.
+You are not required to identify or prove a publication date or to retrieve
+literature during the examination.
+
+The hidden target article and its identifying metadata, figures or captions,
+supplementary material, author code or data, target-specific reproduction
+code, solution or scoring material, online solutions, and worked
+reproductions of this case must not be used. All submitted scientific figures
+and numerical data must be generated by your own implementation of the stated
+problem.
+
+See [submission requirements](../../submission_requirements.md) for the common submission entry points.

cases/case07/grading_rubric.json

@@ -0,0 +1,630 @@
+{
+  "case_id": "Case07",
+  "title": "Case07 — High-order harmonic generation as induced by a quantized field: Phase-space picture",
+  "atoms": [
+    {
+      "criterion_id": "F1",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.",
+      "award_conditions": [
+        "The complete no-RWA Rabi Hamiltonian and all four initial/coupling cases use consistent units, basis phases and physical initial states."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F2",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Derive a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.",
+      "award_conditions": [
+        "A computable complete moving lattice has a valid nonorthogonal initial Gram solution, same-branch metric and cross-branch atomic coupling."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-4-5, Eqs.(17)-(24): nonorthogonal coherent-state initialization, moving-lattice metric and atomic cross-branch mixing."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F3",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Trace the atom out of the propagated complete state and construct a normalized reduced-field phase-space object, accepting equivalent normalized representations explicitly mapped to that reduced state.",
+      "award_conditions": [
+        "The atom is traced out of the complete propagated state and the reduced-field phase-space object is normalized and explicitly related to that state."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-5-6, Sec.III.B, Eqs.(25)-(31), explicit reduced density operator paragraph: partial trace over atom and normalized field phase-space construction."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F4",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.",
+      "award_conditions": [
+        "The harmonic observable is the material dipole spectrum; derivative alternatives derive frequency reweighting without manufacturing ordering or mechanism."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "O1",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.",
+      "award_conditions": [
+        "Normalized first-cycle Case-A phase-space evidence is correctly time-bound and resolves genuine full-model branch motion, mixing, broadening or interference.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (Derive a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.); F3 (Trace the atom out of the propagated complete state and construct a normalized reduced-field phase-space object, accepting equivalent normalized representations explicitly mapped to that reduced state.)",
+        "Preserve independently valid work in O2, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model target."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O2",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.",
+      "award_conditions": [
+        "Case-B 20-cycle material-dipole spectral evidence is reconstructible and resolves principal peaks, plateau/cutoff and global morphology.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F4 (Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.)",
+        "Preserve independently valid work in O3, O4, O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O3",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.",
+      "award_conditions": [
+        "Case-C 20-cycle material-dipole spectral evidence is reconstructible and resolves principal peaks, plateau/cutoff and global morphology.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F4 (Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.)",
+        "Preserve independently valid work in O2, O4, O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O4",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.",
+      "award_conditions": [
+        "Case-D 20-cycle material-dipole spectral evidence is reconstructible and resolves principal peaks, plateau/cutoff and global morphology.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F4 (Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.)",
+        "Preserve independently valid work in O2, O3, O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "I1",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify coherent-field branch motion/separation, return and full-model mixing, broadening or interference in the submitted Case-A evidence; the source's minimal two-state morphology is not required.",
+      "award_conditions": [
+        "The candidate identifies branch motion/separation, return and complete-model changes in their own Case-A evidence without imposing minimal-two-state morphology."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O1 (Present normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.)",
+        "Preserve independently valid work in I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model target."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I2",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify pronounced common harmonic peaks, plateau-like ranges and cutoffs in the submitted B-D spectra, rather than merely reporting spectrum generation.",
+      "award_conditions": [
+        "The candidate identifies material peaks, plateau-like ranges and cutoffs in all submitted B-D spectra."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.)",
+        "Preserve independently valid work in I1, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I3",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify the correct extension of the cutoff with initial amplitude and case-dependent changes in peak detail from B-D evidence.",
+      "award_conditions": [
+        "The candidate identifies growing cutoff with coherent amplitude and actual case-dependent peak changes."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.)",
+        "Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M1",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use any self-consistent Hamiltonian-term decomposition, analytic relation, intervention or equivalent evidence to explain the field/free-plus-interaction contribution to coherent-field or branch motion; atomic-term omission, closed trajectories and phase traces are accepted examples, not prescribed forms.",
+      "award_conditions": [
+        "A valid Hamiltonian decomposition, analytic relation or intervention explains field/free-plus-interaction branch motion with an established physical consequence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M2",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Distinguish relevant full-Hamiltonian contributions to changing material dipole and radiation by a commutator with computed/analytic consequence, term intervention or equivalent evidence. Proving constant dipole after removing the atomic term is one accepted realization, not the sole control.",
+      "award_conditions": [
+        "A commutator, full-vs-RWA or other valid intervention isolates relevant Hamiltonian-term contributions to the changing dipole/radiation, not merely model names."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M3",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.",
+      "award_conditions": [
+        "Submitted evidence closes the physical-term to branch change to time-dependent dipole to radiation causal chain; isolated line/weight changes are insufficient."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: M2 (Distinguish relevant full-Hamiltonian contributions to changing material dipole and radiation by a commutator with computed/analytic consequence, term intervention or equivalent evidence. Proving constant dipole after removing the atomic term is one accepted realization, not the sole control.)",
+        "Preserve independently valid work in M1, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M4",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain which Case-A complete-lattice phase-space structures arise from branch motion, atomic mixing and full-state reduction, without treating a smooth minimal two-state image as uniquely correct.",
+      "award_conditions": [
+        "The candidate attributes actual complete-lattice phase-space structure to branch motion, atomic mixing and reduced-state construction rather than a prescribed smooth picture."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I1 (Identify coherent-field branch motion/separation, return and full-model mixing, broadening or interference in the submitted Case-A evidence; the source's minimal two-state morphology is not required.)",
+        "Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model target."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M5",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.",
+      "award_conditions": [
+        "All B-D spectra ground the cutoff/peak amplitude-dependence explanation and distinguish it from frequency reweighting or display rescaling."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I2 (Identify pronounced common harmonic peaks, plateau-like ranges and cutoffs in the submitted B-D spectra, rather than merely reporting spectrum generation.); I3 (Identify the correct extension of the cutoff with initial amplitude and case-dependent changes in peak detail from B-D evidence.)",
+        "Preserve independently valid work in M1, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M6",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Connect reduced-field reorganization and material-dipole HHG evidence, explaining how they jointly constrain rather than replace the central physical picture.",
+      "award_conditions": [
+        "Phase-space reorganization and material-dipole spectra jointly constrain the physical account; one does not substitute for the other."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I1 (Identify coherent-field branch motion/separation, return and full-model mixing, broadening or interference in the submitted Case-A evidence; the source's minimal two-state morphology is not required.); I2 (Identify pronounced common harmonic peaks, plateau-like ranges and cutoffs in the submitted B-D spectra, rather than merely reporting spectrum generation.)",
+        "Preserve independently valid work in M3, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M7",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Reconcile auxiliary models/controls with the complete no-RWA calculation, answering term contributions and amplitude dependence with the strongest conclusion supported by common physical endpoints.",
+      "award_conditions": [
+        "Auxiliary controls and complete no-RWA endpoints support a mutually consistent account of term contributions and coherent-amplitude dependence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: M3 (Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.); M5 (Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.); M6 (Connect reduced-field reorganization and material-dipole HHG evidence, explaining how they jointly constrain rather than replace the central physical picture.)",
+        "Preserve independently valid work in M1, M2, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V1",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Positively state the two-level, single-mode, complete no-RWA and four-case evidence domain, distinguishing general phase-space/HHG conclusions from model-specific detail.",
+      "award_conditions": [
+        "The candidate positively states the two-level, single-mode, complete no-RWA four-case evidence domain and model-specific limits."
+      ],
+      "applicability_and_na": [
+        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-7-9, Sec.V peak-detail limitation and Sec.VI-VII generalization/scope; normalization and complete-lattice stability follow Eqs.(18),(24). Positive model scope and triggered validation are task duties, not a demand to reproduce one lattice size."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V2",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.",
+      "award_conditions": [
+        "Only a concrete triggered state, metric, transform or claim risk requires discriminating evidence or narrower claims; otherwise N/A."
+      ],
+      "applicability_and_na": [
+        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
+        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.",
+        "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.",
+        "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.",
+        "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.",
+        "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence."
+      ],
+      "source_support": [
+        "Gombkoto et al. (2020), article pp.013418-7-9, Sec.V peak-detail limitation and Sec.VI-VII generalization/scope; normalization and complete-lattice stability follow Eqs.(18),(24). Positive model scope and triggered validation are task duties, not a demand to reproduce one lattice size."
+      ],
+      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    }
+  ],
+  "case_scientific_rules": [
+    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
+    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
+    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
+    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
+    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
+    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
+    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
+    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
+    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
+    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
+    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
+    "The complete Hamiltonian, not an RWA or reduced free-field orbit, is the production target. A nonorthogonal moving basis requires initialization, same-branch metric and time-dependent cross-branch overlaps.",
+    "Clipping, smoothing or time-slice summation cannot manufacture source-panel resemblance. The minimal eight-snapshot montage and a fixed number of figures are not required.",
+    "No absolute spectral normalization is source-fixed. A declared positive display scale is allowed, but cannot support absolute-yield or exact cross-case-magnitude claims.",
+    "M3 can be supported by a valid term intervention reaching the changing-dipole endpoint without a compulsory additional Case-A phase-space identification premise; the separately commissioned phase-space branch remains assessed.",
+    "The canonical Hamiltonian is",
+    "$$\nH=\\frac{\\hbar\\omega_0}{2}\\sigma_z\n+\\hbar\\omega a^\\dagger a\n+\\hbar\\Omega\\sigma_x(a+a^\\dagger),\n$$",
+    "without RWA. A branch-dependent displacement diagonalizes the field plus interaction part $\\widetilde H=H-H_a$. For a $\\sigma_x$ eigenstate, an initial coherent state therefore follows an analytically moving coherent label and accumulates a branch phase. With $H_a$ restored, a complete moving von Neumann lattice expansion is nonorthogonal. Its static Gram problem fixes the initial coefficients, its same-branch Gram matrices provide the generalized metric, and its time-dependent cross-branch overlaps transmit the atomic-term coupling. Students must derive a physically equivalent end-to-end system; the complete recurrence is not stated in task.",
+    "The initial atomic ground-state phase in the $\\sigma_x$ basis and the sign of $\\Omega$ may be changed consistently. Grade invariant physical states after the corresponding branch rephasing or phase-space reflection.",
+    "The material dipole is proportional to $\\langle\\sigma_x\\rangle(t)$. The source HHG object is the squared Fourier modulus of that time record over the stated 20 cycles. A dipole-, velocity- or acceleration-form spectrum may be accepted only when the student derives the transform relation and shows that frequency reweighting does not manufacture the claimed harmonic ordering or mechanism. The reduced field state is obtained by tracing over the atom, and a standard normalized Wigner function provides the canonical phase-space observable. Equivalent normalized phase-space constructions are acceptable only when their relation to the reduced field state is explicit.",
+    "The source's smooth eight-snapshot Fig. 4 top uses a minimal two-moving-state approximation. The present task does not require that approximation or its montage. A correct complete-lattice Wigner function may contain stable multi-lobe or interference structure absent from that panel and must not be penalized for the difference. Conversely, smoothing, clipping or summing time slices cannot manufacture agreement.",
+    "Under $\\widetilde H$, one initial coherent label separates into two branch-dependent moving coherent components and returns after an optical cycle. The branch phase becomes more structured as the coherent amplitude grows.",
+    "Because $[\\widetilde H,\\sigma_x]=0$, the dipole expectation is constant if the atomic Hamiltonian is omitted. The atomic term mixes the moving branches and is essential for a changing dipole and secondary harmonic radiation.",
+    "A complete first-cycle field Wigner calculation must begin from the stated coherent field, preserve normalization and resolve genuine branch motion, mixing, broadening or interference supported by its own full-state data. The exact minimal-source morphology is not required.",
+    "Cases B-D show pronounced harmonic peaks, a plateau-like range and a cutoff. The cutoff extends with increasing $\\alpha_0$, while the detailed peak pattern changes. Fine-structure mechanism is outside the source's claimed scope.",
+    "No source-defined absolute spectral normalization exists. A declared positive display scale is acceptable but cannot support absolute-yield or exact cross-case-magnitude conclusions.",
+    "For F2-F4/M1-M3, article pp.013418-3-5, Eqs.(14),(18),(22)-(26), one consistent branch convention is $\\gamma=-\\Omega/\\omega$,\n$$\\alpha_\\pm(t)=\\pm\\gamma+(\\alpha\\mp\\gamma)e^{-i\\omega t},\\quad\ni\\hbar N^{++}\\dot c^+=(\\hbar\\omega_0/2)N^{+-}c^-,\\quad\ni\\hbar N^{--}\\dot c^-=(\\hbar\\omega_0/2)N^{-+}c^+.$$\nThe static Gram inverse initializes coefficients; the metric norm is $(c^+)^\\dagger N^{++}c^+ +(c^-)^\\dagger N^{--}c^-=1$. The invariant field object is $\\rho_f=\\mathrm{Tr}_a|\\Psi\\rangle\\langle\\Psi|$ and $\\int W(\\alpha)d^2\\alpha=1$. With $\\widetilde H=H-H_a$, $[\\widetilde H,\\sigma_x]=0$, whereas $\\dot{\\langle\\sigma_x\\rangle}=-\\omega_0\\langle\\sigma_y\\rangle$ in the usual Pauli convention for the full Hamiltonian. These identities explain why coherent-label motion alone is not harmonic radiation; equivalent causal term controls are accepted."
+  ],
+  "closure_requirements": {
+    "RC0": [
+      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
+      "Required indispensable claim CL1, central physical object: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F2 (Derive a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC1": [
+      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
+      "Required co primary claim CL2, indispensable material component: O1 (Present normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL3, indispensable material component: all of: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC2": [
+      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
+      "Required co primary claim CL2, principal mechanism or commissioned conclusion: M3 (Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL3, principal mechanism or commissioned conclusion: M5 (Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL4, principal mechanism or commissioned conclusion: M7 (Reconcile auxiliary models/controls with the complete no-RWA calculation, answering term contributions and amplitude dependence with the strongest conclusion supported by common physical endpoints.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC3": [
+      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
+      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
+      "Required co primary claim CL4, material validation/scope: V2 (Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC4": [
+      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
+      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
+      "Close CL1 central physical object: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F2 (Derive a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.).",
+      "Close CL2 indispensable material component: O1 (Present normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.).",
+      "Close CL2 principal mechanism or commissioned conclusion: M3 (Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.).",
+      "Close CL3 indispensable material component: all of: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.).",
+      "Close CL3 principal mechanism or commissioned conclusion: M5 (Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.).",
+      "Close CL4 principal mechanism or commissioned conclusion: M7 (Reconcile auxiliary models/controls with the complete no-RWA calculation, answering term contributions and amplitude dependence with the strongest conclusion supported by common physical endpoints.).",
+      "Close CL4 material validation/scope: V2 (Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.).",
+      "Supporting claim CL5 is separately scored but does not determine overall closure: Positively state the two-level, single-mode, complete no-RWA and four-case evidence domain, distinguishing general phase-space/HHG conclusions from model-specific detail."
+    ]
+  },
+  "references": [
+    {
+      "citation": "Ákos Gombkötő, Sándor Varró, Péter Mati, and Péter Földi. 2020. *High-order harmonic generation as induced by a quantized field: Phase-space picture*. *Physical Review A*, 101, 013418.",
+      "url": "https://doi.org/10.1103/PhysRevA.101.013418",
+      "scientific_scope": "High-order harmonic generation as induced by a quantized field: Phase-space picture",
+      "anchors": [
+        "Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent.",
+        "Gombkoto et al. (2020), article pp.013418-4-5, Eqs.(17)-(24): nonorthogonal coherent-state initialization, moving-lattice metric and atomic cross-branch mixing.",
+        "Gombkoto et al. (2020), article pp.013418-5-6, Sec.III.B, Eqs.(25)-(31), explicit reduced density operator paragraph: partial trace over atom and normalized field phase-space construction.",
+        "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match.",
+        "Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model target.",
+        "Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient.",
+        "Gombkoto et al. (2020), article pp.013418-7-9, Sec.V peak-detail limitation and Sec.VI-VII generalization/scope; normalization and complete-lattice stability follow Eqs.(18),(24). Positive model scope and triggered validation are task duties, not a demand to reproduce one lattice size."
+      ]
+    }
+  ]
+}

cases/case07/grading_rubric.md

@@ -0,0 +1,937 @@
+# Grading Rubric — Case07
+
+Case07 — High-order harmonic generation as induced by a quantized field: Phase-space picture
+
+## Atomic Scoring Criteria
+
+Each criterion awards 0 or 0.5 points, for a maximum of 10. Explicit N/A rules apply where stated.
+
+### F1 — F — 0.5 points
+
+**Scientific requirement**
+
+Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.
+
+**Conditions for credit**
+
+- The complete no-RWA Rabi Hamiltonian and all four initial/coupling cases use consistent units, basis phases and physical initial states.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F2 — F — 0.5 points
+
+**Scientific requirement**
+
+Derive a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.
+
+**Conditions for credit**
+
+- A computable complete moving lattice has a valid nonorthogonal initial Gram solution, same-branch metric and cross-branch atomic coupling.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-4-5, Eqs.(17)-(24): nonorthogonal coherent-state initialization, moving-lattice metric and atomic cross-branch mixing.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F3 — F — 0.5 points
+
+**Scientific requirement**
+
+Trace the atom out of the propagated complete state and construct a normalized reduced-field phase-space object, accepting equivalent normalized representations explicitly mapped to that reduced state.
+
+**Conditions for credit**
+
+- The atom is traced out of the complete propagated state and the reduced-field phase-space object is normalized and explicitly related to that state.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-5-6, Sec.III.B, Eqs.(25)-(31), explicit reduced density operator paragraph: partial trace over atom and normalized field phase-space construction.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F4 — F — 0.5 points
+
+**Scientific requirement**
+
+Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.
+
+**Conditions for credit**
+
+- The harmonic observable is the material dipole spectrum; derivative alternatives derive frequency reweighting without manufacturing ordering or mechanism.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### O1 — O — 0.5 points
+
+**Scientific requirement**
+
+Present normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.
+
+**Conditions for credit**
+
+- Normalized first-cycle Case-A phase-space evidence is correctly time-bound and resolves genuine full-model branch motion, mixing, broadening or interference.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (Derive a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.); F3 (Trace the atom out of the propagated complete state and construct a normalized reduced-field phase-space object, accepting equivalent normalized representations explicitly mapped to that reduced state.)
+
+- Preserve independently valid work in O2, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model target.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O2 — O — 0.5 points
+
+**Scientific requirement**
+
+Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.
+
+**Conditions for credit**
+
+- Case-B 20-cycle material-dipole spectral evidence is reconstructible and resolves principal peaks, plateau/cutoff and global morphology.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F4 (Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.)
+
+- Preserve independently valid work in O3, O4, O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O3 — O — 0.5 points
+
+**Scientific requirement**
+
+Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.
+
+**Conditions for credit**
+
+- Case-C 20-cycle material-dipole spectral evidence is reconstructible and resolves principal peaks, plateau/cutoff and global morphology.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F4 (Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.)
+
+- Preserve independently valid work in O2, O4, O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O4 — O — 0.5 points
+
+**Scientific requirement**
+
+Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.
+
+**Conditions for credit**
+
+- Case-D 20-cycle material-dipole spectral evidence is reconstructible and resolves principal peaks, plateau/cutoff and global morphology.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F4 (Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.)
+
+- Preserve independently valid work in O2, O3, O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### I1 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify coherent-field branch motion/separation, return and full-model mixing, broadening or interference in the submitted Case-A evidence; the source's minimal two-state morphology is not required.
+
+**Conditions for credit**
+
+- The candidate identifies branch motion/separation, return and complete-model changes in their own Case-A evidence without imposing minimal-two-state morphology.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O1 (Present normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.)
+
+- Preserve independently valid work in I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model target.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I2 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify pronounced common harmonic peaks, plateau-like ranges and cutoffs in the submitted B-D spectra, rather than merely reporting spectrum generation.
+
+**Conditions for credit**
+
+- The candidate identifies material peaks, plateau-like ranges and cutoffs in all submitted B-D spectra.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.)
+
+- Preserve independently valid work in I1, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I3 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify the correct extension of the cutoff with initial amplitude and case-dependent changes in peak detail from B-D evidence.
+
+**Conditions for credit**
+
+- The candidate identifies growing cutoff with coherent amplitude and actual case-dependent peak changes.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.)
+
+- Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M1 — M — 0.5 points
+
+**Scientific requirement**
+
+Use any self-consistent Hamiltonian-term decomposition, analytic relation, intervention or equivalent evidence to explain the field/free-plus-interaction contribution to coherent-field or branch motion; atomic-term omission, closed trajectories and phase traces are accepted examples, not prescribed forms.
+
+**Conditions for credit**
+
+- A valid Hamiltonian decomposition, analytic relation or intervention explains field/free-plus-interaction branch motion with an established physical consequence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M2 — M — 0.5 points
+
+**Scientific requirement**
+
+Distinguish relevant full-Hamiltonian contributions to changing material dipole and radiation by a commutator with computed/analytic consequence, term intervention or equivalent evidence. Proving constant dipole after removing the atomic term is one accepted realization, not the sole control.
+
+**Conditions for credit**
+
+- A commutator, full-vs-RWA or other valid intervention isolates relevant Hamiltonian-term contributions to the changing dipole/radiation, not merely model names.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M3 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.
+
+**Conditions for credit**
+
+- Submitted evidence closes the physical-term to branch change to time-dependent dipole to radiation causal chain; isolated line/weight changes are insufficient.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: M2 (Distinguish relevant full-Hamiltonian contributions to changing material dipole and radiation by a commutator with computed/analytic consequence, term intervention or equivalent evidence. Proving constant dipole after removing the atomic term is one accepted realization, not the sole control.)
+
+- Preserve independently valid work in M1, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M4 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain which Case-A complete-lattice phase-space structures arise from branch motion, atomic mixing and full-state reduction, without treating a smooth minimal two-state image as uniquely correct.
+
+**Conditions for credit**
+
+- The candidate attributes actual complete-lattice phase-space structure to branch motion, atomic mixing and reduced-state construction rather than a prescribed smooth picture.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I1 (Identify coherent-field branch motion/separation, return and full-model mixing, broadening or interference in the submitted Case-A evidence; the source's minimal two-state morphology is not required.)
+
+- Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model target.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M5 — M — 0.5 points
+
+**Scientific requirement**
+
+Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.
+
+**Conditions for credit**
+
+- All B-D spectra ground the cutoff/peak amplitude-dependence explanation and distinguish it from frequency reweighting or display rescaling.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: I2 (Identify pronounced common harmonic peaks, plateau-like ranges and cutoffs in the submitted B-D spectra, rather than merely reporting spectrum generation.); I3 (Identify the correct extension of the cutoff with initial amplitude and case-dependent changes in peak detail from B-D evidence.)
+
+- Preserve independently valid work in M1, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M6 — M — 0.5 points
+
+**Scientific requirement**
+
+Connect reduced-field reorganization and material-dipole HHG evidence, explaining how they jointly constrain rather than replace the central physical picture.
+
+**Conditions for credit**
+
+- Phase-space reorganization and material-dipole spectra jointly constrain the physical account; one does not substitute for the other.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: I1 (Identify coherent-field branch motion/separation, return and full-model mixing, broadening or interference in the submitted Case-A evidence; the source's minimal two-state morphology is not required.); I2 (Identify pronounced common harmonic peaks, plateau-like ranges and cutoffs in the submitted B-D spectra, rather than merely reporting spectrum generation.)
+
+- Preserve independently valid work in M3, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M7 — M — 0.5 points
+
+**Scientific requirement**
+
+Reconcile auxiliary models/controls with the complete no-RWA calculation, answering term contributions and amplitude dependence with the strongest conclusion supported by common physical endpoints.
+
+**Conditions for credit**
+
+- Auxiliary controls and complete no-RWA endpoints support a mutually consistent account of term contributions and coherent-amplitude dependence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: M3 (Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.); M5 (Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.); M6 (Connect reduced-field reorganization and material-dipole HHG evidence, explaining how they jointly constrain rather than replace the central physical picture.)
+
+- Preserve independently valid work in M1, M2, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V1 — V — 0.5 points
+
+**Scientific requirement**
+
+Positively state the two-level, single-mode, complete no-RWA and four-case evidence domain, distinguishing general phase-space/HHG conclusions from model-specific detail.
+
+**Conditions for credit**
+
+- The candidate positively states the two-level, single-mode, complete no-RWA four-case evidence domain and model-specific limits.
+
+**Applicability and N/A**
+
+- This positive scientific scope/evidence duty is unconditional; N/A is not permitted.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-7-9, Sec.V peak-detail limitation and Sec.VI-VII generalization/scope; normalization and complete-lattice stability follow Eqs.(18),(24). Positive model scope and triggered validation are task duties, not a demand to reproduce one lattice size.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V2 — V — 0.5 points
+
+**Scientific requirement**
+
+Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.
+
+**Conditions for credit**
+
+- Only a concrete triggered state, metric, transform or claim risk requires discriminating evidence or narrower claims; otherwise N/A.
+
+**Applicability and N/A**
+
+- Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.
+
+- If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.
+
+- A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.
+
+- Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.
+
+- Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.
+
+- Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence.
+
+**Scientific source locations**
+
+- Gombkoto et al. (2020), article pp.013418-7-9, Sec.V peak-detail limitation and Sec.VI-VII generalization/scope; normalization and complete-lattice stability follow Eqs.(18),(24). Positive model scope and triggered validation are task duties, not a demand to reproduce one lattice size.
+
+**Research Closure relation**
+
+Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+## Research Closure Requirements
+
+### RC0
+
+- The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.
+
+- Required indispensable claim CL1, central physical object: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F2 (Derive a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC1
+
+- With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.
+
+- Required co primary claim CL2, indispensable material component: O1 (Present normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL3, indispensable material component: all of: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC2
+
+- With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.
+
+- Required co primary claim CL2, principal mechanism or commissioned conclusion: M3 (Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL3, principal mechanism or commissioned conclusion: M5 (Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL4, principal mechanism or commissioned conclusion: M7 (Reconcile auxiliary models/controls with the complete no-RWA calculation, answering term contributions and amplitude dependence with the strongest conclusion supported by common physical endpoints.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC3
+
+- With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.
+
+- Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.
+
+- Required co primary claim CL4, material validation/scope: V2 (Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC4
+
+- All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.
+
+- Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.
+
+- Close CL1 central physical object: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F2 (Derive a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.).
+
+- Close CL2 indispensable material component: O1 (Present normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.).
+
+- Close CL2 principal mechanism or commissioned conclusion: M3 (Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.).
+
+- Close CL3 indispensable material component: all of: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.).
+
+- Close CL3 principal mechanism or commissioned conclusion: M5 (Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.).
+
+- Close CL4 principal mechanism or commissioned conclusion: M7 (Reconcile auxiliary models/controls with the complete no-RWA calculation, answering term contributions and amplitude dependence with the strongest conclusion supported by common physical endpoints.).
+
+- Close CL4 material validation/scope: V2 (Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.).
+
+- Supporting claim CL5 is separately scored but does not determine overall closure: Positively state the two-level, single-mode, complete no-RWA and four-case evidence domain, distinguishing general phase-space/HHG conclusions from model-specific detail.
+
+## Applicability and Equivalent Evidence
+
+- Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.
+
+- Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.
+
+- For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.
+
+- Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.
+
+- Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.
+
+- Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.
+
+- Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.
+
+- Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.
+
+- Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.
+
+- Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.
+
+- A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.
+
+- The complete Hamiltonian, not an RWA or reduced free-field orbit, is the production target. A nonorthogonal moving basis requires initialization, same-branch metric and time-dependent cross-branch overlaps.
+
+- Clipping, smoothing or time-slice summation cannot manufacture source-panel resemblance. The minimal eight-snapshot montage and a fixed number of figures are not required.
+
+- No absolute spectral normalization is source-fixed. A declared positive display scale is allowed, but cannot support absolute-yield or exact cross-case-magnitude claims.
+
+- M3 can be supported by a valid term intervention reaching the changing-dipole endpoint without a compulsory additional Case-A phase-space identification premise; the separately commissioned phase-space branch remains assessed.
+
+- The canonical Hamiltonian is
+
+$$
+H=\frac{\hbar\omega_0}{2}\sigma_z
++\hbar\omega a^\dagger a
++\hbar\Omega\sigma_x(a+a^\dagger),
+$$
+
+- without RWA. A branch-dependent displacement diagonalizes the field plus interaction part $\widetilde H=H-H_a$. For a $\sigma_x$ eigenstate, an initial coherent state therefore follows an analytically moving coherent label and accumulates a branch phase. With $H_a$ restored, a complete moving von Neumann lattice expansion is nonorthogonal. Its static Gram problem fixes the initial coefficients, its same-branch Gram matrices provide the generalized metric, and its time-dependent cross-branch overlaps transmit the atomic-term coupling. Students must derive a physically equivalent end-to-end system; the complete recurrence is not stated in task.
+
+- The initial atomic ground-state phase in the $\sigma_x$ basis and the sign of $\Omega$ may be changed consistently. Grade invariant physical states after the corresponding branch rephasing or phase-space reflection.
+
+- The material dipole is proportional to $\langle\sigma_x\rangle(t)$. The source HHG object is the squared Fourier modulus of that time record over the stated 20 cycles. A dipole-, velocity- or acceleration-form spectrum may be accepted only when the student derives the transform relation and shows that frequency reweighting does not manufacture the claimed harmonic ordering or mechanism. The reduced field state is obtained by tracing over the atom, and a standard normalized Wigner function provides the canonical phase-space observable. Equivalent normalized phase-space constructions are acceptable only when their relation to the reduced field state is explicit.
+
+- The source's smooth eight-snapshot Fig. 4 top uses a minimal two-moving-state approximation. The present task does not require that approximation or its montage. A correct complete-lattice Wigner function may contain stable multi-lobe or interference structure absent from that panel and must not be penalized for the difference. Conversely, smoothing, clipping or summing time slices cannot manufacture agreement.
+
+- Under $\widetilde H$, one initial coherent label separates into two branch-dependent moving coherent components and returns after an optical cycle. The branch phase becomes more structured as the coherent amplitude grows.
+
+- Because $[\widetilde H,\sigma_x]=0$, the dipole expectation is constant if the atomic Hamiltonian is omitted. The atomic term mixes the moving branches and is essential for a changing dipole and secondary harmonic radiation.
+
+- A complete first-cycle field Wigner calculation must begin from the stated coherent field, preserve normalization and resolve genuine branch motion, mixing, broadening or interference supported by its own full-state data. The exact minimal-source morphology is not required.
+
+- Cases B-D show pronounced harmonic peaks, a plateau-like range and a cutoff. The cutoff extends with increasing $\alpha_0$, while the detailed peak pattern changes. Fine-structure mechanism is outside the source's claimed scope.
+
+- No source-defined absolute spectral normalization exists. A declared positive display scale is acceptable but cannot support absolute-yield or exact cross-case-magnitude conclusions.
+
+For F2-F4/M1-M3, article pp.013418-3-5, Eqs.(14),(18),(22)-(26), one consistent branch convention is $\gamma=-\Omega/\omega$,
+$$\alpha_\pm(t)=\pm\gamma+(\alpha\mp\gamma)e^{-i\omega t},\quad
+i\hbar N^{++}\dot c^+=(\hbar\omega_0/2)N^{+-}c^-,\quad
+i\hbar N^{--}\dot c^-=(\hbar\omega_0/2)N^{-+}c^+.$$
+The static Gram inverse initializes coefficients; the metric norm is $(c^+)^\dagger N^{++}c^+ +(c^-)^\dagger N^{--}c^-=1$. The invariant field object is $\rho_f=\mathrm{Tr}_a|\Psi\rangle\langle\Psi|$ and $\int W(\alpha)d^2\alpha=1$. With $\widetilde H=H-H_a$, $[\widetilde H,\sigma_x]=0$, whereas $\dot{\langle\sigma_x\rangle}=-\omega_0\langle\sigma_y\rangle$ in the usual Pauli convention for the full Hamiltonian. These identities explain why coherent-label motion alone is not harmonic radiation; equivalent causal term controls are accepted.

cases/case07/resource_limits.json

@@ -0,0 +1,8 @@
+{
+  "cpu_cores": 8,
+  "nodes": 1,
+  "time_limit_minutes": 45,
+  "network_access": "disabled",
+  "temporary_storage_gib": 64,
+  "memory_policy": "No separate task-specific RAM limit is specified."
+}

cases/case07/sources.md

@@ -0,0 +1,33 @@
+# Scientific Sources — Case07
+
+## References
+
+Ákos Gombkötő, Sándor Varró, Péter Mati, and Péter Földi. 2020. *High-order harmonic generation as induced by a quantized field: Phase-space picture*. *Physical Review A*, 101, 013418. [Source](https://doi.org/10.1103/PhysRevA.101.013418)
+
+High-order harmonic generation as induced by a quantized field: Phase-space picture
+
+## Criterion-to-source crosswalk
+
+Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.
+
+| Criteria | Source locations, scientific use and limits |
+|---|---|
+| F1, M1, M2 | Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent. |
+| F2 | Gombkoto et al. (2020), article pp.013418-4-5, Eqs.(17)-(24): nonorthogonal coherent-state initialization, moving-lattice metric and atomic cross-branch mixing. |
+| F3 | Gombkoto et al. (2020), article pp.013418-5-6, Sec.III.B, Eqs.(25)-(31), explicit reduced density operator paragraph: partial trace over atom and normalized field phase-space construction. |
+| F4, O2, O3, O4, I2, I3, M5 | Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match. |
+| O1, I1, M4 | Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model target. |
+| M3, M6, M7 | Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient. |
+| V1, V2 | Gombkoto et al. (2020), article pp.013418-7-9, Sec.V peak-detail limitation and Sec.VI-VII generalization/scope; normalization and complete-lattice stability follow Eqs.(18),(24). Positive model scope and triggered validation are task duties, not a demand to reproduce one lattice size. |
+
+## Formula and convention notes
+
+For F2-F4/M1-M3, article pp.013418-3-5, Eqs.(14),(18),(22)-(26), one consistent branch convention is $\gamma=-\Omega/\omega$,
+$$\alpha_\pm(t)=\pm\gamma+(\alpha\mp\gamma)e^{-i\omega t},\quad
+i\hbar N^{++}\dot c^+=(\hbar\omega_0/2)N^{+-}c^-,\quad
+i\hbar N^{--}\dot c^-=(\hbar\omega_0/2)N^{-+}c^+.$$
+The static Gram inverse initializes coefficients; the metric norm is $(c^+)^\dagger N^{++}c^+ +(c^-)^\dagger N^{--}c^-=1$. The invariant field object is $\rho_f=\mathrm{Tr}_a|\Psi\rangle\langle\Psi|$ and $\int W(\alpha)d^2\alpha=1$. With $\widetilde H=H-H_a$, $[\widetilde H,\sigma_x]=0$, whereas $\dot{\langle\sigma_x\rangle}=-\omega_0\langle\sigma_y\rangle$ in the usual Pauli convention for the full Hamiltonian. These identities explain why coherent-label motion alone is not harmonic radiation; equivalent causal term controls are accepted.
+
+## Scope of the source anchors
+
+The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.

cases/case07/task.md

@@ -0,0 +1,121 @@
+# Nonlinear radiation and field-state dynamics in a quantized two-level model
+
+## Background
+
+High-order harmonic generation is usually formulated with a classical driving
+field. A fully quantized driver can also carry signatures of its interaction
+with matter, so the field state itself may contain information about how the
+nonlinear radiation is produced. A useful account must connect this quantum
+phase-space dynamics to the emitted harmonic response without relying on the
+rotating-wave approximation.
+
+## Research problem
+
+Develop and assess a quantum phase-space account of high-order harmonic
+generation in the two-level, single-mode system below. Determine how the
+atom-field interaction reorganizes the initially coherent field, how the
+different physical terms in the full Hamiltonian contribute to the reduced-
+field dynamics and harmonic radiation, and how the resulting high-harmonic
+response changes with the initial field amplitude.
+
+Use calculated field-state and harmonic evidence to support the answer. The
+derivation, numerical realization, diagnostic design, choice of figures and
+structure of the scientific argument are yours. Do not assume the proposed
+physical picture before testing it.
+
+## Physical inputs
+
+Use the standard electric-dipole quantum Rabi model for a two-level system
+coupled to one quantized bosonic mode. The matter transition frequency is
+$\omega_0$, the field frequency is $\omega$, and the dimensionless dipole
+coupling magnitude is
+
+$$
+g=\left|\frac{\Omega}{\omega}\right|.
+$$
+
+Do not make a rotating-wave approximation. Use
+
+$$
+\frac{\omega_0}{\omega}=2.2,
+\qquad T=\frac{2\pi}{\omega}.
+$$
+
+The atom begins in its lower energy state $|g\rangle$. The field begins in a
+positive-real coherent state $|\alpha_0\rangle$. Investigate all four cases:
+
+| Case | $\alpha_0$ | $g$ | Required physical interval |
+|---|---:|---:|---:|
+| A | $10$ | $0.5$ | first optical cycle |
+| B | $10^5$ | $10^{-5}$ | 20 optical cycles |
+| C | $2\times10^5$ | $10^{-5}$ | 20 optical cycles |
+| D | $4\times10^5$ | $10^{-5}$ | 20 optical cycles |
+
+State the atomic-basis phase, field-quadrature orientation, Fourier-sign,
+harmonic-order and display conventions used in your work. Globally equivalent
+branch phases, label exchanges and phase-space reflections are accepted after
+consistent alignment. Absolute harmonic-spectrum normalization is not a
+grading target.
+
+## Method and scope
+
+Use a moving von Neumann lattice of coherent states to treat the complete
+atom-field dynamics. Here this method name refers to a nonorthogonal coherent-
+state representation whose field labels are drawn from
+
+$$
+\alpha^{(mn)}=\sqrt{\pi}\,(m+in),\qquad m,n\in\mathbb Z,
+$$
+
+with an appropriate finite subset chosen by the investigator. Standard
+coherent-state and quantum phase-space identities may be derived or cited. No
+particular auxiliary construction is prescribed.
+
+The final research account must be supported by a computed phase-space
+description of the reduced field state and by high-harmonic radiation obtained
+from the material dipole response. All numerical choices not fixed above are
+yours. Check that the reported signals are sufficiently reliable and
+reproducible to support the conclusions; no particular lattice size, solver,
+time step, tolerance, phase-space grid, Fourier treatment, display range or
+refinement sequence is prescribed.
+
+## Submission
+
+Submit one self-contained scientific report and an offline reproduction
+package. The report must answer the central research question and include
+enough quantitative evidence to audit every case-dependent or mechanistic
+claim. The selection and organization of that evidence are yours.
+
+Include a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge.
+
+Include the derivation actually used, source code, an executable command or
+script, machine-readable data underlying the reported evidence, plotting or
+analysis code, references, and concise run and environment information. No
+fixed file tree, filename scheme, complete exploratory history, named control,
+or examiner-selected intermediate plot is required.
+
+The active examination resources and limits are defined in the companion
+`resource_limits.json`. All retained production calculations must run
+within that fixed allocation and active wall time. More expensive modelling
+does not receive additional credit.
+
+## Reference and integrity policy
+
+This examination is conducted without network access or live literature
+retrieval. You may rely on your existing general scientific knowledge and, if any are
+explicitly supplied with the examination, on those offline materials or
+software documentation. Record every such source actually consulted. For formulas,
+methods, constants, or conventions used from general knowledge rather than a
+consulted source, state enough of the method basis, definition, value, units,
+and convention to make the calculation auditable; do not invent a citation.
+You are not required to identify or prove a publication date or to retrieve
+literature during the examination.
+
+The hidden target article and its identifying metadata, figures or captions,
+supplementary material, author code or data, target-specific reproduction
+code, solution or scoring material, online solutions, and worked
+reproductions of this case must not be used. All submitted scientific figures
+and numerical data must be generated by your own implementation of the stated
+problem.
+
+See [submission requirements](../../submission_requirements.md) for the common submission entry points.

cases/case08/grading_rubric.json

@@ -0,0 +1,588 @@
+{
+  "case_id": "Case08",
+  "title": "Case08 — Revealing the wave-function-dependent zeptosecond birth time delay in molecular photoionization with double-slit interference minima",
+  "atoms": [
+    {
+      "criterion_id": "F1",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Instantiate the specified two-dimensional soft-core H2+, fixed separation, symmetric/antisymmetric initial states and spatially propagating ultrashort pulse with nondipole velocity-gauge TDSE or a strictly equivalent representation.",
+      "award_conditions": [
+        "Both symmetric and antisymmetric states belong to the specified fixed-separation 2D soft-core H2+ model and spatially propagating nondipole pulse with consistent gauge."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F2, F3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article p.043105-2, Eqs.(1),(2) and theoretical-method paragraphs: spatially propagating pulse, 2D soft-core fixed-nuclei TDSE and outgoing-wave Fourier extraction."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F2",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.",
+      "award_conditions": [
+        "A probability-preserving outgoing-wave extraction defines comparable molecule-frame final PMDs for both states."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F1 (Instantiate the specified two-dimensional soft-core H2+, fixed separation, symmetric/antisymmetric initial states and spatially propagating ultrashort pulse with nondipole velocity-gauge TDSE or a strictly equivalent representation.)",
+        "Preserve independently valid work in F3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article p.043105-2, Eqs.(1),(2) and theoretical-method paragraphs: spatially propagating pulse, 2D soft-core fixed-nuclei TDSE and outgoing-wave Fourier extraction."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F3",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Establish a quantitative inversion from final angular phase to relative birth time, explicitly treating two-centre geometry, parity, sign/phase branch, periodic aliases and identifiability.",
+      "award_conditions": [
+        "The candidate quantitatively maps final interference phase to relative delay with geometry, parity, sign, branch, aliases and identifiability explicit."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in O1, O2, I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "O1",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.",
+      "award_conditions": [
+        "The symmetric-state final probability signal is reconstructible and resolves one-photon support and angular two-centre structure.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.)",
+        "Preserve independently valid work in O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article pp.043105-2-3, Fig.1(a-c): symmetric-ground-state one-photon momentum and angular interference; source maxima are background-sensitive."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O2",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.",
+      "award_conditions": [
+        "The antisymmetric-state signal is reconstructible and resolves one-photon support and parity-specific angular nodes/structure.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.)",
+        "Preserve independently valid work in O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article pp.043105-3-4, Fig.1(d-f): antisymmetric first-excited-state signal, central minimum and parity-shifted interference."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O3",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.",
+      "award_conditions": [
+        "Two-state phase/interference evidence resolves timing-bearing minima, periods or an equivalent phase object distinguishable from smooth background.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.); O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.)",
+        "Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O4",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present initial-to-final spatial evidence supporting state dependence, exposing inter-centre symmetric density versus outward antisymmetric density/effective emission geometry, or a strictly equivalent spatial relation.",
+      "award_conditions": [
+        "Spatial evidence exposes symmetric inter-centre versus antisymmetric outward density/effective-emission geometry, or a valid equivalent spatial relation.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F1 (Instantiate the specified two-dimensional soft-core H2+, fixed separation, symmetric/antisymmetric initial states and spatially propagating ultrashort pulse with nondipole velocity-gauge TDSE or a strictly equivalent representation.)",
+        "Preserve independently valid work in M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "I1",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Explicitly identify one-photon support and angular two-centre phase structure in the presented symmetric-state signal, rather than merely supplying data or a figure.",
+      "award_conditions": [
+        "The candidate identifies one-photon support and angular two-centre phase structure in the symmetric-state presentation."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.)",
+        "Preserve independently valid work in I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article pp.043105-2-3, Fig.1(a-c): symmetric-ground-state one-photon momentum and angular interference; source maxima are background-sensitive."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I2",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Explicitly identify one-photon support, parity-specific nodes/angular structure and differences from the symmetric case in the antisymmetric-state signal.",
+      "award_conditions": [
+        "The candidate identifies parity-specific nodes and state differences in the antisymmetric-state presentation."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.)",
+        "Preserve independently valid work in I1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article pp.043105-3-4, Fig.1(d-f): antisymmetric first-excited-state signal, central minimum and parity-shifted interference."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I3",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Explicitly identify from presented evidence the two states' interference periods/phase branches, effective emission scales or equivalent quantities, and numerical delay classes and ordering.",
+      "award_conditions": [
+        "Candidate identification includes state-specific period/phase branch, effective scale or equivalent quantity, numerical delay class and ordering."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.)",
+        "Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I4",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify the material initial-density/emission-geometry difference, symmetric inter-centre versus antisymmetric outward support, or physically equivalent spatial evidence.",
+      "award_conditions": [
+        "The candidate identifies the relevant initial-density/emission-geometry difference from presented spatial evidence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O4 (Present initial-to-final spatial evidence supporting state dependence, exposing inter-centre symmetric density versus outward antisymmetric density/effective emission geometry, or a strictly equivalent spatial relation.)",
+        "Preserve independently valid work in M6, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M1",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.",
+      "award_conditions": [
+        "The candidate explains how propagating-field space-time phase enters angular two-centre interference and why arbitrary angular texture is not a clock."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.)",
+        "Preserve independently valid work in M2, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M2",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Quantitatively connect angular period/phase displacement, effective emission scale and delay through the two-centre phase relation, correctly treating parity phase, signs and periodic aliases.",
+      "award_conditions": [
+        "A quantitative phase relation connects period, effective separation and delay with the correct parity phase and sign/alias mapping."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F3 (Establish a quantitative inversion from final angular phase to relative birth time, explicitly treating two-centre geometry, parity, sign/phase branch, periodic aliases and identifiability.)",
+        "Preserve independently valid work in M1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M3",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Infer a symmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.",
+      "award_conditions": [
+        "The symmetric-state delay follows its computed signal and is physically compared with its effective-scale light-crossing time."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I1 (Explicitly identify one-photon support and angular two-centre phase structure in the presented symmetric-state signal, rather than merely supplying data or a figure.); I3 (Explicitly identify from presented evidence the two states' interference periods/phase branches, effective emission scales or equivalent quantities, and numerical delay classes and ordering.)",
+        "Preserve independently valid work in M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M4",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Infer an antisymmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.",
+      "award_conditions": [
+        "The antisymmetric-state delay follows its computed signal and is physically compared with its effective-scale light-crossing time."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I2 (Explicitly identify one-photon support, parity-specific nodes/angular structure and differences from the symmetric case in the antisymmetric-state signal.); I3 (Explicitly identify from presented evidence the two states' interference periods/phase branches, effective emission scales or equivalent quantities, and numerical delay classes and ordering.)",
+        "Preserve independently valid work in M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M5",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.",
+      "award_conditions": [
+        "The two initial states' distinct emission scales explain different timing, without forcing either scale to equal nuclear separation."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: M3 (Infer a symmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.); M4 (Infer an antisymmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.)",
+        "Preserve independently valid work in M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M6",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.",
+      "award_conditions": [
+        "Density support, effective emission positions and light propagation form an evidence-linked state-to-geometry-to-delay chain."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I4 (Identify the material initial-density/emission-geometry difference, symmetric inter-centre versus antisymmetric outward support, or physically equivalent spatial evidence.)",
+        "Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M7",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Synthesize both signals, quantitative timing and geometry mechanism into the strongest identifiable conclusion, without promoting a mere angular shift or smooth response into a unique clock.",
+      "award_conditions": [
+        "Both signals, quantitative inversion and geometry mechanism support the strongest identifiable relative-timing claim, not an unproven unique clock."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: M1 (Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.); M5 (Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.); M6 (Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.)",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V1",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "When smooth-background confusion, periodic aliases, parity/sign branches, alternative angular-shift explanations or numerical resolution threaten timing, provide discriminating evidence or restrict the threatened conclusion.",
+      "award_conditions": [
+        "When background, phase aliases, parity/sign, competing shift mechanisms or resolution threaten timing, capable evidence discriminates them or the claim is narrowed; otherwise N/A."
+      ],
+      "applicability_and_na": [
+        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
+        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory."
+      ],
+      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V2",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Positively state the specified two-dimensional fixed-nuclei soft-core H2+, two initial states, nondipole pulse and achieved final-PES inference domain; do not extrapolate to general molecules or a unique absolute birth clock.",
+      "award_conditions": [
+        "The candidate positively bounds the conclusion to the specified fixed-nuclei 2D soft-core states/pulse and actual final-PES inference domain."
+      ],
+      "applicability_and_na": [
+        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.",
+        "Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.",
+        "Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination."
+      ],
+      "source_support": [
+        "Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    }
+  ],
+  "case_scientific_rules": [
+    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
+    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
+    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
+    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
+    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
+    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
+    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
+    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
+    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
+    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
+    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
+    "Representative structural anchors, not tolerances, include a one-photon band near p=4 a.u., symmetric minima near mu=-0.41,+0.44, antisymmetric minima near -0.56,0,+0.59, and parity-distinct periods.",
+    "Representative effective scales are about 1.77-1.79 and 2.62-2.64 a.u.; principal delays about 0.31-0.34 and 0.45-0.49 as. The symmetric delay is below R/c, the antisymmetric delay above R/c, each near its own Rw/c; convention-equivalent aliases remain accepted.",
+    "A different angular shift that cannot distinguish smooth single-centre background does not solve the same inference problem even if internally consistent. Bound-contaminated continuum data and incorrect angular measures do not establish the target probability.",
+    "Initial-state geometry evidence and its interpretation retain independent credit when quantitative timing fails; conversely, state labels alone do not establish computed structural support.",
+    "For a representative one-photon momentum $p$, the symmetric-state two-centre model can be written",
+    "$$\nF(\\mu)=1+\\cos\\!\\left[2\\pi\\left(\n\\frac{\\mu R_w}{\\lambda_e}-\\frac{\\tau_b v_{\\rm ph}}{\\lambda_e}\n\\right)\\right],\n\\qquad \\mu=\\cos\\alpha,\n$$",
+    "with $\\lambda_e=2\\pi/p$ and $v_{\\rm ph}=E/p$. The antisymmetric initial state adds the parity phase $\\pi$ (or an equivalent global convention). The canonical route obtains a positive effective emission separation $R_w$ from the stable angular period and then the delay equivalence class from the phase displacement. It uses robust interior interference minima because the smooth single-centre photoionization background shifts maxima but does not move a true zero in the same way.",
+    "both states show a one-photon momentum band near $p\\simeq4$ a.u. with resolved, parity-distinct angular interference;",
+    "the symmetric case has the principal interior depressions near $\\mu\\simeq-0.41$ and $+0.44$;",
+    "the antisymmetric case has a central depression and principal minima near $\\mu\\simeq-0.56,0,+0.59$;",
+    "representative effective separations are about $1.77$--$1.79$ a.u. and $2.62$--$2.64$ a.u.; principal delays are approximately $0.31$--$0.34$ as and $0.45$--$0.49$ as, respectively;",
+    "the symmetric delay lies below $R/c$ and the antisymmetric delay above it, while each is close to its own $R_w/c$;",
+    "the computed symmetric density is concentrated between the centres whereas the antisymmetric density is displaced outward, supporting the effective emission-geometry interpretation.",
+    "These are structural anchors, not pixel targets. An energy-resolved, momentum-resolved, phase-fit, likelihood or other estimator may replace the canonical radial PAD route if it demonstrably measures the same phase and controls the same background ambiguity. A delay shifted by an exact period or global sign is equivalent when the student derives and reports the mapping; the grader must not choose a branch by proximity to the reference values.",
+    "The task deliberately does not name the radial measure, cosine fit, minima, $R_w$, parity phase or principal delay interval. None may be awarded merely for matching terminology. Full credit follows physical function and computed correctness. Conversely, a route that measures a different angular shift and cannot distinguish single-centre background has not solved the same inference problem, even if it is internally consistent.",
+    "Charge a continuum-extraction, measure or fit defect first to the affected Output criterion. A dependent scientific inference loses credit only when the same defect makes the physical inference false or unsupported. Do not also deduct for absence of a named convergence test. Do not require source figure layout, colours, exact crop, absolute yield or a fixed output package.",
+    "For F3/O3/M1-M4, the phase model already stated is article p.043105-3, Eq.(3). Equivalently,\n$$\\Phi(\\mu)=pR_w\\mu-E\\tau_b+\\phi_{\\rm parity},\\quad\n\\Delta\\mu=\\frac{2\\pi}{pR_w},\\quad\n\\phi_{\\rm parity}=0\\ (\\text{symmetric}),\\ \\pi\\ (\\text{antisymmetric}).$$\nHere $E/p=v_{\\rm ph}$ is the electron phase velocity under the source convention, not an independently substituted group velocity. An observed phase fixes a delay equivalence class modulo $2\\pi/E$; selecting a principal delay needs a stated branch/physical justification, not nearest-reference-value matching. Source Fig.2 compares each inferred delay with its own $R_w/c$ and with bare $R/c$; those are different physical scales."
+  ],
+  "closure_requirements": {
+    "RC0": [
+      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
+      "Required indispensable claim CL0, central physical object: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC1": [
+      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
+      "Required co primary claim CL1, indispensable material component: all of: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.); O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL2, indispensable material component: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC2": [
+      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
+      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M1 (Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.); M2 (Quantitatively connect angular period/phase displacement, effective emission scale and delay through the two-centre phase relation, correctly treating parity phase, signs and periodic aliases.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL3, principal mechanism or commissioned conclusion: all of: M5 (Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.); M6 (Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC3": [
+      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
+      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
+      "Required co primary claim CL4, material validation/scope: V1 (When smooth-background confusion, periodic aliases, parity/sign branches, alternative angular-shift explanations or numerical resolution threaten timing, provide discriminating evidence or restrict the threatened conclusion.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC4": [
+      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
+      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
+      "Close CL0 central physical object: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.).",
+      "Close CL1 indispensable material component: all of: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.); O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.).",
+      "Close CL2 indispensable material component: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.).",
+      "Close CL2 principal mechanism or commissioned conclusion: all of: M1 (Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.); M2 (Quantitatively connect angular period/phase displacement, effective emission scale and delay through the two-centre phase relation, correctly treating parity phase, signs and periodic aliases.).",
+      "Close CL3 principal mechanism or commissioned conclusion: all of: M5 (Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.); M6 (Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.).",
+      "Close CL4 material validation/scope: V1 (When smooth-background confusion, periodic aliases, parity/sign branches, alternative angular-shift explanations or numerical resolution threaten timing, provide discriminating evidence or restrict the threatened conclusion.)."
+    ]
+  },
+  "references": [
+    {
+      "citation": "XuanYang Lai, SongPo Xu, ShaoGang Yu, MengWen Shi, Wei Quan, and XiaoJun Liu. 2021. *Revealing the wave-function-dependent zeptosecond birth time delay in molecular photoionization with double-slit interference minima*. *Physical Review A*, 104, 043105.",
+      "url": "https://doi.org/10.1103/PhysRevA.104.043105",
+      "scientific_scope": "Revealing the wave-function-dependent zeptosecond birth time delay in molecular photoionization with double-slit interference minima",
+      "anchors": [
+        "Lai et al. (2021), article p.043105-2, Eqs.(1),(2) and theoretical-method paragraphs: spatially propagating pulse, 2D soft-core fixed-nuclei TDSE and outgoing-wave Fourier extraction.",
+        "Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4.",
+        "Lai et al. (2021), article pp.043105-2-3, Fig.1(a-c): symmetric-ground-state one-photon momentum and angular interference; source maxima are background-sensitive.",
+        "Lai et al. (2021), article pp.043105-3-4, Fig.1(d-f): antisymmetric first-excited-state signal, central minimum and parity-shifted interference.",
+        "Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity.",
+        "Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions.",
+        "Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory."
+      ]
+    }
+  ]
+}

cases/case08/grading_rubric.md

@@ -0,0 +1,854 @@
+# Grading Rubric — Case08
+
+Case08 — Revealing the wave-function-dependent zeptosecond birth time delay in molecular photoionization with double-slit interference minima
+
+## Atomic Scoring Criteria
+
+Each criterion awards 0 or 0.5 points, for a maximum of 10. Explicit N/A rules apply where stated.
+
+### F1 — F — 0.5 points
+
+**Scientific requirement**
+
+Instantiate the specified two-dimensional soft-core H2+, fixed separation, symmetric/antisymmetric initial states and spatially propagating ultrashort pulse with nondipole velocity-gauge TDSE or a strictly equivalent representation.
+
+**Conditions for credit**
+
+- Both symmetric and antisymmetric states belong to the specified fixed-separation 2D soft-core H2+ model and spatially propagating nondipole pulse with consistent gauge.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in F2, F3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article p.043105-2, Eqs.(1),(2) and theoretical-method paragraphs: spatially propagating pulse, 2D soft-core fixed-nuclei TDSE and outgoing-wave Fourier extraction.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F2 — F — 0.5 points
+
+**Scientific requirement**
+
+Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.
+
+**Conditions for credit**
+
+- A probability-preserving outgoing-wave extraction defines comparable molecule-frame final PMDs for both states.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F1 (Instantiate the specified two-dimensional soft-core H2+, fixed separation, symmetric/antisymmetric initial states and spatially propagating ultrashort pulse with nondipole velocity-gauge TDSE or a strictly equivalent representation.)
+
+- Preserve independently valid work in F3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article p.043105-2, Eqs.(1),(2) and theoretical-method paragraphs: spatially propagating pulse, 2D soft-core fixed-nuclei TDSE and outgoing-wave Fourier extraction.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F3 — F — 0.5 points
+
+**Scientific requirement**
+
+Establish a quantitative inversion from final angular phase to relative birth time, explicitly treating two-centre geometry, parity, sign/phase branch, periodic aliases and identifiability.
+
+**Conditions for credit**
+
+- The candidate quantitatively maps final interference phase to relative delay with geometry, parity, sign, branch, aliases and identifiability explicit.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve independently valid work in O1, O2, I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### O1 — O — 0.5 points
+
+**Scientific requirement**
+
+Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.
+
+**Conditions for credit**
+
+- The symmetric-state final probability signal is reconstructible and resolves one-photon support and angular two-centre structure.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.)
+
+- Preserve independently valid work in O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article pp.043105-2-3, Fig.1(a-c): symmetric-ground-state one-photon momentum and angular interference; source maxima are background-sensitive.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O2 — O — 0.5 points
+
+**Scientific requirement**
+
+Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.
+
+**Conditions for credit**
+
+- The antisymmetric-state signal is reconstructible and resolves one-photon support and parity-specific angular nodes/structure.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.)
+
+- Preserve independently valid work in O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article pp.043105-3-4, Fig.1(d-f): antisymmetric first-excited-state signal, central minimum and parity-shifted interference.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O3 — O — 0.5 points
+
+**Scientific requirement**
+
+Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.
+
+**Conditions for credit**
+
+- Two-state phase/interference evidence resolves timing-bearing minima, periods or an equivalent phase object distinguishable from smooth background.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.); O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.)
+
+- Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O4 — O — 0.5 points
+
+**Scientific requirement**
+
+Present initial-to-final spatial evidence supporting state dependence, exposing inter-centre symmetric density versus outward antisymmetric density/effective emission geometry, or a strictly equivalent spatial relation.
+
+**Conditions for credit**
+
+- Spatial evidence exposes symmetric inter-centre versus antisymmetric outward density/effective-emission geometry, or a valid equivalent spatial relation.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F1 (Instantiate the specified two-dimensional soft-core H2+, fixed separation, symmetric/antisymmetric initial states and spatially propagating ultrashort pulse with nondipole velocity-gauge TDSE or a strictly equivalent representation.)
+
+- Preserve independently valid work in M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### I1 — I — 0.5 points
+
+**Scientific requirement**
+
+Explicitly identify one-photon support and angular two-centre phase structure in the presented symmetric-state signal, rather than merely supplying data or a figure.
+
+**Conditions for credit**
+
+- The candidate identifies one-photon support and angular two-centre phase structure in the symmetric-state presentation.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.)
+
+- Preserve independently valid work in I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article pp.043105-2-3, Fig.1(a-c): symmetric-ground-state one-photon momentum and angular interference; source maxima are background-sensitive.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I2 — I — 0.5 points
+
+**Scientific requirement**
+
+Explicitly identify one-photon support, parity-specific nodes/angular structure and differences from the symmetric case in the antisymmetric-state signal.
+
+**Conditions for credit**
+
+- The candidate identifies parity-specific nodes and state differences in the antisymmetric-state presentation.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.)
+
+- Preserve independently valid work in I1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article pp.043105-3-4, Fig.1(d-f): antisymmetric first-excited-state signal, central minimum and parity-shifted interference.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I3 — I — 0.5 points
+
+**Scientific requirement**
+
+Explicitly identify from presented evidence the two states' interference periods/phase branches, effective emission scales or equivalent quantities, and numerical delay classes and ordering.
+
+**Conditions for credit**
+
+- Candidate identification includes state-specific period/phase branch, effective scale or equivalent quantity, numerical delay class and ordering.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.)
+
+- Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I4 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify the material initial-density/emission-geometry difference, symmetric inter-centre versus antisymmetric outward support, or physically equivalent spatial evidence.
+
+**Conditions for credit**
+
+- The candidate identifies the relevant initial-density/emission-geometry difference from presented spatial evidence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O4 (Present initial-to-final spatial evidence supporting state dependence, exposing inter-centre symmetric density versus outward antisymmetric density/effective emission geometry, or a strictly equivalent spatial relation.)
+
+- Preserve independently valid work in M6, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M1 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.
+
+**Conditions for credit**
+
+- The candidate explains how propagating-field space-time phase enters angular two-centre interference and why arbitrary angular texture is not a clock.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.)
+
+- Preserve independently valid work in M2, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M2 — M — 0.5 points
+
+**Scientific requirement**
+
+Quantitatively connect angular period/phase displacement, effective emission scale and delay through the two-centre phase relation, correctly treating parity phase, signs and periodic aliases.
+
+**Conditions for credit**
+
+- A quantitative phase relation connects period, effective separation and delay with the correct parity phase and sign/alias mapping.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F3 (Establish a quantitative inversion from final angular phase to relative birth time, explicitly treating two-centre geometry, parity, sign/phase branch, periodic aliases and identifiability.)
+
+- Preserve independently valid work in M1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M3 — M — 0.5 points
+
+**Scientific requirement**
+
+Infer a symmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.
+
+**Conditions for credit**
+
+- The symmetric-state delay follows its computed signal and is physically compared with its effective-scale light-crossing time.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: I1 (Explicitly identify one-photon support and angular two-centre phase structure in the presented symmetric-state signal, rather than merely supplying data or a figure.); I3 (Explicitly identify from presented evidence the two states' interference periods/phase branches, effective emission scales or equivalent quantities, and numerical delay classes and ordering.)
+
+- Preserve independently valid work in M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M4 — M — 0.5 points
+
+**Scientific requirement**
+
+Infer an antisymmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.
+
+**Conditions for credit**
+
+- The antisymmetric-state delay follows its computed signal and is physically compared with its effective-scale light-crossing time.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: I2 (Explicitly identify one-photon support, parity-specific nodes/angular structure and differences from the symmetric case in the antisymmetric-state signal.); I3 (Explicitly identify from presented evidence the two states' interference periods/phase branches, effective emission scales or equivalent quantities, and numerical delay classes and ordering.)
+
+- Preserve independently valid work in M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M5 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.
+
+**Conditions for credit**
+
+- The two initial states' distinct emission scales explain different timing, without forcing either scale to equal nuclear separation.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: M3 (Infer a symmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.); M4 (Infer an antisymmetric-state relative birth time supported by its signal and compare it physically with the relevant effective-scale light-crossing time.)
+
+- Preserve independently valid work in M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M6 — M — 0.5 points
+
+**Scientific requirement**
+
+Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.
+
+**Conditions for credit**
+
+- Density support, effective emission positions and light propagation form an evidence-linked state-to-geometry-to-delay chain.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: I4 (Identify the material initial-density/emission-geometry difference, symmetric inter-centre versus antisymmetric outward support, or physically equivalent spatial evidence.)
+
+- Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M7 — M — 0.5 points
+
+**Scientific requirement**
+
+Synthesize both signals, quantitative timing and geometry mechanism into the strongest identifiable conclusion, without promoting a mere angular shift or smooth response into a unique clock.
+
+**Conditions for credit**
+
+- Both signals, quantitative inversion and geometry mechanism support the strongest identifiable relative-timing claim, not an unproven unique clock.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: M1 (Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.); M5 (Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.); M6 (Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.)
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V1 — V — 0.5 points
+
+**Scientific requirement**
+
+When smooth-background confusion, periodic aliases, parity/sign branches, alternative angular-shift explanations or numerical resolution threaten timing, provide discriminating evidence or restrict the threatened conclusion.
+
+**Conditions for credit**
+
+- When background, phase aliases, parity/sign, competing shift mechanisms or resolution threaten timing, capable evidence discriminates them or the claim is narrowed; otherwise N/A.
+
+**Applicability and N/A**
+
+- Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.
+
+- If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory.
+
+**Research Closure relation**
+
+Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V2 — V — 0.5 points
+
+**Scientific requirement**
+
+Positively state the specified two-dimensional fixed-nuclei soft-core H2+, two initial states, nondipole pulse and achieved final-PES inference domain; do not extrapolate to general molecules or a unique absolute birth clock.
+
+**Conditions for credit**
+
+- The candidate positively bounds the conclusion to the specified fixed-nuclei 2D soft-core states/pulse and actual final-PES inference domain.
+
+**Applicability and N/A**
+
+- This positive scientific scope/evidence duty is unconditional; N/A is not permitted.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Global axes, Fourier, phase, delay-sign and exact-period changes are accepted when the candidate derives and reports the mapping. Never choose an alias by proximity to reference values.
+
+- Energy-resolved, momentum-resolved, phase-fit, likelihood and other estimators may replace radial PAD/minima extraction if they preserve final probability, measure the same relative timing phase and control the same smooth/state-dependent background ambiguity.
+
+- Robust interior minima are canonical because smooth single-centre background shifts maxima but not a genuine zero in the same way; a different diagnostic must establish equivalent physical discrimination.
+
+**Scientific source locations**
+
+- Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+## Research Closure Requirements
+
+### RC0
+
+- The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.
+
+- Required indispensable claim CL0, central physical object: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC1
+
+- With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.
+
+- Required co primary claim CL1, indispensable material component: all of: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.); O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL2, indispensable material component: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC2
+
+- With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.
+
+- Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M1 (Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.); M2 (Quantitatively connect angular period/phase displacement, effective emission scale and delay through the two-centre phase relation, correctly treating parity phase, signs and periodic aliases.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL3, principal mechanism or commissioned conclusion: all of: M5 (Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.); M6 (Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC3
+
+- With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.
+
+- Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.
+
+- Required co primary claim CL4, material validation/scope: V1 (When smooth-background confusion, periodic aliases, parity/sign branches, alternative angular-shift explanations or numerical resolution threaten timing, provide discriminating evidence or restrict the threatened conclusion.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC4
+
+- All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.
+
+- Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.
+
+- Close CL0 central physical object: F2 (Construct a probability-preserving molecule-frame final photoelectron momentum distribution from the outgoing propagated wavepacket, using the same comparable definition for both initial states.).
+
+- Close CL1 indispensable material component: all of: O1 (Present the symmetric-state molecule-frame final photoelectron probability signal with one-photon momentum support and resolution sufficient to judge angular two-centre structure.); O2 (Present the antisymmetric-state molecule-frame final photoelectron probability signal with one-photon support and resolution sufficient to judge parity-specific angular structure.).
+
+- Close CL2 indispensable material component: O3 (Construct two-state timing-bearing phase/interference evidence exposing angular minima, period or a strictly equivalent phase structure and its distinction from smooth background.).
+
+- Close CL2 principal mechanism or commissioned conclusion: all of: M1 (Explain why two-centre angular interference contains the propagating field's space-time phase along the molecular axis and can encode relative birth timing; arbitrary angular texture is not automatically a clock.); M2 (Quantitatively connect angular period/phase displacement, effective emission scale and delay through the two-centre phase relation, correctly treating parity phase, signs and periodic aliases.).
+
+- Close CL3 principal mechanism or commissioned conclusion: all of: M5 (Explain why the two initial states yield different effective emission scales and birth times, explicitly recognizing that the effective scale need not equal fixed internuclear separation.); M6 (Connect inter-centre/outward initial density differences to effective emission positions, propagation paths and relative timing, closing the state-structure -> geometry -> delay causal chain.).
+
+- Close CL4 material validation/scope: V1 (When smooth-background confusion, periodic aliases, parity/sign branches, alternative angular-shift explanations or numerical resolution threaten timing, provide discriminating evidence or restrict the threatened conclusion.).
+
+## Applicability and Equivalent Evidence
+
+- Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.
+
+- Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.
+
+- For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.
+
+- Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.
+
+- Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.
+
+- Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.
+
+- Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.
+
+- Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.
+
+- Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.
+
+- Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.
+
+- A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.
+
+- Representative structural anchors, not tolerances, include a one-photon band near p=4 a.u., symmetric minima near mu=-0.41,+0.44, antisymmetric minima near -0.56,0,+0.59, and parity-distinct periods.
+
+- Representative effective scales are about 1.77-1.79 and 2.62-2.64 a.u.; principal delays about 0.31-0.34 and 0.45-0.49 as. The symmetric delay is below R/c, the antisymmetric delay above R/c, each near its own Rw/c; convention-equivalent aliases remain accepted.
+
+- A different angular shift that cannot distinguish smooth single-centre background does not solve the same inference problem even if internally consistent. Bound-contaminated continuum data and incorrect angular measures do not establish the target probability.
+
+- Initial-state geometry evidence and its interpretation retain independent credit when quantitative timing fails; conversely, state labels alone do not establish computed structural support.
+
+- For a representative one-photon momentum $p$, the symmetric-state two-centre model can be written
+
+$$
+F(\mu)=1+\cos\!\left[2\pi\left(
+\frac{\mu R_w}{\lambda_e}-\frac{\tau_b v_{\rm ph}}{\lambda_e}
+\right)\right],
+\qquad \mu=\cos\alpha,
+$$
+
+- with $\lambda_e=2\pi/p$ and $v_{\rm ph}=E/p$. The antisymmetric initial state adds the parity phase $\pi$ (or an equivalent global convention). The canonical route obtains a positive effective emission separation $R_w$ from the stable angular period and then the delay equivalence class from the phase displacement. It uses robust interior interference minima because the smooth single-centre photoionization background shifts maxima but does not move a true zero in the same way.
+
+- both states show a one-photon momentum band near $p\simeq4$ a.u. with resolved, parity-distinct angular interference;
+
+- the symmetric case has the principal interior depressions near $\mu\simeq-0.41$ and $+0.44$;
+
+- the antisymmetric case has a central depression and principal minima near $\mu\simeq-0.56,0,+0.59$;
+
+- representative effective separations are about $1.77$--$1.79$ a.u. and $2.62$--$2.64$ a.u.; principal delays are approximately $0.31$--$0.34$ as and $0.45$--$0.49$ as, respectively;
+
+- the symmetric delay lies below $R/c$ and the antisymmetric delay above it, while each is close to its own $R_w/c$;
+
+- the computed symmetric density is concentrated between the centres whereas the antisymmetric density is displaced outward, supporting the effective emission-geometry interpretation.
+
+- These are structural anchors, not pixel targets. An energy-resolved, momentum-resolved, phase-fit, likelihood or other estimator may replace the canonical radial PAD route if it demonstrably measures the same phase and controls the same background ambiguity. A delay shifted by an exact period or global sign is equivalent when the student derives and reports the mapping; the grader must not choose a branch by proximity to the reference values.
+
+- The task deliberately does not name the radial measure, cosine fit, minima, $R_w$, parity phase or principal delay interval. None may be awarded merely for matching terminology. Full credit follows physical function and computed correctness. Conversely, a route that measures a different angular shift and cannot distinguish single-centre background has not solved the same inference problem, even if it is internally consistent.
+
+- Charge a continuum-extraction, measure or fit defect first to the affected Output criterion. A dependent scientific inference loses credit only when the same defect makes the physical inference false or unsupported. Do not also deduct for absence of a named convergence test. Do not require source figure layout, colours, exact crop, absolute yield or a fixed output package.
+
+For F3/O3/M1-M4, the phase model already stated is article p.043105-3, Eq.(3). Equivalently,
+$$\Phi(\mu)=pR_w\mu-E\tau_b+\phi_{\rm parity},\quad
+\Delta\mu=\frac{2\pi}{pR_w},\quad
+\phi_{\rm parity}=0\ (\text{symmetric}),\ \pi\ (\text{antisymmetric}).$$
+Here $E/p=v_{\rm ph}$ is the electron phase velocity under the source convention, not an independently substituted group velocity. An observed phase fixes a delay equivalence class modulo $2\pi/E$; selecting a principal delay needs a stated branch/physical justification, not nearest-reference-value matching. Source Fig.2 compares each inferred delay with its own $R_w/c$ and with bare $R/c$; those are different physical scales.

cases/case08/resource_limits.json

@@ -0,0 +1,8 @@
+{
+  "cpu_cores": 32,
+  "nodes": 1,
+  "time_limit_minutes": 60,
+  "network_access": "disabled",
+  "temporary_storage_gib": 128,
+  "memory_policy": "No separate task-specific RAM limit is specified."
+}

cases/case08/sources.md

@@ -0,0 +1,33 @@
+# Scientific Sources — Case08
+
+## References
+
+XuanYang Lai, SongPo Xu, ShaoGang Yu, MengWen Shi, Wei Quan, and XiaoJun Liu. 2021. *Revealing the wave-function-dependent zeptosecond birth time delay in molecular photoionization with double-slit interference minima*. *Physical Review A*, 104, 043105. [Source](https://doi.org/10.1103/PhysRevA.104.043105)
+
+Revealing the wave-function-dependent zeptosecond birth time delay in molecular photoionization with double-slit interference minima
+
+## Criterion-to-source crosswalk
+
+Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.
+
+| Criteria | Source locations, scientific use and limits |
+|---|---|
+| F1, F2 | Lai et al. (2021), article p.043105-2, Eqs.(1),(2) and theoretical-method paragraphs: spatially propagating pulse, 2D soft-core fixed-nuclei TDSE and outgoing-wave Fourier extraction. |
+| F3, M1, M2 | Lai et al. (2021), article p.043105-3, Eq.(3), period-to-emission-separation paragraph and interference-minima/background discussion: geometric plus temporal phase, phase velocity and quantitative inversion. Antisymmetric pi phase is explicit on p.043105-4. |
+| O1, I1 | Lai et al. (2021), article pp.043105-2-3, Fig.1(a-c): symmetric-ground-state one-photon momentum and angular interference; source maxima are background-sensitive. |
+| O2, I2 | Lai et al. (2021), article pp.043105-3-4, Fig.1(d-f): antisymmetric first-excited-state signal, central minimum and parity-shifted interference. |
+| O3, I3, M3, M4 | Lai et al. (2021), article pp.043105-3-4, Fig.1(c,f), Eq.(3), Fig.2: fitted effective separations about 1.77/2.64 a.u. and state-specific delays below/above R/c. These canonical principal-branch values are not permission to select aliases by proximity. |
+| O4, I4, M5, M6 | Lai et al. (2021), article p.043105-4, Fig.3(a,b) antisymmetric/outward and Fig.3(c,d) symmetric/inter-centre distributions, plus following explanation: bound density shifts effective emission geometry away from nuclear positions. |
+| M7, V1, V2 | Lai et al. (2021), article pp.043105-3-4, minima/background explanation, Eq.(3), Fig.2 and paragraph noting enhanced soft-core state dependence. Scope/alias/alternative tests are task-defined safeguards; one canonical fit or radial reduction is not compulsory. |
+
+## Formula and convention notes
+
+For F3/O3/M1-M4, the phase model already stated is article p.043105-3, Eq.(3). Equivalently,
+$$\Phi(\mu)=pR_w\mu-E\tau_b+\phi_{\rm parity},\quad
+\Delta\mu=\frac{2\pi}{pR_w},\quad
+\phi_{\rm parity}=0\ (\text{symmetric}),\ \pi\ (\text{antisymmetric}).$$
+Here $E/p=v_{\rm ph}$ is the electron phase velocity under the source convention, not an independently substituted group velocity. An observed phase fixes a delay equivalence class modulo $2\pi/E$; selecting a principal delay needs a stated branch/physical justification, not nearest-reference-value matching. Source Fig.2 compares each inferred delay with its own $R_w/c$ and with bare $R/c$; those are different physical scales.
+
+## Scope of the source anchors
+
+The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.

cases/case08/task.md

@@ -0,0 +1,115 @@
+# Timing information in molecular photoionization
+
+## Background
+
+Photoelectron wave packets emitted from the two regions of an aligned
+diatomic ion can interfere. When a short, high-energy pulse propagates across
+the molecule, relative emission timing may be encoded in the final
+molecule-frame signal. The same angular structure can also be reshaped by the
+state-dependent photoionization response, so a numerical shift is not by
+itself a timing measurement.
+
+## Research problem
+
+Using the physical model below, determine what quantitative information about
+the relative birth time of the two emitted wave packets, if any, can be
+reliably inferred from the final photoelectron signal. Apply the investigation
+to the lowest symmetric and first antisymmetric initial states and determine
+whether the evidence supports an initial-state dependence.
+
+How the inference is constructed and substantiated is for you to decide.
+Establish its physical meaning and identifiability from the computed evidence
+rather than assuming in advance that a particular angular feature is a valid
+clock.
+
+## Physical inputs
+
+Use atomic units and the two-dimensional soft-core $\mathrm H_2^+$ model below.
+Work in coordinates $(z,x)$ with nuclei at $z=\pm R/2$, the molecular and
+pulse-propagation axes along $\hat{\mathbf z}$, and pulse polarization along
+$\hat{\mathbf x}$. The field-free potential is
+
+$$
+V(z,x)=-\frac{1}{\sqrt{(z-R/2)^2+x^2+a}}
+-\frac{1}{\sqrt{(z+R/2)^2+x^2+a}}.
+$$
+
+Use $R=2$ and $a=4.33$. The two initial states are the lowest symmetric and
+first antisymmetric eigenstates of this same field-free Hamiltonian.
+
+Retain propagation of the pulse across the molecule. Its finite-support vector
+potential is
+
+$$
+\begin{aligned}
+\mathbf A(z,t)={}&A_0
+\sin^2\!\left[\frac{\omega_e}{c}(z+a_0)-\omega_e t\right]
+\sin\!\left[\frac{\omega}{c}(z-ct)\right]\hat{\mathbf x}\\
+&\times\left[
+\theta_H\!\left(z-ct+\frac{\pi c}{\omega_e}+a_0\right)
+-\theta_H(z-ct+a_0)
+\right],
+\end{aligned}
+$$
+
+where $\omega_e=\omega/(2N_{\mathrm{cyc}})$. Use
+
+| Quantity | Value |
+|---|---:|
+| Peak intensity | $1.0\times10^{14}\ \mathrm{W\,cm^{-2}}$ |
+| Central wavelength | $5$ nm |
+| Pulse duration | $N_{\mathrm{cyc}}=30$ cycles |
+| Initial pulse displacement | $a_0=10$ a.u. |
+
+Determine $\omega$ and $A_0$ using conventions consistent with a standard
+velocity-gauge nondipole TDSE. State the Fourier, momentum-axis, angular and
+delay-sign conventions used.
+
+## Method boundary
+
+A standard velocity-gauge nondipole TDSE treatment is required. All
+task-specific analytical, numerical and evidential constructions are yours.
+Any comparison between the two initial states must use the same operational
+definition or demonstrate that the definitions are equivalent.
+
+You are responsible for establishing that the computed evidence is
+sufficiently reliable and physically discriminating for the conclusion made.
+No numerical implementation, post-processing recipe, display convention or
+validation procedure is prescribed. Absolute photoelectron yield is not a
+grading target.
+
+## Submission
+
+Submit one self-contained scientific report and an offline reproduction
+package containing the derivation, executable code, reconstructible final
+photoelectron data for both initial states, the data underlying any
+quantitative timing claim, a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge, and concise run and
+environment information. The choice and number of figures are yours. No fixed
+file tree, filename scheme, complete exploratory history or examiner-selected
+diagnostic is required.
+
+The active examination resources and limits are defined in the companion
+`resource_limits.json`. All retained production calculations must run
+within that fixed allocation and active wall time. More expensive modelling
+does not receive additional credit.
+
+## Reference and integrity policy
+
+This examination is conducted without network access or live literature
+retrieval. You may rely on your existing general scientific knowledge and, if any are
+explicitly supplied with the examination, on those offline materials or
+software documentation. Record every such source actually consulted. For formulas,
+methods, constants, or conventions used from general knowledge rather than a
+consulted source, state enough of the method basis, definition, value, units,
+and convention to make the calculation auditable; do not invent a citation.
+You are not required to identify or prove a publication date or to retrieve
+literature during the examination.
+
+The hidden target article and its identifying metadata, figures or captions,
+supplementary material, author code or data, target-specific reproduction
+code, solution or scoring material, online solutions, and worked
+reproductions of this case must not be used. All submitted scientific figures
+and numerical data must be generated by your own implementation of the stated
+problem.
+
+See [submission requirements](../../submission_requirements.md) for the common submission entry points.

cases/case09/grading_rubric.json

@@ -0,0 +1,593 @@
+{
+  "case_id": "Case09",
+  "title": "Case09 — High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses",
+  "atoms": [
+    {
+      "criterion_id": "F1",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Construct a coordinate-space B-spline TDSE for the specified one-dimensional periodic potential and both drives with consistent executable and auditable field coupling.",
+      "award_conditions": [
+        "The primary coordinate-space B-spline TDSE preserves the specified periodic potential and both physical drives with auditable field coupling."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-1-2, Eqs.(1)-(7), Fig.1(a-d), paragraph choosing k=0 in band 2: B-spline generalized metric and physical initial-state identity, not finite-box ordinal."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F2",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.",
+      "award_conditions": [
+        "The initial state is physically band 2 at k=0 and is demonstrably preserved in every representation or auxiliary calculation."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-1-2, Eqs.(1)-(7), Fig.1(a-d), paragraph choosing k=0 in band 2: B-spline generalized metric and physical initial-state identity, not finite-box ordinal."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F3",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.",
+      "award_conditions": [
+        "A consistent radiation/current observable and its gauge, field amplitude, frequency, carrier time/phase and units define the HHG comparison."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article p.033852-2, Eq.(8), and p.033852-3 Fourier/window paragraph: laser-induced current and spectrum. Gauge/derivative equivalence requires actual observable mapping, not appearance alone."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F4",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.",
+      "award_conditions": [
+        "The actual theoretical/control framework has reproducible physical observables and can test interpretation/reliability; a relabelled duplicate or static-only driven check is insufficient."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "O1",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present correct, reconstructible, claim-sufficient Case-A harmonic evidence spanning the full material response, including the first plateau and weaker second plateau beyond the first cutoff.",
+      "award_conditions": [
+        "Case-A spectrum resolves the full material response, including the first plateau and much weaker second plateau beyond its first cutoff, with correct state/object identity.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Construct a coordinate-space B-spline TDSE for the specified one-dimensional periodic potential and both drives with consistent executable and auditable field coupling.); F2 (Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.); F3 (Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.)",
+        "Preserve independently valid work in O2, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article p.033852-3, Fig.2 and two-plateau paragraph: first plateau and roughly five-orders-weaker second plateau, with cutoff scales near harmonic orders 40 and 120; bands 2/3 and higher-band pathways differ."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O2",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present correct, reconstructible, claim-sufficient Case-B full material harmonic response with proper case, initial-state, observable and representation identity.",
+      "award_conditions": [
+        "Case-B full material response is reconstructible and correctly bound to its drive, initial state, observable and representation.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F1 (Construct a coordinate-space B-spline TDSE for the specified one-dimensional periodic potential and both drives with consistent executable and auditable field coupling.); F2 (Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.); F3 (Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.)",
+        "Preserve independently valid work in O1, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O3",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present reconstructible Case-B causal decomposition or genuinely equivalent evidence distinguishing low-order and higher-first-plateau contributions; static labels, duplicate currents, swapped components or false spectral-power addition are insufficient.",
+      "award_conditions": [
+        "A causal current-level or truly equivalent distinction separates low-order and higher-first-plateau mechanisms without duplicate/swapped components or false power addition.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.); F3 (Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.); F4 (Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.)",
+        "Preserve independently valid work in O1, O2, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O4",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present a reconstructible comparison between the primary B-spline result and a control exposing a distinct material failure mode, stating the physical range in which agreement or conflict is established.",
+      "award_conditions": [
+        "The candidate presents a reconstructible control comparison that can expose a distinct material failure mode and states the actual physical range of agreement/conflict.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F4 (Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.)",
+        "Preserve independently valid work in O1, O2, O3, V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "I1",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify both Case-A plateaus, approximate cutoff scales near orders 40 and 120, and the much weaker second plateau in the submitted evidence.",
+      "award_conditions": [
+        "The candidate identifies Case-A plateaus, cutoff scales near 40/120 and much weaker second branch in their presented evidence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O1 (Present correct, reconstructible, claim-sufficient Case-A harmonic evidence spanning the full material response, including the first plateau and weaker second plateau beyond the first cutoff.)",
+        "Preserve independently valid work in I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article p.033852-3, Fig.2 and two-plateau paragraph: first plateau and roughly five-orders-weaker second plateau, with cutoff scales near harmonic orders 40 and 120; bands 2/3 and higher-band pathways differ."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I2",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify the important same-band/intraband contribution among the first few Case-B harmonics, or a genuinely physically equivalent low-order contribution, from presented causal evidence.",
+      "award_conditions": [
+        "The candidate identifies an important same-band/intraband contribution at low Case-B orders or a genuinely equivalent causal contribution."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O3 (Present reconstructible Case-B causal decomposition or genuinely equivalent evidence distinguishing low-order and higher-first-plateau contributions; static labels, duplicate currents, swapped components or false spectral-power addition are insufficient.)",
+        "Preserve independently valid work in I1, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I3",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify different-band/interband dominance at higher orders of the Case-B first plateau, or a genuinely physically equivalent high-order contribution, from presented causal evidence.",
+      "award_conditions": [
+        "The candidate identifies different-band/interband dominance at higher first-plateau orders or a genuinely equivalent causal contribution."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O3 (Present reconstructible Case-B causal decomposition or genuinely equivalent evidence distinguishing low-order and higher-first-plateau contributions; static labels, duplicate currents, swapped components or false spectral-power addition are insufficient.)",
+        "Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M1",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Link calculated band structure and driven dynamics to Case A's two plateaus, cutoff scales and weak second branch in an evidence-grounded causal account.",
+      "award_conditions": [
+        "Calculated bands and driven evidence explain Case-A plateau/cutoff ordering and weak higher branch rather than naming two plateaus alone."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I1 (Identify both Case-A plateaus, approximate cutoff scales near orders 40 and 120, and the much weaker second plateau in the submitted evidence.); F4 (Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.)",
+        "Preserve independently valid work in M2, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article p.033852-3, Fig.2 and two-plateau paragraph: first plateau and roughly five-orders-weaker second plateau, with cutoff scales near harmonic orders 40 and 120; bands 2/3 and higher-band pathways differ."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M2",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain from submitted evidence the important low-order Case-B intraband/same-band contribution or a physically equivalent low-order causal account.",
+      "award_conditions": [
+        "Presented causal evidence grounds the important low-order Case-B contribution and its physical origin."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I2 (Identify the important same-band/intraband contribution among the first few Case-B harmonics, or a genuinely physically equivalent low-order contribution, from presented causal evidence.); F4 (Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.)",
+        "Preserve independently valid work in M1, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M3",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain from submitted evidence the higher-first-plateau Case-B interband/different-band dominance or a physically equivalent high-order causal account.",
+      "award_conditions": [
+        "Presented causal evidence grounds higher-first-plateau Case-B dominance and its physical origin."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I3 (Identify different-band/interband dominance at higher orders of the Case-B first plateau, or a genuinely physically equivalent high-order contribution, from presented causal evidence.); F4 (Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.)",
+        "Preserve independently valid work in M1, M2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M4",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "State where the Case-B physical account applies or changes between low and higher-first-plateau orders, without extending a local mechanism to the full response without evidence.",
+      "award_conditions": [
+        "The candidate locates where the Case-B mechanism applies or changes and does not extend a local decomposition globally without evidence."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I2 (Identify the important same-band/intraband contribution among the first few Case-B harmonics, or a genuinely physically equivalent low-order contribution, from presented causal evidence.); I3 (Identify different-band/interband dominance at higher orders of the Case-B first plateau, or a genuinely physically equivalent high-order contribution, from presented causal evidence.)",
+        "Preserve independently valid work in M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M5",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "For Case A, decide coordinate-space reliability from evidence covering every material response range in the claim and challenged by a distinct-failure-mode control; explicitly localize the conclusion when evidence is local.",
+      "award_conditions": [
+        "Case-A reliability is supported over every material response range included in the claim and challenged by a distinct-failure-mode control; a local claim is explicitly localized."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O1 (Present correct, reconstructible, claim-sufficient Case-A harmonic evidence spanning the full material response, including the first plateau and weaker second plateau beyond the first cutoff.); O4 (Present a reconstructible comparison between the primary B-spline result and a control exposing a distinct material failure mode, stating the physical range in which agreement or conflict is established.)",
+        "Preserve independently valid work in M6, M2, M3, V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M6",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "For Case B, reach an evidence-bounded coordinate-space reliability decision using that case's material response and a control exposing a distinct failure mode.",
+      "award_conditions": [
+        "Case-B reliability follows that case's actual response and a control capable of exposing a distinct material failure mode."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O2 (Present correct, reconstructible, claim-sufficient Case-B full material harmonic response with proper case, initial-state, observable and representation identity.); O4 (Present a reconstructible comparison between the primary B-spline result and a control exposing a distinct material failure mode, stating the physical range in which agreement or conflict is established.)",
+        "Preserve independently valid work in M5, M1, V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M7",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explicitly reconcile material agreement/conflict among primary, auxiliary/control and mechanism evidence and explain its effect on retained reliability and physical conclusions; do not suppress a conclusion-changing conflict.",
+      "award_conditions": [
+        "The candidate reconciles conclusion-changing agreement/conflict among primary, control and causal evidence instead of suppressing it."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O4 (Present a reconstructible comparison between the primary B-spline result and a control exposing a distinct material failure mode, stating the physical range in which agreement or conflict is established.)",
+        "Preserve independently valid work in V2, M1, M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-1-4, SAE model boundary, Sec.III.A numerical-stability comparison and last p.033852-4 model-potential qualification. Reconciling material disagreements and bounded reliability claims are task-defined, not universal experimental equivalence."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V1",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "When the method, data, anomaly or retained claim exposes a concrete material failure risk, challenge it with functionally capable evidence and state its effective physical range. A same-integrator basis comparison sharing the error class is not sufficient by itself.",
+      "award_conditions": [
+        "A concrete triggered failure risk is challenged by functionally capable evidence over its actual range; shared-integrator basis convergence alone does not establish distinct sensitivity."
+      ],
+      "applicability_and_na": [
+        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
+        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O4 (Present a reconstructible comparison between the primary B-spline result and a control exposing a distinct material failure mode, stating the physical range in which agreement or conflict is established.)",
+        "Preserve independently valid work in O1, O2, M1, M2, M3, V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations."
+      ],
+      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V2",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Restrict conclusions to the established one-dimensional single-active-electron model and physical domain, without equating numerical smoothness, precision or apparent convergence with physical certainty.",
+      "award_conditions": [
+        "The conclusion remains within the 1D SAE model and established physical range, without treating smoothness or precision as certainty."
+      ],
+      "applicability_and_na": [
+        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.",
+        "Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.",
+        "Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels."
+      ],
+      "source_support": [
+        "Guan et al. (2016), article pp.033852-1-4, SAE model boundary, Sec.III.A numerical-stability comparison and last p.033852-4 model-potential qualification. Reconciling material disagreements and bounded reliability claims are task-defined, not universal experimental equivalence."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    }
+  ],
+  "case_scientific_rules": [
+    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
+    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
+    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
+    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
+    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
+    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
+    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
+    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
+    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
+    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
+    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
+    "Approximate band-family ranges are -14.31 to -14.13, -4.86 to -2.66, 1.52 to 9.19 and 9.99 to 23.88 eV. These support physical identity, not fixed plot bounds.",
+    "A survey ending near the first Case-A cutoff cannot establish the full response. Correct explicitly local results retain their own credit, but cannot supply the omitted weak high-energy branch.",
+    "Component spectral powers must not be arithmetically forced to equal the coherent total. A correct total retains independent credit when causal decomposition fails.",
+    "Two bases sharing a one-cell sector, integrator and observable reduction may verify basis convergence but do not automatically provide independent failure-mode sensitivity.",
+    "No source basis size, finite-box ordinal, box, absorber, window, projector, fixed grid or plot layout is a target; physical equivalence must be demonstrated rather than inferred from code sharing or visual similarity.",
+    "A standard B-spline Galerkin construction produces a nonorthogonal field-free problem and driven TDSE for the supplied periodic potential and field. The physical initial state is band 2 at $k=0$; it must remain the same state under any representation change. Source-used values such as 3600 splines, the $[-240,240]$ box, midpoint Crank-Nicolson, outer absorber and Hanning window are reproduction evidence, not grading requirements.",
+    "Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target and produce converged evidence. A finite-box ordinal, shared code path or visually similar spectrum does not by itself establish physical equivalence.",
+    "Canonical field-free evidence contains four corresponding band families with approximate ranges $-14.31$ to $-14.13$ eV, $-4.86$ to $-2.66$ eV, $1.52$ to $9.19$ eV and $9.99$ to $23.88$ eV.",
+    "For Case A, the physical harmonic response has two plateau regions. Their approximate cutoffs are near orders 40 and 120, with the second plateau much weaker than the first. A calculation or displayed survey that stops around the first cutoff has not established the full response even if that range is smooth and converged.",
+    "For Case B, source-backed causal evidence shows an important same-band or intraband contribution among the first few harmonics and different-band or interband dominance over higher orders of the first plateau. Equivalent current-level causal distinctions are accepted. Component spectral powers must not be arithmetically forced to equal the coherent total.",
+    "The source canonical route uses periodic Bloch and moving-band/Houston descriptions. They are not secretly required by name. Full credit requires evidence capable of exposing a material failure mode not shared with the primary calculation. This may be an independently formulated periodic method, an analytically controlled limit, or another comparably strong falsification route.",
+    "Two bases that converge to the same one-cell sector with the same integrator and observable reduction can provide useful basis verification, but they do not automatically receive full independence credit. Grade the error classes the comparison can expose, not whether two filenames or basis labels differ.",
+    "For F1-F3/O3/M2-M4, article p.033852-2, Eqs.(4),(6)-(12), a nonorthogonal B-spline representation obeys $iS\\dot C=H(t)C$, with norm $C^\\dagger SC$. For physical band projectors $P_b$,\n$$j_{\\rm intra}=-\\frac em\\sum_b\\langle\\psi|P_b\\hat pP_b|\\psi\\rangle,\\quad\nj_{\\rm inter}=-\\frac em\\sum_{b\\ne b'}\\langle\\psi|P_b\\hat pP_{b'}|\\psi\\rangle,\\quad j=j_{\\rm intra}+j_{\\rm inter}.$$\nThus $|\\widetilde j|^2=|\\widetilde j_{\\rm intra}|^2+|\\widetilde j_{\\rm inter}|^2+2\\Re(\\widetilde j_{\\rm intra}\\widetilde j_{\\rm inter}^*)$. In a different gauge the current and projectors must be transformed consistently. Equivalent methods must preserve the same physical k=0 band-2 state and causal content; matching a finite-box ordinal, swapping component names, or comparing two implementations sharing the relevant error class does not establish equivalence or independent reliability."
+  ],
+  "closure_requirements": {
+    "RC0": [
+      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
+      "Required indispensable claim CL1, central physical object: all of: F1 (Construct a coordinate-space B-spline TDSE for the specified one-dimensional periodic potential and both drives with consistent executable and auditable field coupling.); F3 (Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC1": [
+      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
+      "Required indispensable claim CL1, indispensable material component: all of: F2 (Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.); O1 (Present correct, reconstructible, claim-sufficient Case-A harmonic evidence spanning the full material response, including the first plateau and weaker second plateau beyond the first cutoff.); O2 (Present correct, reconstructible, claim-sufficient Case-B full material harmonic response with proper case, initial-state, observable and representation identity.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL2, indispensable material component: O3 (Present reconstructible Case-B causal decomposition or genuinely equivalent evidence distinguishing low-order and higher-first-plateau contributions; static labels, duplicate currents, swapped components or false spectral-power addition are insufficient.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC2": [
+      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
+      "Required indispensable claim CL1, principal mechanism or commissioned conclusion: all of: M5 (For Case A, decide coordinate-space reliability from evidence covering every material response range in the claim and challenged by a distinct-failure-mode control; explicitly localize the conclusion when evidence is local.); M6 (For Case B, reach an evidence-bounded coordinate-space reliability decision using that case's material response and a control exposing a distinct failure mode.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M1 (Link calculated band structure and driven dynamics to Case A's two plateaus, cutoff scales and weak second branch in an evidence-grounded causal account.); M2 (Explain from submitted evidence the important low-order Case-B intraband/same-band contribution or a physically equivalent low-order causal account.); M3 (Explain from submitted evidence the higher-first-plateau Case-B interband/different-band dominance or a physically equivalent high-order causal account.); M4 (State where the Case-B physical account applies or changes between low and higher-first-plateau orders, without extending a local mechanism to the full response without evidence.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required indispensable claim CL3, principal mechanism or commissioned conclusion: M7 (Explicitly reconcile material agreement/conflict among primary, auxiliary/control and mechanism evidence and explain its effect on retained reliability and physical conclusions; do not suppress a conclusion-changing conflict.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC3": [
+      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
+      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
+      "Required indispensable claim CL3, material validation/scope: V1 (When the method, data, anomaly or retained claim exposes a concrete material failure risk, challenge it with functionally capable evidence and state its effective physical range. A same-integrator basis comparison sharing the error class is not sufficient by itself.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC4": [
+      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
+      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
+      "Close CL1 central physical object: all of: F1 (Construct a coordinate-space B-spline TDSE for the specified one-dimensional periodic potential and both drives with consistent executable and auditable field coupling.); F3 (Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.).",
+      "Close CL1 indispensable material component: all of: F2 (Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.); O1 (Present correct, reconstructible, claim-sufficient Case-A harmonic evidence spanning the full material response, including the first plateau and weaker second plateau beyond the first cutoff.); O2 (Present correct, reconstructible, claim-sufficient Case-B full material harmonic response with proper case, initial-state, observable and representation identity.).",
+      "Close CL1 principal mechanism or commissioned conclusion: all of: M5 (For Case A, decide coordinate-space reliability from evidence covering every material response range in the claim and challenged by a distinct-failure-mode control; explicitly localize the conclusion when evidence is local.); M6 (For Case B, reach an evidence-bounded coordinate-space reliability decision using that case's material response and a control exposing a distinct failure mode.).",
+      "Close CL2 indispensable material component: O3 (Present reconstructible Case-B causal decomposition or genuinely equivalent evidence distinguishing low-order and higher-first-plateau contributions; static labels, duplicate currents, swapped components or false spectral-power addition are insufficient.).",
+      "Close CL2 principal mechanism or commissioned conclusion: all of: M1 (Link calculated band structure and driven dynamics to Case A's two plateaus, cutoff scales and weak second branch in an evidence-grounded causal account.); M2 (Explain from submitted evidence the important low-order Case-B intraband/same-band contribution or a physically equivalent low-order causal account.); M3 (Explain from submitted evidence the higher-first-plateau Case-B interband/different-band dominance or a physically equivalent high-order causal account.); M4 (State where the Case-B physical account applies or changes between low and higher-first-plateau orders, without extending a local mechanism to the full response without evidence.).",
+      "Close CL3 principal mechanism or commissioned conclusion: M7 (Explicitly reconcile material agreement/conflict among primary, auxiliary/control and mechanism evidence and explain its effect on retained reliability and physical conclusions; do not suppress a conclusion-changing conflict.).",
+      "Close CL3 material validation/scope: V1 (When the method, data, anomaly or retained claim exposes a concrete material failure risk, challenge it with functionally capable evidence and state its effective physical range. A same-integrator basis comparison sharing the error class is not sufficient by itself.)."
+    ]
+  },
+  "references": [
+    {
+      "citation": "Zhong Guan, Xiao-Xin Zhou, and Xue-Bin Bian. 2016. *High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses*. *Physical Review A*, 93, 033852.",
+      "url": "https://doi.org/10.1103/PhysRevA.93.033852",
+      "scientific_scope": "High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses",
+      "anchors": [
+        "Guan et al. (2016), article pp.033852-1-2, Eqs.(1)-(7), Fig.1(a-d), paragraph choosing k=0 in band 2: B-spline generalized metric and physical initial-state identity, not finite-box ordinal.",
+        "Guan et al. (2016), article p.033852-2, Eq.(8), and p.033852-3 Fourier/window paragraph: laser-induced current and spectrum. Gauge/derivative equivalence requires actual observable mapping, not appearance alone.",
+        "Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations.",
+        "Guan et al. (2016), article p.033852-3, Fig.2 and two-plateau paragraph: first plateau and roughly five-orders-weaker second plateau, with cutoff scales near harmonic orders 40 and 120; bands 2/3 and higher-band pathways differ.",
+        "Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add.",
+        "Guan et al. (2016), article pp.033852-1-4, SAE model boundary, Sec.III.A numerical-stability comparison and last p.033852-4 model-potential qualification. Reconciling material disagreements and bounded reliability claims are task-defined, not universal experimental equivalence."
+      ]
+    },
+    {
+      "citation": "Mengxi Wu, Shambhu Ghimire, David A. Reis, Kenneth J. Schafer, and Mette B. Gaarde. 2015. *High-harmonic generation from Bloch electrons in solids*. *Physical Review A*, 91, 043839.",
+      "url": "https://doi.org/10.1103/PhysRevA.91.043839",
+      "scientific_scope": "Secondary periodic Bloch/Houston method and physical-equivalence boundary, not a required auxiliary implementation.",
+      "anchors": [
+        "Article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23), Fig.5."
+      ]
+    }
+  ]
+}

cases/case09/grading_rubric.md

@@ -0,0 +1,844 @@
+# Grading Rubric — Case09
+
+Case09 — High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses
+
+## Atomic Scoring Criteria
+
+Each criterion awards 0 or 0.5 points, for a maximum of 10. Explicit N/A rules apply where stated.
+
+### F1 — F — 0.5 points
+
+**Scientific requirement**
+
+Construct a coordinate-space B-spline TDSE for the specified one-dimensional periodic potential and both drives with consistent executable and auditable field coupling.
+
+**Conditions for credit**
+
+- The primary coordinate-space B-spline TDSE preserves the specified periodic potential and both physical drives with auditable field coupling.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-1-2, Eqs.(1)-(7), Fig.1(a-d), paragraph choosing k=0 in band 2: B-spline generalized metric and physical initial-state identity, not finite-box ordinal.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F2 — F — 0.5 points
+
+**Scientific requirement**
+
+Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.
+
+**Conditions for credit**
+
+- The initial state is physically band 2 at k=0 and is demonstrably preserved in every representation or auxiliary calculation.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-1-2, Eqs.(1)-(7), Fig.1(a-d), paragraph choosing k=0 in band 2: B-spline generalized metric and physical initial-state identity, not finite-box ordinal.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F3 — F — 0.5 points
+
+**Scientific requirement**
+
+Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.
+
+**Conditions for credit**
+
+- A consistent radiation/current observable and its gauge, field amplitude, frequency, carrier time/phase and units define the HHG comparison.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article p.033852-2, Eq.(8), and p.033852-3 Fourier/window paragraph: laser-induced current and spectrum. Gauge/derivative equivalence requires actual observable mapping, not appearance alone.
+
+**Research Closure relation**
+
+Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### F4 — F — 0.5 points
+
+**Scientific requirement**
+
+Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.
+
+**Conditions for credit**
+
+- The actual theoretical/control framework has reproducible physical observables and can test interpretation/reliability; a relabelled duplicate or static-only driven check is insufficient.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### O1 — O — 0.5 points
+
+**Scientific requirement**
+
+Present correct, reconstructible, claim-sufficient Case-A harmonic evidence spanning the full material response, including the first plateau and weaker second plateau beyond the first cutoff.
+
+**Conditions for credit**
+
+- Case-A spectrum resolves the full material response, including the first plateau and much weaker second plateau beyond its first cutoff, with correct state/object identity.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Construct a coordinate-space B-spline TDSE for the specified one-dimensional periodic potential and both drives with consistent executable and auditable field coupling.); F2 (Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.); F3 (Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.)
+
+- Preserve independently valid work in O2, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article p.033852-3, Fig.2 and two-plateau paragraph: first plateau and roughly five-orders-weaker second plateau, with cutoff scales near harmonic orders 40 and 120; bands 2/3 and higher-band pathways differ.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O2 — O — 0.5 points
+
+**Scientific requirement**
+
+Present correct, reconstructible, claim-sufficient Case-B full material harmonic response with proper case, initial-state, observable and representation identity.
+
+**Conditions for credit**
+
+- Case-B full material response is reconstructible and correctly bound to its drive, initial state, observable and representation.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F1 (Construct a coordinate-space B-spline TDSE for the specified one-dimensional periodic potential and both drives with consistent executable and auditable field coupling.); F2 (Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.); F3 (Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.)
+
+- Preserve independently valid work in O1, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O3 — O — 0.5 points
+
+**Scientific requirement**
+
+Present reconstructible Case-B causal decomposition or genuinely equivalent evidence distinguishing low-order and higher-first-plateau contributions; static labels, duplicate currents, swapped components or false spectral-power addition are insufficient.
+
+**Conditions for credit**
+
+- A causal current-level or truly equivalent distinction separates low-order and higher-first-plateau mechanisms without duplicate/swapped components or false power addition.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: F2 (Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.); F3 (Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.); F4 (Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.)
+
+- Preserve independently valid work in O1, O2, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add.
+
+**Research Closure relation**
+
+Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### O4 — O — 0.5 points
+
+**Scientific requirement**
+
+Present a reconstructible comparison between the primary B-spline result and a control exposing a distinct material failure mode, stating the physical range in which agreement or conflict is established.
+
+**Conditions for credit**
+
+- The candidate presents a reconstructible control comparison that can expose a distinct material failure mode and states the actual physical range of agreement/conflict.
+
+- Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: F4 (Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.)
+
+- Preserve independently valid work in O1, O2, O3, V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid.
+
+### I1 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify both Case-A plateaus, approximate cutoff scales near orders 40 and 120, and the much weaker second plateau in the submitted evidence.
+
+**Conditions for credit**
+
+- The candidate identifies Case-A plateaus, cutoff scales near 40/120 and much weaker second branch in their presented evidence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O1 (Present correct, reconstructible, claim-sufficient Case-A harmonic evidence spanning the full material response, including the first plateau and weaker second plateau beyond the first cutoff.)
+
+- Preserve independently valid work in I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article p.033852-3, Fig.2 and two-plateau paragraph: first plateau and roughly five-orders-weaker second plateau, with cutoff scales near harmonic orders 40 and 120; bands 2/3 and higher-band pathways differ.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I2 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify the important same-band/intraband contribution among the first few Case-B harmonics, or a genuinely physically equivalent low-order contribution, from presented causal evidence.
+
+**Conditions for credit**
+
+- The candidate identifies an important same-band/intraband contribution at low Case-B orders or a genuinely equivalent causal contribution.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O3 (Present reconstructible Case-B causal decomposition or genuinely equivalent evidence distinguishing low-order and higher-first-plateau contributions; static labels, duplicate currents, swapped components or false spectral-power addition are insufficient.)
+
+- Preserve independently valid work in I1, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### I3 — I — 0.5 points
+
+**Scientific requirement**
+
+Identify different-band/interband dominance at higher orders of the Case-B first plateau, or a genuinely physically equivalent high-order contribution, from presented causal evidence.
+
+**Conditions for credit**
+
+- The candidate identifies different-band/interband dominance at higher first-plateau orders or a genuinely equivalent causal contribution.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O3 (Present reconstructible Case-B causal decomposition or genuinely equivalent evidence distinguishing low-order and higher-first-plateau contributions; static labels, duplicate currents, swapped components or false spectral-power addition are insufficient.)
+
+- Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M1 — M — 0.5 points
+
+**Scientific requirement**
+
+Link calculated band structure and driven dynamics to Case A's two plateaus, cutoff scales and weak second branch in an evidence-grounded causal account.
+
+**Conditions for credit**
+
+- Calculated bands and driven evidence explain Case-A plateau/cutoff ordering and weak higher branch rather than naming two plateaus alone.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: I1 (Identify both Case-A plateaus, approximate cutoff scales near orders 40 and 120, and the much weaker second plateau in the submitted evidence.); F4 (Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.)
+
+- Preserve independently valid work in M2, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article p.033852-3, Fig.2 and two-plateau paragraph: first plateau and roughly five-orders-weaker second plateau, with cutoff scales near harmonic orders 40 and 120; bands 2/3 and higher-band pathways differ.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M2 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain from submitted evidence the important low-order Case-B intraband/same-band contribution or a physically equivalent low-order causal account.
+
+**Conditions for credit**
+
+- Presented causal evidence grounds the important low-order Case-B contribution and its physical origin.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: I2 (Identify the important same-band/intraband contribution among the first few Case-B harmonics, or a genuinely physically equivalent low-order contribution, from presented causal evidence.); F4 (Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.)
+
+- Preserve independently valid work in M1, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M3 — M — 0.5 points
+
+**Scientific requirement**
+
+Explain from submitted evidence the higher-first-plateau Case-B interband/different-band dominance or a physically equivalent high-order causal account.
+
+**Conditions for credit**
+
+- Presented causal evidence grounds higher-first-plateau Case-B dominance and its physical origin.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: I3 (Identify different-band/interband dominance at higher orders of the Case-B first plateau, or a genuinely physically equivalent high-order contribution, from presented causal evidence.); F4 (Give the actual theoretical/auxiliary framework for interpreting radiation and testing reliability with reproducible observables; a renamed duplicate, static-only driven-validation claim or undefined mechanism object is insufficient.)
+
+- Preserve independently valid work in M1, M2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M4 — M — 0.5 points
+
+**Scientific requirement**
+
+State where the Case-B physical account applies or changes between low and higher-first-plateau orders, without extending a local mechanism to the full response without evidence.
+
+**Conditions for credit**
+
+- The candidate locates where the Case-B mechanism applies or changes and does not extend a local decomposition globally without evidence.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: I2 (Identify the important same-band/intraband contribution among the first few Case-B harmonics, or a genuinely physically equivalent low-order contribution, from presented causal evidence.); I3 (Identify different-band/interband dominance at higher orders of the Case-B first plateau, or a genuinely physically equivalent high-order contribution, from presented causal evidence.)
+
+- Preserve independently valid work in M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M5 — M — 0.5 points
+
+**Scientific requirement**
+
+For Case A, decide coordinate-space reliability from evidence covering every material response range in the claim and challenged by a distinct-failure-mode control; explicitly localize the conclusion when evidence is local.
+
+**Conditions for credit**
+
+- Case-A reliability is supported over every material response range included in the claim and challenged by a distinct-failure-mode control; a local claim is explicitly localized.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O1 (Present correct, reconstructible, claim-sufficient Case-A harmonic evidence spanning the full material response, including the first plateau and weaker second plateau beyond the first cutoff.); O4 (Present a reconstructible comparison between the primary B-spline result and a control exposing a distinct material failure mode, stating the physical range in which agreement or conflict is established.)
+
+- Preserve independently valid work in M6, M2, M3, V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M6 — M — 0.5 points
+
+**Scientific requirement**
+
+For Case B, reach an evidence-bounded coordinate-space reliability decision using that case's material response and a control exposing a distinct failure mode.
+
+**Conditions for credit**
+
+- Case-B reliability follows that case's actual response and a control capable of exposing a distinct material failure mode.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: all of: O2 (Present correct, reconstructible, claim-sufficient Case-B full material harmonic response with proper case, initial-state, observable and representation identity.); O4 (Present a reconstructible comparison between the primary B-spline result and a control exposing a distinct material failure mode, stating the physical range in which agreement or conflict is established.)
+
+- Preserve independently valid work in M5, M1, V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### M7 — M — 0.5 points
+
+**Scientific requirement**
+
+Explicitly reconcile material agreement/conflict among primary, auxiliary/control and mechanism evidence and explain its effect on retained reliability and physical conclusions; do not suppress a conclusion-changing conflict.
+
+**Conditions for credit**
+
+- The candidate reconciles conclusion-changing agreement/conflict among primary, control and causal evidence instead of suppressing it.
+
+**Applicability and N/A**
+
+- This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O4 (Present a reconstructible comparison between the primary B-spline result and a control exposing a distinct material failure mode, stating the physical range in which agreement or conflict is established.)
+
+- Preserve independently valid work in V2, M1, M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-1-4, SAE model boundary, Sec.III.A numerical-stability comparison and last p.033852-4 model-potential qualification. Reconciling material disagreements and bounded reliability claims are task-defined, not universal experimental equivalence.
+
+**Research Closure relation**
+
+Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V1 — V — 0.5 points
+
+**Scientific requirement**
+
+When the method, data, anomaly or retained claim exposes a concrete material failure risk, challenge it with functionally capable evidence and state its effective physical range. A same-integrator basis comparison sharing the error class is not sufficient by itself.
+
+**Conditions for credit**
+
+- A concrete triggered failure risk is challenged by functionally capable evidence over its actual range; shared-integrator basis convergence alone does not establish distinct sensitivity.
+
+**Applicability and N/A**
+
+- Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.
+
+- If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: O4 (Present a reconstructible comparison between the primary B-spline result and a control exposing a distinct material failure mode, stating the physical range in which agreement or conflict is established.)
+
+- Preserve independently valid work in O1, O2, M1, M2, M3, V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations.
+
+**Research Closure relation**
+
+Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+### V2 — V — 0.5 points
+
+**Scientific requirement**
+
+Restrict conclusions to the established one-dimensional single-active-electron model and physical domain, without equating numerical smoothness, precision or apparent convergence with physical certainty.
+
+**Conditions for credit**
+
+- The conclusion remains within the 1D SAE model and established physical range, without treating smoothness or precision as certainty.
+
+**Applicability and N/A**
+
+- This positive scientific scope/evidence duty is unconditional; N/A is not permitted.
+
+**Scientific dependencies and independent credit**
+
+- Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.
+
+- Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied.
+
+**Accepted equivalent evidence**
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target, especially band-2 k=0 identity, and produce converged evidence.
+
+- Physically equivalent current-level causal distinctions are accepted in place of the canonical same-band/different-band decomposition; no named Houston or Bloch auxiliary route is compulsory.
+
+- Independent periodic formulations, controlled analytic limits or comparably strong falsification routes are accepted by the error classes they expose, not their filenames or basis labels.
+
+**Scientific source locations**
+
+- Guan et al. (2016), article pp.033852-1-4, SAE model boundary, Sec.III.A numerical-stability comparison and last p.033852-4 model-potential qualification. Reconciling material disagreements and bounded reliability claims are task-defined, not universal experimental equivalence.
+
+**Research Closure relation**
+
+Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure.
+
+## Research Closure Requirements
+
+### RC0
+
+- The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.
+
+- Required indispensable claim CL1, central physical object: all of: F1 (Construct a coordinate-space B-spline TDSE for the specified one-dimensional periodic potential and both drives with consistent executable and auditable field coupling.); F3 (Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC1
+
+- With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.
+
+- Required indispensable claim CL1, indispensable material component: all of: F2 (Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.); O1 (Present correct, reconstructible, claim-sufficient Case-A harmonic evidence spanning the full material response, including the first plateau and weaker second plateau beyond the first cutoff.); O2 (Present correct, reconstructible, claim-sufficient Case-B full material harmonic response with proper case, initial-state, observable and representation identity.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL2, indispensable material component: O3 (Present reconstructible Case-B causal decomposition or genuinely equivalent evidence distinguishing low-order and higher-first-plateau contributions; static labels, duplicate currents, swapped components or false spectral-power addition are insufficient.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC2
+
+- With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.
+
+- Required indispensable claim CL1, principal mechanism or commissioned conclusion: all of: M5 (For Case A, decide coordinate-space reliability from evidence covering every material response range in the claim and challenged by a distinct-failure-mode control; explicitly localize the conclusion when evidence is local.); M6 (For Case B, reach an evidence-bounded coordinate-space reliability decision using that case's material response and a control exposing a distinct failure mode.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M1 (Link calculated band structure and driven dynamics to Case A's two plateaus, cutoff scales and weak second branch in an evidence-grounded causal account.); M2 (Explain from submitted evidence the important low-order Case-B intraband/same-band contribution or a physically equivalent low-order causal account.); M3 (Explain from submitted evidence the higher-first-plateau Case-B interband/different-band dominance or a physically equivalent high-order causal account.); M4 (State where the Case-B physical account applies or changes between low and higher-first-plateau orders, without extending a local mechanism to the full response without evidence.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+- Required indispensable claim CL3, principal mechanism or commissioned conclusion: M7 (Explicitly reconcile material agreement/conflict among primary, auxiliary/control and mechanism evidence and explain its effect on retained reliability and physical conclusions; do not suppress a conclusion-changing conflict.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC3
+
+- With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.
+
+- Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.
+
+- Required indispensable claim CL3, material validation/scope: V1 (When the method, data, anomaly or retained claim exposes a concrete material failure risk, challenge it with functionally capable evidence and state its effective physical range. A same-integrator basis comparison sharing the error class is not sufficient by itself.). Judge the role-specific failure facts, not the corresponding atom scores.
+
+### RC4
+
+- All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.
+
+- Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.
+
+- Close CL1 central physical object: all of: F1 (Construct a coordinate-space B-spline TDSE for the specified one-dimensional periodic potential and both drives with consistent executable and auditable field coupling.); F3 (Define a physically consistent HHG radiation observable in the chosen gauge/representation and consistently state field amplitude, frequency, carrier phase/time origin and units.).
+
+- Close CL1 indispensable material component: all of: F2 (Prepare band 2 at k=0 as the same physical initial state and preserve that identity under every representation change and auxiliary calculation.); O1 (Present correct, reconstructible, claim-sufficient Case-A harmonic evidence spanning the full material response, including the first plateau and weaker second plateau beyond the first cutoff.); O2 (Present correct, reconstructible, claim-sufficient Case-B full material harmonic response with proper case, initial-state, observable and representation identity.).
+
+- Close CL1 principal mechanism or commissioned conclusion: all of: M5 (For Case A, decide coordinate-space reliability from evidence covering every material response range in the claim and challenged by a distinct-failure-mode control; explicitly localize the conclusion when evidence is local.); M6 (For Case B, reach an evidence-bounded coordinate-space reliability decision using that case's material response and a control exposing a distinct failure mode.).
+
+- Close CL2 indispensable material component: O3 (Present reconstructible Case-B causal decomposition or genuinely equivalent evidence distinguishing low-order and higher-first-plateau contributions; static labels, duplicate currents, swapped components or false spectral-power addition are insufficient.).
+
+- Close CL2 principal mechanism or commissioned conclusion: all of: M1 (Link calculated band structure and driven dynamics to Case A's two plateaus, cutoff scales and weak second branch in an evidence-grounded causal account.); M2 (Explain from submitted evidence the important low-order Case-B intraband/same-band contribution or a physically equivalent low-order causal account.); M3 (Explain from submitted evidence the higher-first-plateau Case-B interband/different-band dominance or a physically equivalent high-order causal account.); M4 (State where the Case-B physical account applies or changes between low and higher-first-plateau orders, without extending a local mechanism to the full response without evidence.).
+
+- Close CL3 principal mechanism or commissioned conclusion: M7 (Explicitly reconcile material agreement/conflict among primary, auxiliary/control and mechanism evidence and explain its effect on retained reliability and physical conclusions; do not suppress a conclusion-changing conflict.).
+
+- Close CL3 material validation/scope: V1 (When the method, data, anomaly or retained claim exposes a concrete material failure risk, challenge it with functionally capable evidence and state its effective physical range. A same-integrator basis comparison sharing the error class is not sufficient by itself.).
+
+## Applicability and Equivalent Evidence
+
+- Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.
+
+- Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.
+
+- For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.
+
+- Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.
+
+- Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.
+
+- Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.
+
+- Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.
+
+- Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.
+
+- Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.
+
+- Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.
+
+- A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.
+
+- Approximate band-family ranges are -14.31 to -14.13, -4.86 to -2.66, 1.52 to 9.19 and 9.99 to 23.88 eV. These support physical identity, not fixed plot bounds.
+
+- A survey ending near the first Case-A cutoff cannot establish the full response. Correct explicitly local results retain their own credit, but cannot supply the omitted weak high-energy branch.
+
+- Component spectral powers must not be arithmetically forced to equal the coherent total. A correct total retains independent credit when causal decomposition fails.
+
+- Two bases sharing a one-cell sector, integrator and observable reduction may verify basis convergence but do not automatically provide independent failure-mode sensitivity.
+
+- No source basis size, finite-box ordinal, box, absorber, window, projector, fixed grid or plot layout is a target; physical equivalence must be demonstrated rather than inferred from code sharing or visual similarity.
+
+- A standard B-spline Galerkin construction produces a nonorthogonal field-free problem and driven TDSE for the supplied periodic potential and field. The physical initial state is band 2 at $k=0$; it must remain the same state under any representation change. Source-used values such as 3600 splines, the $[-240,240]$ box, midpoint Crank-Nicolson, outer absorber and Hanning window are reproduction evidence, not grading requirements.
+
+- Gauge-, basis-, boundary-, propagator- and transform-equivalent realizations are accepted when they preserve the physical target and produce converged evidence. A finite-box ordinal, shared code path or visually similar spectrum does not by itself establish physical equivalence.
+
+- Canonical field-free evidence contains four corresponding band families with approximate ranges $-14.31$ to $-14.13$ eV, $-4.86$ to $-2.66$ eV, $1.52$ to $9.19$ eV and $9.99$ to $23.88$ eV.
+
+- For Case A, the physical harmonic response has two plateau regions. Their approximate cutoffs are near orders 40 and 120, with the second plateau much weaker than the first. A calculation or displayed survey that stops around the first cutoff has not established the full response even if that range is smooth and converged.
+
+- For Case B, source-backed causal evidence shows an important same-band or intraband contribution among the first few harmonics and different-band or interband dominance over higher orders of the first plateau. Equivalent current-level causal distinctions are accepted. Component spectral powers must not be arithmetically forced to equal the coherent total.
+
+- The source canonical route uses periodic Bloch and moving-band/Houston descriptions. They are not secretly required by name. Full credit requires evidence capable of exposing a material failure mode not shared with the primary calculation. This may be an independently formulated periodic method, an analytically controlled limit, or another comparably strong falsification route.
+
+- Two bases that converge to the same one-cell sector with the same integrator and observable reduction can provide useful basis verification, but they do not automatically receive full independence credit. Grade the error classes the comparison can expose, not whether two filenames or basis labels differ.
+
+For F1-F3/O3/M2-M4, article p.033852-2, Eqs.(4),(6)-(12), a nonorthogonal B-spline representation obeys $iS\dot C=H(t)C$, with norm $C^\dagger SC$. For physical band projectors $P_b$,
+$$j_{\rm intra}=-\frac em\sum_b\langle\psi|P_b\hat pP_b|\psi\rangle,\quad
+j_{\rm inter}=-\frac em\sum_{b\ne b'}\langle\psi|P_b\hat pP_{b'}|\psi\rangle,\quad j=j_{\rm intra}+j_{\rm inter}.$$
+Thus $|\widetilde j|^2=|\widetilde j_{\rm intra}|^2+|\widetilde j_{\rm inter}|^2+2\Re(\widetilde j_{\rm intra}\widetilde j_{\rm inter}^*)$. In a different gauge the current and projectors must be transformed consistently. Equivalent methods must preserve the same physical k=0 band-2 state and causal content; matching a finite-box ordinal, swapping component names, or comparing two implementations sharing the relevant error class does not establish equivalence or independent reliability.

cases/case09/resource_limits.json

@@ -0,0 +1,8 @@
+{
+  "cpu_cores": 16,
+  "nodes": 1,
+  "time_limit_minutes": 30,
+  "network_access": "disabled",
+  "temporary_storage_gib": 64,
+  "memory_policy": "No separate task-specific RAM limit is specified."
+}

cases/case09/sources.md

@@ -0,0 +1,35 @@
+# Scientific Sources — Case09
+
+## References
+
+Zhong Guan, Xiao-Xin Zhou, and Xue-Bin Bian. 2016. *High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses*. *Physical Review A*, 93, 033852. [Source](https://doi.org/10.1103/PhysRevA.93.033852)
+
+High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses
+
+Mengxi Wu, Shambhu Ghimire, David A. Reis, Kenneth J. Schafer, and Mette B. Gaarde. 2015. *High-harmonic generation from Bloch electrons in solids*. *Physical Review A*, 91, 043839. [Source](https://doi.org/10.1103/PhysRevA.91.043839)
+
+Secondary periodic Bloch/Houston method and physical-equivalence boundary, not a required auxiliary implementation.
+
+## Criterion-to-source crosswalk
+
+Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.
+
+| Criteria | Source locations, scientific use and limits |
+|---|---|
+| F1, F2 | Guan et al. (2016), article pp.033852-1-2, Eqs.(1)-(7), Fig.1(a-d), paragraph choosing k=0 in band 2: B-spline generalized metric and physical initial-state identity, not finite-box ordinal. |
+| F3 | Guan et al. (2016), article p.033852-2, Eq.(8), and p.033852-3 Fourier/window paragraph: laser-induced current and spectrum. Gauge/derivative equivalence requires actual observable mapping, not appearance alone. |
+| F4, O4, M5, M6, V1 | Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations. |
+| O1, I1, M1 | Guan et al. (2016), article p.033852-3, Fig.2 and two-plateau paragraph: first plateau and roughly five-orders-weaker second plateau, with cutoff scales near harmonic orders 40 and 120; bands 2/3 and higher-band pathways differ. |
+| O2, O3, I2, I3, M2, M3, M4 | Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add. |
+| M7, V2 | Guan et al. (2016), article pp.033852-1-4, SAE model boundary, Sec.III.A numerical-stability comparison and last p.033852-4 model-potential qualification. Reconciling material disagreements and bounded reliability claims are task-defined, not universal experimental equivalence. |
+
+## Formula and convention notes
+
+For F1-F3/O3/M2-M4, article p.033852-2, Eqs.(4),(6)-(12), a nonorthogonal B-spline representation obeys $iS\dot C=H(t)C$, with norm $C^\dagger SC$. For physical band projectors $P_b$,
+$$j_{\rm intra}=-\frac em\sum_b\langle\psi|P_b\hat pP_b|\psi\rangle,\quad
+j_{\rm inter}=-\frac em\sum_{b\ne b'}\langle\psi|P_b\hat pP_{b'}|\psi\rangle,\quad j=j_{\rm intra}+j_{\rm inter}.$$
+Thus $|\widetilde j|^2=|\widetilde j_{\rm intra}|^2+|\widetilde j_{\rm inter}|^2+2\Re(\widetilde j_{\rm intra}\widetilde j_{\rm inter}^*)$. In a different gauge the current and projectors must be transformed consistently. Equivalent methods must preserve the same physical k=0 band-2 state and causal content; matching a finite-box ordinal, swapping component names, or comparing two implementations sharing the relevant error class does not establish equivalence or independent reliability.
+
+## Scope of the source anchors
+
+The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.

cases/case09/task.md

@@ -0,0 +1,91 @@
+# High-harmonic emission from a one-dimensional periodic system
+
+## Background and research question
+
+A coordinate-space finite-basis calculation can generate a smooth radiation
+spectrum without necessarily preserving all of the relevant physics of a
+periodic system. For the model and driving conditions below, assess whether a
+coordinate-space B-spline treatment provides a physically reliable account of
+high-harmonic emission and determine what physical conclusions are supported
+by your calculations.
+
+Design the derivation, computation, tests, evidence and scientific argument
+needed to answer this question. Do not assume in advance that the method is
+reliable or that a single interpretation applies to the full response.
+
+## Physical system
+
+Use atomic units unless stated otherwise. Treat one active electron in the
+one-dimensional periodic potential
+
+$$
+V(x)=-V_0\left[1+\cos\left(\frac{2\pi x}{a_0}\right)\right],
+\qquad V_0=0.37,
+\qquad a_0=8,
+$$
+
+under the electric-dipole approximation. The initial physical state belongs
+to band 2 at crystal momentum $k=0$.
+
+Use a linearly polarized finite-support field
+
+$$
+E(t)=E_0\cos^2\!\left(\frac{\pi t}{T}\right)
+\cos(\omega t+\varphi),
+\qquad |t|<\frac{T}{2},
+\qquad T=8\frac{2\pi}{\omega},
+$$
+
+and set it to zero outside the support. The carrier-phase and time-origin
+convention is not fixed; declare one and use the same physical field in every
+calculation being compared.
+
+| Case | Peak intensity | Wavelength |
+|---|---:|---:|
+| A | $8.087\times10^{11}\ \mathrm{W\,cm^{-2}}$ | $3.2\ \mu\mathrm m$ |
+| B | $4.5\times10^{11}\ \mathrm{W\,cm^{-2}}$ | $3.2\ \mu\mathrm m$ |
+
+Determine the field amplitude and carrier frequency using standard
+atomic-unit conversions and state the conventions used.
+
+## Research boundary
+
+Use a coordinate-space B-spline TDSE as the primary method. Standard
+periodic-state, analytical or numerical methods may be used as needed. All
+other modelling, numerical, diagnostic and presentation choices are yours.
+Establish that the evidence supporting each retained claim is sufficiently
+reliable and reproducible. Absolute spectral yield is not a grading target.
+
+## Submission and resources
+
+Submit one self-contained scientific report and an offline reproduction
+package containing the producing code, numerical data underlying the retained
+evidence, a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge, and concise run and environment
+information. No fixed scientific figure set, file tree or exploratory history
+is required.
+
+The active examination resources and limits are defined in the companion
+`resource_limits.json`. All retained production calculations must run
+within that fixed allocation and active wall time. More expensive modelling
+does not receive additional credit.
+
+## Reference and integrity policy
+
+This examination is conducted without network access or live literature
+retrieval. You may rely on your existing general scientific knowledge and, if any are
+explicitly supplied with the examination, on those offline materials or
+software documentation. Record every such source actually consulted. For formulas,
+methods, constants, or conventions used from general knowledge rather than a
+consulted source, state enough of the method basis, definition, value, units,
+and convention to make the calculation auditable; do not invent a citation.
+You are not required to identify or prove a publication date or to retrieve
+literature during the examination.
+
+The hidden target article and its identifying metadata, figures or captions,
+supplementary material, author code or data, target-specific reproduction
+code, solution or scoring material, online solutions, and worked
+reproductions of this case must not be used. All submitted scientific figures
+and numerical data must be generated by your own implementation of the stated
+problem.
+
+See [submission requirements](../../submission_requirements.md) for the common submission entry points.

cases/case10/grading_rubric.json

@@ -0,0 +1,602 @@
+{
+  "case_id": "Case10",
+  "title": "Case10 — Phase structure of below-threshold harmonics in aligned molecules: A few-level model system",
+  "atoms": [
+    {
+      "criterion_id": "F1",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Establish both specified few-level TDSEs and construct complex harmonic observables retaining intensity and phase from complex dipole/radiation response; preserve both orthogonal components in System B.",
+      "award_conditions": [
+        "Both specified TDSEs yield complex intensity-and-phase-bearing radiation observables, retaining both orthogonal System-B components."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F2, F3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-1-2, Eqs.(1)-(6): TLS dynamics, dipole, complex transform and finite Gaussian pulse; pp.L022022-3-4, Eqs.(8)-(11) for the orthogonal four-level extension."
+      ],
+      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F2",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Derive a System-A theoretical relation connecting complex harmonic coefficients, odd-harmonic phases and organization on both sides of the transition frequency; recurrence, perturbative or strictly equivalent routes are accepted.",
+      "award_conditions": [
+        "A theoretical recurrence, perturbative relation or equivalent derivation explains odd-harmonic phases on both sides of the transition."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F3, O1, O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article p.L022022-3, Eq.(7) and denominator-sign explanation; Supplemental Material pp.1-4, Eqs.(10),(12),(16)-(22): monochromatic adiabatic weaker-successive-harmonic recurrence and nonresonant phase organization."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "F3",
+      "dimension": "F",
+      "points": 0.5,
+      "scientific_requirement": "Correctly assemble System B's two uncoupled orthogonal-transition TLS blocks, coherent equal-weight lower-state preparation and drive-angle-dependent complex x/y response, defining a line-polarization axis or strictly equivalent observable.",
+      "award_conditions": [
+        "System B consists of the correct uncoupled orthogonal TLS blocks with coherent equal-weight lower-state preparation and a reconstructible complex-vector/line-axis observable."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in F2, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-3-4, Eqs.(8)-(11), Fig.5 and paragraph defining linear polarization from relative 0/pi component phase. A normalized coherent equal-weight lower-state preparation and modulo-pi line axis are task-explicit conventions."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "O1",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present System-A complex harmonic response and intensity over a chosen frequency domain spanning the transition, resolving odd harmonics and the finite-pulse resonant neighborhood.",
+      "award_conditions": [
+        "System-A complex response and intensity span the transition and resolve odd harmonics plus the finite-pulse resonant neighborhood.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F1 (Establish both specified few-level TDSEs and construct complex harmonic observables retaining intensity and phase from complex dipole/radiation response; preserve both orthogonal components in System B.)",
+        "Preserve independently valid work in O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O2",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present System-A phase organization across the transition, exposing alternating real phase classes below it, a common real phase class above it, and the resonant neighborhood.",
+      "award_conditions": [
+        "System-A phase evidence exposes amplitude-supported alternating real classes below and common real class above transition, with resonance separately resolved.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O1 (Present System-A complex harmonic response and intensity over a chosen frequency domain spanning the transition, resolving odd harmonics and the finite-pulse resonant neighborhood.)",
+        "Preserve independently valid work in O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O3",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present complex x/y response or equivalent polarization evidence for System B's lower odd-harmonic family over a sufficient chosen angular/frequency domain to assess its line-axis relation to drive angle.",
+      "award_conditions": [
+        "System-B complex-vector or equivalent polarization evidence exposes the lower odd family's line-axis relation over a sufficient angular/frequency domain.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F3 (Correctly assemble System B's two uncoupled orthogonal-transition TLS blocks, coherent equal-weight lower-state preparation and drive-angle-dependent complex x/y response, defining a line-polarization axis or strictly equivalent observable.)",
+        "Preserve independently valid work in O4, O1, O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article p.L022022-4, Fig.5 lower odd family (orders 1-7), Fig.4 and same-phase subsystem discussion: co-rotating polarization with nonlinear amplitude-dependent axis, not necessarily equal to the driver angle."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "O4",
+      "dimension": "O",
+      "points": 0.5,
+      "scientific_requirement": "Present complex x/y response or equivalent polarization evidence for System B's higher odd-harmonic family beyond the higher transition, exposing its changed relation relative to the lower family.",
+      "award_conditions": [
+        "The higher odd family's complex polarization beyond the higher transition exposes the changed relation relative to the lower family.",
+        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F3 (Correctly assemble System B's two uncoupled orthogonal-transition TLS blocks, coherent equal-weight lower-state preparation and drive-angle-dependent complex x/y response, defining a line-polarization axis or strictly equivalent observable.)",
+        "Preserve independently valid work in O3, O1, O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article p.L022022-4, Fig.5 higher family (beginning at 9), Fig.3 reference frequency lines and counterrotation paragraph: relative pi phase mirrors the harmonic line axis."
+      ],
+      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
+    },
+    {
+      "criterion_id": "I1",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Explicitly identify System-A odd harmonics, transition/resonance neighborhood and amplitude-supported alternating-below/common-above real phase classes.",
+      "award_conditions": [
+        "The candidate identifies odd orders, resonance neighborhood and supported alternating-below/common-above phase classes in their own data."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: O1 (Present System-A complex harmonic response and intensity over a chosen frequency domain spanning the transition, resolving odd harmonics and the finite-pulse resonant neighborhood.); O2 (Present System-A phase organization across the transition, exposing alternating real phase classes below it, a common real phase class above it, and the resonant neighborhood.)",
+        "Preserve independently valid work in I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I2",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify the co-directional/co-rotating or physically equivalent polarization relation of System B's lower odd-harmonic family to the driver.",
+      "award_conditions": [
+        "The candidate identifies the lower family's co-directional/co-rotating relation, allowing nonlinear deviation from exact driver alignment."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O3 (Present complex x/y response or equivalent polarization evidence for System B's lower odd-harmonic family over a sufficient chosen angular/frequency domain to assess its line-axis relation to drive angle.)",
+        "Preserve independently valid work in I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article p.L022022-4, Fig.5 lower odd family (orders 1-7), Fig.4 and same-phase subsystem discussion: co-rotating polarization with nonlinear amplitude-dependent axis, not necessarily equal to the driver angle."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "I3",
+      "dimension": "I",
+      "points": 0.5,
+      "scientific_requirement": "Identify the counterrotating/mirrored or physically equivalent higher-family polarization relation, its change from the lower family and its association with transition scale.",
+      "award_conditions": [
+        "The candidate identifies the higher family's mirrored/counterrotating relation and its connection to the transition scale."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: O4 (Present complex x/y response or equivalent polarization evidence for System B's higher odd-harmonic family beyond the higher transition, exposing its changed relation relative to the lower family.)",
+        "Preserve independently valid work in I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article p.L022022-4, Fig.5 higher family (beginning at 9), Fig.3 reference frequency lines and counterrotation paragraph: relative pi phase mirrors the harmonic line axis."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M1",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain the change of odd-harmonic real phase organization across System A's transition through the sign of the theoretical denominator/recurrence factor or a strictly equivalent mechanism.",
+      "award_conditions": [
+        "The theoretical prefactor/denominator sign or equivalent mechanism explains the phase-organization change across transition."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: F2 (Derive a System-A theoretical relation connecting complex harmonic coefficients, odd-harmonic phases and organization on both sides of the transition frequency; recurrence, perturbative or strictly equivalent routes are accepted.); I1 (Explicitly identify System-A odd harmonics, transition/resonance neighborhood and amplitude-supported alternating-below/common-above real phase classes.)",
+        "Preserve independently valid work in M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article p.L022022-3, Eq.(7) and denominator-sign explanation; Supplemental Material pp.1-4, Eqs.(10),(12),(16)-(22): monochromatic adiabatic weaker-successive-harmonic recurrence and nonresonant phase organization."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M2",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Distinguish the finite Gaussian pulse's resonant neighborhood from monochromatic/infinite-time theory, explain unreliable phase at unresolved weak coefficients and do not force exact-resonance agreement.",
+      "award_conditions": [
+        "Finite-pulse resonance and weak-coefficient phase reliability are distinguished from monochromatic adiabatic theory; exact-resonance agreement is not forced."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: I1 (Explicitly identify System-A odd harmonics, transition/resonance neighborhood and amplitude-supported alternating-below/common-above real phase classes.)",
+        "Preserve independently valid work in M1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M3",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Match System-A numerical complex response to the theoretical phase relation, reaching a self-consistent transition-structure inference from harmonic intensity/phase rather than merely listing lines.",
+      "award_conditions": [
+        "Numerical intensity and complex phase are matched to the theory to support a transition-structure inference rather than a line list."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I1 (Explicitly identify System-A odd harmonics, transition/resonance neighborhood and amplitude-supported alternating-below/common-above real phase classes.); M1 (Explain the change of odd-harmonic real phase organization across System A's transition through the sign of the theoretical denominator/recurrence factor or a strictly equivalent mechanism.)",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M4",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Construct the line-polarization axis or strictly equivalent quantity from complex x/y harmonic components, correctly treating the modulo-pi axis branch and relative complex phase.",
+      "award_conditions": [
+        "The candidate derives the line axis from complex x/y components with relative phase and modulo-pi branch handled consistently."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: F3 (Correctly assemble System B's two uncoupled orthogonal-transition TLS blocks, coherent equal-weight lower-state preparation and drive-angle-dependent complex x/y response, defining a line-polarization axis or strictly equivalent observable.)",
+        "Preserve independently valid work in M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-3-4, Eqs.(8)-(11), Fig.5 and paragraph defining linear polarization from relative 0/pi component phase. A normalized coherent equal-weight lower-state preparation and modulo-pi line axis are task-explicit conventions."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M5",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain lower-family co-directional/co-rotating polarization by connecting the two orthogonal TLS complex amplitude/phase contributions.",
+      "award_conditions": [
+        "The lower-family explanation connects its orthogonal TLS amplitudes and relative phases to co-rotation."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I2 (Identify the co-directional/co-rotating or physically equivalent polarization relation of System B's lower odd-harmonic family to the driver.); M4 (Construct the line-polarization axis or strictly equivalent quantity from complex x/y harmonic components, correctly treating the modulo-pi axis branch and relative complex phase.)",
+        "Preserve independently valid work in M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article p.L022022-4, Fig.5 lower odd family (orders 1-7), Fig.4 and same-phase subsystem discussion: co-rotating polarization with nonlinear amplitude-dependent axis, not necessarily equal to the driver angle."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M6",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Explain higher-family counterrotating/mirrored polarization beyond the higher transition through transition-dependent amplitude/phase reorganization of the two TLS responses.",
+      "award_conditions": [
+        "Transition-dependent amplitude/phase reorganization explains higher-family mirroring beyond the upper transition."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: I3 (Identify the counterrotating/mirrored or physically equivalent higher-family polarization relation, its change from the lower family and its association with transition scale.); M4 (Construct the line-polarization axis or strictly equivalent quantity from complex x/y harmonic components, correctly treating the modulo-pi axis branch and relative complex phase.)",
+        "Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article p.L022022-4, Fig.5 higher family (beginning at 9), Fig.3 reference frequency lines and counterrotation paragraph: relative pi phase mirrors the harmonic line axis."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M7",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Use submitted numerical evidence to establish that phase/polarization structures are not artefacts of unresolved weak coefficients, line-axis branches, chosen frequency/angle domains or fragile reduction, and define the supported harmonic range.",
+      "award_conditions": [
+        "Actual numerical evidence excludes unresolved weak coefficients, axis wrapping, domain truncation or fragile reduction as the source of the claimed pattern."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve independently valid work in M8. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-3-4, Eq.(7) approximation/resonance limitation and final realistic-molecule discussion. Amplitude-supported phase, axis-branch stability and bounded spectral inference are task-defined scientific safeguards, not fixed plotting domains."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "M8",
+      "dimension": "M",
+      "points": 0.5,
+      "scientific_requirement": "Synthesize System-A cross-transition phases and System-B polarization families to determine inferable transition information, diagnostic domain and their shared physical basis.",
+      "award_conditions": [
+        "Both systems' phase/polarization evidence supports the stated transition information, diagnostic domain and common mechanism."
+      ],
+      "applicability_and_na": [
+        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: all of: M1 (Explain the change of odd-harmonic real phase organization across System A's transition through the sign of the theoretical denominator/recurrence factor or a strictly equivalent mechanism.); M5 (Explain lower-family co-directional/co-rotating polarization by connecting the two orthogonal TLS complex amplitude/phase contributions.); M6 (Explain higher-family counterrotating/mirrored polarization beyond the higher transition through transition-dependent amplitude/phase reorganization of the two TLS responses.)",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-3-4, Eq.(7) approximation/resonance limitation and final realistic-molecule discussion. Amplitude-supported phase, axis-branch stability and bounded spectral inference are task-defined scientific safeguards, not fixed plotting domains."
+      ],
+      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V1",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "When weak-coefficient phase, insufficient frequency/angle domain, finite-pulse/monochromatic mismatch, axis branches or reduction artefacts threaten conclusions, provide discriminating evidence or narrow the threatened claim.",
+      "award_conditions": [
+        "Only a concrete triggered phase, resonance, branch, domain or reduction risk requires discriminating evidence or narrowed claims; otherwise N/A."
+      ],
+      "applicability_and_na": [
+        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
+        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-3-4, Eq.(7) approximation/resonance limitation and final realistic-molecule discussion. Amplitude-supported phase, axis-branch stability and bounded spectral inference are task-defined scientific safeguards, not fixed plotting domains."
+      ],
+      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    },
+    {
+      "criterion_id": "V2",
+      "dimension": "V",
+      "points": 0.5,
+      "scientific_requirement": "Positively restrict conclusions to the specified closed few-level systems, coherent preparation, finite Gaussian pulses and calculated harmonic/angular domain; do not extrapolate to general multilevel materials or arbitrary strong-field limits.",
+      "award_conditions": [
+        "The candidate positively limits conclusions to closed few-level systems, coherent preparation, finite Gaussian pulses and actual calculated harmonic/angular support."
+      ],
+      "applicability_and_na": [
+        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
+      ],
+      "dependencies": [
+        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
+        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
+      ],
+      "equivalent_evidence": [
+        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
+        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
+        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
+      ],
+      "source_support": [
+        "Schopa et al. (2026), article pp.L022022-3-4, Eq.(7) approximation/resonance limitation and final realistic-molecule discussion. Amplitude-supported phase, axis-branch stability and bounded spectral inference are task-defined scientific safeguards, not fixed plotting domains."
+      ],
+      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
+    }
+  ],
+  "case_scientific_rules": [
+    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
+    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
+    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
+    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
+    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
+    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
+    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
+    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
+    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
+    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
+    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
+    "The canonical System-B preparation is proportional to (1,1,0,0)^T in one ordering, with simultaneous Ex d and Ey d couplings. Separate runs or unsigned intensity components do not preserve the required coherent response.",
+    "Canonical lower orders 1,3,5,7 co-rotate and higher orders beginning at 9 through 11,13 mirror/counterrotate. These recognize the two families, not a fixed required frequency or angle grid.",
+    "The relative 0/pi component phase carries the family change; nonlinear amplitude differences determine detailed curves. Weak unresolved coefficients cannot support phase assertions.",
+    "The simplified uncoupled bound-bound model does not establish survival in realistic aligned molecules with additional states, collective response, continuum emission or imperfect alignment.",
+    "A standard field-free basis gives",
+    "$$\nH_A(t)=\n\\begin{pmatrix}\n-\\omega_{10}/2&E(t)d\\\\\nE(t)d&\\omega_{10}/2\n\\end{pmatrix},\n$$",
+    "with lower-state initial amplitude. The canonical dipole is",
+    "$$\nD(t)=d\\left(C_0^*C_1+C_1^*C_0\\right).\n$$",
+    "The source intensity is constructed from the transformed dipole acceleration, whereas transition-dependent phase information requires a declared complex coefficient. Fourier-, derivative- and global-phase-equivalent conventions are accepted when treated consistently. Absolute scale is not graded.",
+    "Canonical evidence contains resolved odd harmonics, localized resonant enhancement, alternating real phase classes below the transition, one common real phase class above it, and a distinct finite-pulse response near strict resonance. A weak coefficient cannot support a phase claim.",
+    "With $w=|C_1|^2-|C_0|^2$, the source relations include",
+    "$$\n\\ddot D+\\omega_{10}^2D=2\\omega_{10}E(t)d^2w,\n\\qquad\n\\dot w=-\\frac{2E(t)}{\\omega_{10}}\\dot D.\n$$",
+    "For a monochromatic field, adiabatic occupation of one Floquet state and the successively weaker-harmonic approximation give",
+    "$$\nd_n=-e^{-2i\\varphi_L}\\frac{n-2}{n-1}\n\\left[\n\\frac{2n^2}{n^2-1}\n+\\frac{\\omega_{10}^2-n^2\\omega_L^2}{E_0^2d^2}\n\\right]^{-1}d_{n-2}.\n$$",
+    "Its real prefactor changes sign across the transition and explains the two nonresonant phase organizations. The approximation does not replace the finite-pulse propagation and must not be forced through strict resonance. A different derivation can earn full credit if it explains the same physical organization and applicability boundary.",
+    "The canonical four-level Hamiltonian is the direct sum of the two stated TLS blocks, with simultaneous couplings $E_xd$ and $E_yd$. The coherent lower- state preparation is proportional to $(1,1,0,0)^{\\mathsf T}$ in one canonical ordering. Equivalent state orderings and global phases are accepted.",
+    "The computed complex harmonic vector defines its polarization. A standard line-axis representative in a sufficiently linear region is",
+    "$$\n\\alpha_N=\\frac12\\operatorname{atan2}\\!\\left(\n2\\operatorname{Re}[\\widetilde D_x\\widetilde D_y^*],\n|\\widetilde D_x|^2-|\\widetilde D_y|^2\n\\right)\\pmod\\pi.\n$$",
+    "Canonical evidence separates a co-rotating family for orders 1, 3, 5 and 7 from a counterrotating or mirrored family beginning at order 9 and continuing through 11 and 13. The relative $0/\\pi$ component phase carries the family change; nonlinear amplitude differences determine the detailed curves.",
+    "The result is a phase-sensitive polarization effect in a deliberately simplified uncoupled bound-bound model. It does not prove that a realistic aligned molecule preserves it in the presence of additional states, collective response, continuum emission or imperfect alignment.",
+    "The System-A recurrence and System-B line-axis formula are tied respectively to article p.L022022-3, Eq.(7), and the complex-vector interpretation of Eqs.(10),(11)/Fig.5. The latter is a derived Stokes-axis representation, not a separately printed article equation. For $D_x,D_y$ at one harmonic, line polarization requires a negligible ellipticity invariant $2\\Im(D_xD_y^*)$ relative to total power; an axis cannot be assigned physical certainty at vanishing amplitude. The shared real component phases $0/\\pi$ cause co-rotation/mirroring, while unequal nonlinear amplitudes mean the lower-family axis need not exactly equal the driver angle. No particular angle grid or line-axis display branch is required."
+  ],
+  "closure_requirements": {
+    "RC0": [
+      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
+      "Required indispensable claim CL0, central physical object: F1 (Establish both specified few-level TDSEs and construct complex harmonic observables retaining intensity and phase from complex dipole/radiation response; preserve both orthogonal components in System B.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC1": [
+      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
+      "Required co primary claim CL1, indispensable material component: all of: O1 (Present System-A complex harmonic response and intensity over a chosen frequency domain spanning the transition, resolving odd harmonics and the finite-pulse resonant neighborhood.); O2 (Present System-A phase organization across the transition, exposing alternating real phase classes below it, a common real phase class above it, and the resonant neighborhood.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL2, indispensable material component: all of: O3 (Present complex x/y response or equivalent polarization evidence for System B's lower odd-harmonic family over a sufficient chosen angular/frequency domain to assess its line-axis relation to drive angle.); O4 (Present complex x/y response or equivalent polarization evidence for System B's higher odd-harmonic family beyond the higher transition, exposing its changed relation relative to the lower family.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC2": [
+      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
+      "Required co primary claim CL1, principal mechanism or commissioned conclusion: M1 (Explain the change of odd-harmonic real phase organization across System A's transition through the sign of the theoretical denominator/recurrence factor or a strictly equivalent mechanism.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M5 (Explain lower-family co-directional/co-rotating polarization by connecting the two orthogonal TLS complex amplitude/phase contributions.); M6 (Explain higher-family counterrotating/mirrored polarization beyond the higher transition through transition-dependent amplitude/phase reorganization of the two TLS responses.). Judge the role-specific failure facts, not the corresponding atom scores.",
+      "Required co primary claim CL3, principal mechanism or commissioned conclusion: M8 (Synthesize System-A cross-transition phases and System-B polarization families to determine inferable transition information, diagnostic domain and their shared physical basis.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC3": [
+      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
+      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
+      "Required co primary claim CL4, material validation/scope: V1 (When weak-coefficient phase, insufficient frequency/angle domain, finite-pulse/monochromatic mismatch, axis branches or reduction artefacts threaten conclusions, provide discriminating evidence or narrow the threatened claim.). Judge the role-specific failure facts, not the corresponding atom scores."
+    ],
+    "RC4": [
+      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
+      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
+      "Close CL0 central physical object: F1 (Establish both specified few-level TDSEs and construct complex harmonic observables retaining intensity and phase from complex dipole/radiation response; preserve both orthogonal components in System B.).",
+      "Close CL1 indispensable material component: all of: O1 (Present System-A complex harmonic response and intensity over a chosen frequency domain spanning the transition, resolving odd harmonics and the finite-pulse resonant neighborhood.); O2 (Present System-A phase organization across the transition, exposing alternating real phase classes below it, a common real phase class above it, and the resonant neighborhood.).",
+      "Close CL1 principal mechanism or commissioned conclusion: M1 (Explain the change of odd-harmonic real phase organization across System A's transition through the sign of the theoretical denominator/recurrence factor or a strictly equivalent mechanism.).",
+      "Close CL2 indispensable material component: all of: O3 (Present complex x/y response or equivalent polarization evidence for System B's lower odd-harmonic family over a sufficient chosen angular/frequency domain to assess its line-axis relation to drive angle.); O4 (Present complex x/y response or equivalent polarization evidence for System B's higher odd-harmonic family beyond the higher transition, exposing its changed relation relative to the lower family.).",
+      "Close CL2 principal mechanism or commissioned conclusion: all of: M5 (Explain lower-family co-directional/co-rotating polarization by connecting the two orthogonal TLS complex amplitude/phase contributions.); M6 (Explain higher-family counterrotating/mirrored polarization beyond the higher transition through transition-dependent amplitude/phase reorganization of the two TLS responses.).",
+      "Close CL3 principal mechanism or commissioned conclusion: M8 (Synthesize System-A cross-transition phases and System-B polarization families to determine inferable transition information, diagnostic domain and their shared physical basis.).",
+      "Close CL4 material validation/scope: V1 (When weak-coefficient phase, insufficient frequency/angle domain, finite-pulse/monochromatic mismatch, axis branches or reduction artefacts threaten conclusions, provide discriminating evidence or narrow the threatened claim.)."
+    ]
+  },
+  "references": [
+    {
+      "citation": "Samuel Schöpa, Lina Bielke, Falk-Erik Wiechmann, Franziska Fennel, and Dieter Bauer. 2026. *Phase structure of below-threshold harmonics in aligned molecules: A few-level model system*. *Physical Review Research*, 8, L022022.",
+      "url": "https://doi.org/10.1103/5fjm-8ps7",
+      "scientific_scope": "Phase structure of below-threshold harmonics in aligned molecules: A few-level model system",
+      "anchors": [
+        "Schopa et al. (2026), article pp.L022022-1-2, Eqs.(1)-(6): TLS dynamics, dipole, complex transform and finite Gaussian pulse; pp.L022022-3-4, Eqs.(8)-(11) for the orthogonal four-level extension.",
+        "Schopa et al. (2026), article p.L022022-3, Eq.(7) and denominator-sign explanation; Supplemental Material pp.1-4, Eqs.(10),(12),(16)-(22): monochromatic adiabatic weaker-successive-harmonic recurrence and nonresonant phase organization.",
+        "Schopa et al. (2026), article pp.L022022-3-4, Eqs.(8)-(11), Fig.5 and paragraph defining linear polarization from relative 0/pi component phase. A normalized coherent equal-weight lower-state preparation and modulo-pi line axis are task-explicit conventions.",
+        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence.",
+        "Schopa et al. (2026), article p.L022022-4, Fig.5 lower odd family (orders 1-7), Fig.4 and same-phase subsystem discussion: co-rotating polarization with nonlinear amplitude-dependent axis, not necessarily equal to the driver angle.",
+        "Schopa et al. (2026), article p.L022022-4, Fig.5 higher family (beginning at 9), Fig.3 reference frequency lines and counterrotation paragraph: relative pi phase mirrors the harmonic line axis.",
+        "Schopa et al. (2026), article pp.L022022-3-4, Eq.(7) approximation/resonance limitation and final realistic-molecule discussion. Amplitude-supported phase, axis-branch stability and bounded spectral inference are task-defined scientific safeguards, not fixed plotting domains."
+      ]
+    },
+    {
+      "citation": "Samuel Schopa, Lina Bielke, Falk-Erik Wiechmann, Franziska Fennel, and Dieter Bauer. 2026. *Supplemental Material: Analytical derivation for the phase of the below-threshold harmonics in a two-level model system*, accompanying Physical Review Research 8, L022022.",
+      "url": "https://journals.aps.org/prresearch/supplemental/10.1103/5fjm-8ps7",
+      "scientific_scope": "Analytical dipole/population equations and adiabatic monochromatic harmonic recurrence.",
+      "anchors": [
+        "Supplemental Material pp.1-4, Eqs.(10),(12),(16)-(22); Eq.(22) corresponds to main-text Eq.(7)."
+      ]
+    }
+  ]
+}