diff --git a/.gitattributes b/.gitattributes index bed0738c7eeb449bca98b5d2f33c89a1ee56349a..d70e879771a4b341fb7e670cd20c8d80feda16ed 100644 --- a/.gitattributes +++ b/.gitattributes @@ -58,3 +58,4 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text # Video files - compressed *.mp4 filter=lfs diff=lfs merge=lfs -text *.webm filter=lfs diff=lfs merge=lfs -text +case_source_publications.pdf filter=lfs diff=lfs merge=lfs -text diff --git a/LICENSE.md b/LICENSE.md new file mode 100644 index 0000000000000000000000000000000000000000..3da581e269b6344b56fc4769a837a812554ac891 --- /dev/null +++ b/LICENSE.md @@ -0,0 +1,11 @@ +# 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. diff --git a/README.md b/README.md index 32897cd3e640101ba184f8c4ccd896981de3804a..e1a8f531bb6f74b59a3bebb5783866692f82a05a 100644 --- a/README.md +++ b/README.md @@ -1,3 +1,78 @@ ---- -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. diff --git a/case_source_publications.pdf b/case_source_publications.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7bf98fc19da45f03ace11067e099217a9548cee6 --- /dev/null +++ b/case_source_publications.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0114fd6643672b8615c93415f64938d1bf666e89dcef412b41cfc2ef358c0285 +size 120086 diff --git a/cases/case01/grading_rubric.json b/cases/case01/grading_rubric.json new file mode 100644 index 0000000000000000000000000000000000000000..469b9444b75065604affab74f50e11226a9b1b3f --- /dev/null +++ b/cases/case01/grading_rubric.json @@ -0,0 +1,588 @@ +{ + "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." + ] + } + ] +} diff --git a/cases/case01/grading_rubric.md b/cases/case01/grading_rubric.md new file mode 100644 index 0000000000000000000000000000000000000000..e9a7ac1ebe03a9c3485887558530ef564e924142 --- /dev/null +++ b/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. diff --git a/cases/case01/resource_limits.json b/cases/case01/resource_limits.json new file mode 100644 index 0000000000000000000000000000000000000000..4189ba9776c8299f963f295e1a35d5fc1999db28 --- /dev/null +++ b/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." +} diff --git a/cases/case01/sources.md b/cases/case01/sources.md new file mode 100644 index 0000000000000000000000000000000000000000..a9f5549fffc7bfd953556b580351251dd7d9036c --- /dev/null +++ b/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. diff --git a/cases/case01/task.md b/cases/case01/task.md new file mode 100644 index 0000000000000000000000000000000000000000..4e4397a3e2967262627c00e228dbe7e24e527b04 --- /dev/null +++ b/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. diff --git a/cases/case02/grading_rubric.json b/cases/case02/grading_rubric.json new file mode 100644 index 0000000000000000000000000000000000000000..644becea82860b36e76ce63dad5cbafbdae5f1e2 --- /dev/null +++ b/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_p0.$$ +With the article's outgoing Coulomb convention and final index $n$, +$$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.$$ +The SI conversion factor is $a_0^{2K}t_0^{K-1}$, giving area$^K$ time$^{K-1}$. The canonical extraction uses $M_{pq}=W\{F_\ell(k_n;r),H_\ell(k_q;r)\}_{r_p}$ and $b_p=W\{F_\ell(k_n;r),\widehat P_\ell(r)\}_{r_p}$, with $W\{f,g\}=fg'-f'g$ and $r_p0.$$ +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