cases/case15/grading_rubric.json

{
  "case_id": "Case15",
  "title": "Case15 — Photoionization of H₂⁺ beyond the dipole approximation with zeptosecond time resolution",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Construct the fixed-nuclei gerade molecular state and nondipole weak-field branch with the specified light-cone field, consistent field-free energy and ionization potential, branch-specific amplitude, signs and units.",
      "award_conditions": [
        "The fixed-nuclei gerade state and nondipole weak-field branch preserve the specified light-cone driver, field-free energy/Ip, branch amplitude and consistent signs/units."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F2, F3, F4, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-2-3, Eqs.(1),(4)-(9): light-cone nondipole amplitude, gerade initial molecular state and weak-field LCAO limit with field-free Ip matching."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Construct an independent fixed-nuclei nondipole TDSE branch with the declared molecular state, energy-matched soft-core potential, aligned-geometry boundary or consistent rotation, light-cone coupling and distinct representative field amplitude.",
      "award_conditions": [
        "An independent nondipole TDSE branch has an energy-matched molecular potential, correct aligned/rotated geometry and its own stated representative field amplitude."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F1, F3, F4, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article p.033112-2, Eqs.(2),(3) and 2D soft-core/energy-matching paragraphs: independent fixed-nuclei TDSE. Article p.033112-4 Fig.3 caption explicitly uses A0=1.0 for TDSE and 0.01 for NSFA."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Define a reconstructible longitudinal/angular photoelectron observable, common projection/normalization and stable central branch or equivalent timing-sensitive diagnostic without substituting an unjustified mean.",
      "award_conditions": [
        "The longitudinal/angular observable, projection, normalization and stable central timing branch are reconstructible; an unjustified mean is not substituted for the peak."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F1, F2, F4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article p.033112-3, longitudinal-marginal paragraphs and stationary central-peak definition; Eq.(9),(10) for angular branch. The central maximum is not generally a mean."
      ],
      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F4",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Derive separation/orientation dependence of the nondipole timing phase, bind the selected central signal to that phase and distinguish effective emission separation from bare internuclear distance where required.",
      "award_conditions": [
        "The candidate derives how separation/orientation enters timing phase and binds the chosen signal to it, distinguishing effective emission scale from bare separation."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F1, F2, F3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-2-3, Eqs.(4)-(12), and p.033112-4 bound-state phase paragraph: light-front interference phase includes photon momentum and Ip, with separated asymptote (Ek+Ip)/c."
      ],
      "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 valid, reconstructible compact/separated molecular longitudinal or equivalent angular evidence resolving topology change and nondipole displacement under consistent branch/normalization conventions.",
      "award_conditions": [
        "Compact/separated longitudinal or equivalent angular evidence resolves topology change and nondipole displacement under declared branch/projection conventions.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in O2, O3, O4, I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-3-4, Fig.2(a,b), Eq.(9), compact-density/diffraction discussion: broad compact R=2 signal versus dense R=10 two-centre fringes and propagation-direction displacement."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present valid, reconstructible separation-dependent central-branch or equivalent timing-sensitive evidence sufficient for the claimed compact-to-separated transition, without hidden lobe switches or normalization-made trends.",
      "award_conditions": [
        "Separation-dependent evidence tracks the same central timing branch through compact deformation toward a separated-centre limit without hidden lobe switches.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in O1, O3, O4, I1, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-3-5, Eqs.(10)-(12), Fig.3 and compact/separated interpretation: stable central branch approaches omega/c at large separation; a hidden switch to another lobe does not establish timing."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present valid, reconstructible orientation evidence sufficient for timing, using consistently rotated TDSE geometry or the accepted weak-field nondipole branch.",
      "award_conditions": [
        "Orientation evidence from consistently rotated TDSE or accepted weak-field nondipole calculation is reconstructible and sufficient for the timing claim.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in O1, O2, O4, I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article p.033112-5, Fig.5, caption and projected R*cos(beta) paragraph: orientation-dependent central angular signal at R=2 and 10. Orientation may use the weak-field branch; an off-axis TDSE must rotate the geometry consistently."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present valid, reconstructible independent NSFA/TDSE central-signal evidence with branch-specific amplitudes and conventions distinguishing physical compatibility from matched-intensity or processing artefacts.",
      "award_conditions": [
        "Independent NSFA/TDSE central-signal evidence declares distinct amplitudes and conventions and distinguishes structural compatibility from processing/matched-intensity artefacts.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in O1, O2, O3, 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": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article p.033112-4, Fig.3 caption and NSFA/TDSE comparison paragraph: distinct-amplitude models agree in structural single-photon central shift, not pointwise matched-intensity spectra."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from compact/separated evidence broad compact structure changing to denser two-centre fringes together with propagation-direction nondipole displacement.",
      "award_conditions": [
        "The candidate identifies broad compact structure, denser separated interference and propagation-direction nondipole displacement in their data."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O1 (Present valid, reconstructible compact/separated molecular longitudinal or equivalent angular evidence resolving topology change and nondipole displacement under consistent branch/normalization conventions.)",
        "Preserve independently valid work in I2, I3, M1, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-3-4, Fig.2(a,b), Eq.(9), compact-density/diffraction discussion: broad compact R=2 signal versus dense R=10 two-centre fringes and propagation-direction displacement."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from separation evidence evolution of the stable timing branch from compact deformation toward a separated-centre asymptote without importing a hidden transition coordinate.",
      "award_conditions": [
        "The candidate identifies stable-branch separation evolution from compact deformation toward the separated asymptote without requiring a fixed transition coordinate."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O2 (Present valid, reconstructible separation-dependent central-branch or equivalent timing-sensitive evidence sufficient for the claimed compact-to-separated transition, without hidden lobe switches or normalization-made trends.)",
        "Preserve independently valid work in I1, I3, M1, M2, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-3-5, Eqs.(10)-(12), Fig.3 and compact/separated interpretation: stable central branch approaches omega/c at large separation; a hidden switch to another lobe does not establish timing."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from orientation evidence material projected-separation dependence and its relation to the timing-sensitive longitudinal/equivalent observable under declared conventions.",
      "award_conditions": [
        "The candidate identifies projected-separation orientation dependence and its relation to the declared timing-sensitive observable."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O3 (Present valid, reconstructible orientation evidence sufficient for timing, using consistently rotated TDSE geometry or the accepted weak-field nondipole branch.)",
        "Preserve independently valid work in I1, I2, M1, M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article p.033112-5, Fig.5, caption and projected R*cos(beta) paragraph: orientation-dependent central angular signal at R=2 and 10. Orientation may use the weak-field branch; an off-axis TDSE must rotate the geometry consistently."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain how finite light-front phase breaks dipole longitudinal symmetry and encodes propagation-direction displacement without treating momentum shift alone as a complete clock.",
      "award_conditions": [
        "Finite light-front phase explains broken dipole longitudinal symmetry and displacement, without treating shift alone as a complete clock."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F1 (Construct the fixed-nuclei gerade molecular state and nondipole weak-field branch with the specified light-cone field, consistent field-free energy and ionization potential, branch-specific amplitude, signs and units.)",
        "Preserve independently valid work in M2, M3, M4, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-2-3, Eqs.(4)-(12), and p.033112-4 bound-state phase paragraph: light-front interference phase includes photon momentum and Ip, with separated asymptote (Ek+Ip)/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": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain compact signals through distributed molecular bound-state density and effective emission width rather than automatically using bare separation or a pure separated-double-slit account.",
      "award_conditions": [
        "Distributed compact bound density/effective aperture explains compact signals rather than an automatic separated-double-slit or bare-R 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: I1 (Identify from compact/separated evidence broad compact structure changing to denser two-centre fringes together with propagation-direction nondipole displacement.)",
        "Preserve independently valid work in M1, M3, M4, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-3-4, Fig.2(a,b), Eq.(9), compact-density/diffraction discussion: broad compact R=2 signal versus dense R=10 two-centre fringes and propagation-direction displacement."
      ],
      "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 separated-regime timing through two-centre interference and finite propagation phase and establish only where delay approaches bare-separation light-crossing time.",
      "award_conditions": [
        "Two-centre interference and propagation phase establish where separated-regime delay approaches R/c, not at every separation."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I2 (Identify from separation evidence evolution of the stable timing branch from compact deformation toward a separated-centre asymptote without importing a hidden transition coordinate.)",
        "Preserve independently valid work in 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": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-2-3, Eqs.(4)-(12), and p.033112-4 bound-state phase paragraph: light-front interference phase includes photon momentum and Ip, with separated asymptote (Ek+Ip)/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": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain orientation through projected light-front separation and declared geometry, accepting equivalent observables with a derived timing relation.",
      "award_conditions": [
        "Projected light-front separation and declared geometry explain orientation, with a derived timing relation for any alternative observable."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I3 (Identify from orientation evidence material projected-separation dependence and its relation to the timing-sensitive longitudinal/equivalent observable under declared conventions.)",
        "Preserve independently valid work in M1, M2, M3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article p.033112-5, Fig.5, caption and projected R*cos(beta) paragraph: orientation-dependent central angular signal at R=2 and 10. Orientation may use the weak-field branch; an off-axis TDSE must rotate the geometry consistently."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Integrate compact, separation and orientation signals with light-front, bound-state and interference mechanisms to infer the strongest supported relative timing and effective-separation boundary.",
      "award_conditions": [
        "Compact, separation and orientation evidence are integrated with bound-state/interference mechanisms into a bounded relative-timing inference."
      ],
      "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 how finite light-front phase breaks dipole longitudinal symmetry and encodes propagation-direction displacement without treating momentum shift alone as a complete clock.); M2 (Explain compact signals through distributed molecular bound-state density and effective emission width rather than automatically using bare separation or a pure separated-double-slit account.); M3 (Explain separated-regime timing through two-centre interference and finite propagation phase and establish only where delay approaches bare-separation light-crossing time.); M4 (Explain orientation through projected light-front separation and declared geometry, accepting equivalent observables with a derived timing relation.)",
        "Preserve independently valid work in M6, V1, V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-3-5, Eqs.(10)-(12), Fig.3 and compact/separated interpretation: stable central branch approaches omega/c at large separation; a hidden switch to another lobe does not establish timing."
      ],
      "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 what independent NSFA/TDSE central-signal agreement/conflict establishes after accounting for different amplitudes, dimensional/model conventions and limited long-range dynamics, without claiming pointwise equality.",
      "award_conditions": [
        "The candidate interprets independent NSFA/TDSE agreement/conflict with different amplitudes and dimensional/model conventions, without claiming pointwise equality."
      ],
      "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 valid, reconstructible independent NSFA/TDSE central-signal evidence with branch-specific amplitudes and conventions distinguishing physical compatibility from matched-intensity or processing artefacts.)",
        "Preserve independently valid work in 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": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article p.033112-4, Fig.3 caption and NSFA/TDSE comparison paragraph: distinct-amplitude models agree in structural single-photon central shift, not pointwise matched-intensity spectra."
      ],
      "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": "Synthesize timing, compact-to-separated mechanism, orientation, cross-model adequacy and limitations into the strongest conclusion supported by reconstructible calculation.",
      "award_conditions": [
        "Timing, regime change, orientation, model comparison and limitations support the strongest mutually consistent reconstructible 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: M5 (Integrate compact, separation and orientation signals with light-front, bound-state and interference mechanisms to infer the strongest supported relative timing and effective-separation boundary.); M6 (Determine what independent NSFA/TDSE central-signal agreement/conflict establishes after accounting for different amplitudes, dimensional/model conventions and limited long-range dynamics, without claiming pointwise equality.)",
        "Preserve independently valid work in V1, V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-2-5, effective-dimensional fixed-nuclei model, compact/separated discussion and Sec.IV: relative timing remains molecular-state/branch dependent. Extraction alternatives and claim limits are task-defined; no universal absolute clock or source transition coordinate is compulsory."
      ],
      "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": "Restrict conclusions to fixed nuclei, one-photon XUV, declared effective-dimensional TDSE and NSFA/molecular-state approximations; a model-dependent central shift is not a universal experimental clock.",
      "award_conditions": [
        "The conclusion is restricted to fixed nuclei, one-photon XUV and declared effective-dimensional TDSE/NSFA/molecular-state approximations, not a universal experimental clock."
      ],
      "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": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-2-5, effective-dimensional fixed-nuclei model, compact/separated discussion and Sec.IV: relative timing remains molecular-state/branch dependent. Extraction alternatives and claim limits are task-defined; no universal absolute clock or source transition coordinate 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 extraction, lobe identity, field convention, state, projection, model comparison, anomaly or claim raises a concrete conclusion-changing alternative, provide discriminating evidence or proportionately narrow the claim; otherwise record N/A.",
      "award_conditions": [
        "A concrete triggered state, projection, central-branch, field or model-comparison alternative is discriminated or the claim 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 independently valid work in V1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent probability-preserving projections, angular distributions, shell lineouts and coordinate conventions are accepted with reconstructible definitions preserving longitudinal content.",
        "A stable peak fit, stationary-point estimator or equivalent may track the same central branch. The most probable momentum is not generally the mean.",
        "Orientation may be supplied by the weak-field nondipole branch; nonaligned TDSE must rotate the molecular potential consistently. No hidden soft-core alpha(R) table is required: match a qualified same-R field-free molecular reference energy.",
        "An independently derived finite-pulse NSFA evaluation is equivalent to the weak-field LCAO angular representative when it preserves the same one-photon phase and bound-state content."
      ],
      "source_support": [
        "Zhang and He (2021), article pp.033112-2-5, effective-dimensional fixed-nuclei model, compact/separated discussion and Sec.IV: relative timing remains molecular-state/branch dependent. Extraction alternatives and claim limits are task-defined; no universal absolute clock or source transition coordinate 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 field depends on eta=t-z/c. The dipole limit has longitudinal symmetry; finite light-front dependence breaks it. TDSE W(pz)=integral |phi(px,pz)|^2 dpx and the NSFA three-dimensional marginal require consistent projection before comparison.",
    "Source amplitudes differ deliberately: A0=1.0 for TDSE and 0.01 for NSFA. Their agreement supports a shared single-photon structural trend, not strict matched-intensity equality.",
    "At R=2 the molecular distribution is broad with few lobes; at R=10 dense interference has a 2pi/R scale. Separation-dependent central displacement approaches (Ek+Ip)/c=omega/c from above for the specified omega=10 case.",
    "The compact state is concentrated between nuclei and behaves predominantly as distributed-aperture diffraction; sufficiently separated centres support the double-slit interpretation. The source boundary around R=4 a.u. is not a compulsory scan point.",
    "Orientation enters through R cos(beta); the source longitudinal/angular displacement increases with cos(beta) for both representative separations. An equivalent diagnostic needs its own derived mapping.",
    "In the separated limit inferred relative timing approaches R/c; compact timing uses effective distributed emission width. Quoting R/c at every R or reading time from an arbitrary momentum offset is not a valid inference.",
    "Restricted TDSE references establish selected central peaks and topology, not a complete source separation/orientation scan or exact original-grid result. Source orientation relations and submitted data are needed when they decide a material claim.",
    "The source field is circularly polarized and depends on the light-cone time $\\eta=t-z/c$. In the dipole limit $c\\to\\infty$, the longitudinal momentum distribution is symmetric about $p_z=0$. The nondipole light-cone dependence breaks that symmetry.",
    "For a two-dimensional TDSE wave packet $\\phi(p_x,p_z)$, the source longitudinal observable is",
    "$$\nW(p_z)=\\int |\\phi(p_x,p_z)|^2\\,dp_x.\n$$",
    "For an NSFA amplitude $M(\\mathbf p)$, its three-dimensional counterpart is",
    "$$\nW(p_z)=\\iint |M(p_x,p_y,p_z)|^2\\,dp_x\\,dp_y.\n$$",
    "Equivalent projections, angular distributions, shell-resolved lineouts and coordinate conventions are accepted when the student gives a reconstructible definition and preserves the same longitudinal physical content. The central maximum is the most probable longitudinal momentum, not generally the mean. For the source geometry its coordinate is both $p\\cos\\alpha_0$ and the central-peak displacement $\\Delta p_z$ from the dipole origin. A peak fit, a local stationary point or another stable estimator is accepted if it tracks the same central branch.",
    "The visible two-dimensional soft-core potential is the aligned $\\beta=0$ representative. Away from alignment, a TDSE realization must rotate the two-centre geometry consistently; orientation evidence may instead come from the visible weak-field nondipole branch. Its soft-core parameter is fixed by matching the reference field-free $\\mathrm{H}_2^+$ electronic energy at the same $R$, so no hidden table of $\\alpha(R)$ is required. A qualified field-free molecular calculation or eligible standard literature may supply that reference energy. In the simplified analytic LCAO route, an effective charge may be defined consistently through $I_p(R)=Z(R)^2/2$. The lower action limit $\\eta_i$ fixes a phase reference and does not affect a consistently formed probability. The source abbreviations are",
    "$$\n\\nu_p=pR,\\qquad \\nu_k=kR,\\qquad\n\\nu_c=\\frac{2pk}{p^2+k^2+Z^2},\\qquad k=\\frac{\\omega}{c}.\n$$",
    "These identities are answer material, not required notation.",
    "For a symmetric two-centre $1s$ LCAO in the one-photon weak-field limit, the source angular dependence can be reduced, up to shell and normalization factors, to",
    "$$\nW(\\alpha)\\propto\n\\frac{1-\\cos^2\\alpha}{[1-\\nu_c\\cos\\alpha]^4}\n\\left\\{1+\\cos[\\nu_p\\cos\\alpha-\\nu_k]\\right\\}.\n$$",
    "This formula is an accepted canonical route, not a required public recipe. Its phase combines molecular emission geometry with the finite propagation phase. A valid independently derived NSFA evaluation of the finite pulse is equivalent.",
    "Source-supported structural anchors are:",
    "at $R=2$, the normalized molecular distribution has a broad central family and only a few large lobes; at $R=10$, it contains a dense two-centre fringe family with spacing on the $2\\pi/R$ scale;",
    "the dipole/SFA distributions are symmetric, while the nondipole/NSFA distributions have a propagation-direction central displacement;",
    "the hydrogen curves in the source are smooth reference envelopes. They are useful controls but are not a material task output and may be replaced by another physically adequate reference;",
    "absolute probability and the author's line colours, crop and normalization are not grading targets.",
    "For $\\omega=10$, the source central peak moves from the compact-molecule regime toward the large-$R$ one-photon asymptote",
    "$$\n\\Delta p_z\\longrightarrow\\frac{E_k+I_p}{c}=\\frac{\\omega}{c}.\n$$",
    "The source curve decreases toward that positive asymptote as $R$ increases. The compact region deviates materially from a simple separated-centre model because the initial electronic density is concentrated between the nuclei. The physical interpretation changes continuously from predominantly single-aperture-like diffraction at short separation to a two-centre interference picture at sufficiently large separation. The source places the robust two-centre regime beyond roughly $R=4$ a.u.; grade the demonstrated regime change and evidence, not that hidden numerical boundary as a required student scan point.",
    "When the molecular axis makes an angle $\\beta$ with the propagation direction, the light-front samples the projected separation $R\\cos\\beta$. The source orientation result has the central angular/longitudinal displacement increase with $\\cos\\beta$ for both $R=2$ and $R=10$, with distinct magnitudes. Equivalent orientation-sensitive observables are accepted if their physical relation to the timing claim is derived.",
    "The finite time for the light front to cross the molecule supplies a relative emission phase. In the separated-centre limit, the timing inferred from the interference geometry approaches $R/c$. In the compact regime, the relevant emission separation is an effective width of the distributed bound state, not automatically the internuclear distance. The source describes the resulting delay as a few hundred zeptoseconds and its short-$R$ limit through an effective molecular traversal distance. Full credit requires a derivation from the student's signal and declared phase convention; quoting $R/c$ for all $R$ is not correct.",
    "The conclusion is confined to fixed nuclei, the one-photon XUV regime, the declared effective-dimensional TDSE and NSFA/LCAO approximations. A central peak is not by itself a unique clock unless molecular-state structure, interference branch identity and model dependence are addressed.",
    "For F1/F4/M1/M3-M4, article pp.033112-2-3, Eqs.(4)-(9), the nondipole canonical momentum is\n$$\\mathbf q(\\eta)=\\mathbf p+\\mathbf A(\\eta)-\\frac{p^2/2+I_p}{c}\\mathbf n,\\qquad \\eta=t-\\mathbf n\\cdot\\mathbf r/c.$$\nThe weak-field gerade interference factor contains $1+\\cos[pR\\cos\\alpha-kR]$, $k=\\omega/c$, with the full molecular envelope retained. Thus the separated central phase gives $p\\cos\\alpha_0\\to\\omega/c$, using $\\omega=E_k+I_p$, not only $E_k/c$. At angle beta to propagation, the light-front geometric separation is $R\\cos\\beta$. A delay inferred from this phase must retain its energy and branch conventions; the envelope shifts a compact central maximum away from a pure interference maximum. Source Eq.(3) is attractive; the subsequently typeset soft-core model must retain negative attractive terms even where its prose formula omits signs."
  ],
  "closure_requirements": {
    "RC0": [
      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
      "Required indispensable claim CL1, central physical object: all of: F3 (Define a reconstructible longitudinal/angular photoelectron observable, common projection/normalization and stable central branch or equivalent timing-sensitive diagnostic without substituting an unjustified mean.); F4 (Derive separation/orientation dependence of the nondipole timing phase, bind the selected central signal to that phase and distinguish effective emission separation from bare internuclear distance where required.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC1": [
      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
      "Required co primary claim CL2, indispensable material component: all of: O1 (Present valid, reconstructible compact/separated molecular longitudinal or equivalent angular evidence resolving topology change and nondipole displacement under consistent branch/normalization conventions.); O2 (Present valid, reconstructible separation-dependent central-branch or equivalent timing-sensitive evidence sufficient for the claimed compact-to-separated transition, without hidden lobe switches or normalization-made trends.); O3 (Present valid, reconstructible orientation evidence sufficient for timing, using consistently rotated TDSE geometry or the accepted weak-field nondipole branch.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL3, indispensable material component: O4 (Present valid, reconstructible independent NSFA/TDSE central-signal evidence with branch-specific amplitudes and conventions distinguishing physical compatibility from matched-intensity or processing artefacts.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC2": [
      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
      "Required co primary claim CL2, principal mechanism or commissioned conclusion: M5 (Integrate compact, separation and orientation signals with light-front, bound-state and interference mechanisms to infer the strongest supported relative timing and effective-separation boundary.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL3, principal mechanism or commissioned conclusion: M6 (Determine what independent NSFA/TDSE central-signal agreement/conflict establishes after accounting for different amplitudes, dimensional/model conventions and limited long-range dynamics, without claiming pointwise equality.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL4, principal mechanism or commissioned conclusion: M7 (Synthesize timing, compact-to-separated mechanism, orientation, cross-model adequacy and limitations into the strongest conclusion supported by reconstructible calculation.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC3": [
      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
      "Required co primary claim CL4, material validation/scope: V2 (When extraction, lobe identity, field convention, state, projection, model comparison, anomaly or claim raises a concrete conclusion-changing alternative, provide discriminating evidence or proportionately narrow the claim; otherwise record N/A.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC4": [
      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
      "Close CL1 central physical object: all of: F3 (Define a reconstructible longitudinal/angular photoelectron observable, common projection/normalization and stable central branch or equivalent timing-sensitive diagnostic without substituting an unjustified mean.); F4 (Derive separation/orientation dependence of the nondipole timing phase, bind the selected central signal to that phase and distinguish effective emission separation from bare internuclear distance where required.).",
      "Close CL2 indispensable material component: all of: O1 (Present valid, reconstructible compact/separated molecular longitudinal or equivalent angular evidence resolving topology change and nondipole displacement under consistent branch/normalization conventions.); O2 (Present valid, reconstructible separation-dependent central-branch or equivalent timing-sensitive evidence sufficient for the claimed compact-to-separated transition, without hidden lobe switches or normalization-made trends.); O3 (Present valid, reconstructible orientation evidence sufficient for timing, using consistently rotated TDSE geometry or the accepted weak-field nondipole branch.).",
      "Close CL2 principal mechanism or commissioned conclusion: M5 (Integrate compact, separation and orientation signals with light-front, bound-state and interference mechanisms to infer the strongest supported relative timing and effective-separation boundary.).",
      "Close CL3 indispensable material component: O4 (Present valid, reconstructible independent NSFA/TDSE central-signal evidence with branch-specific amplitudes and conventions distinguishing physical compatibility from matched-intensity or processing artefacts.).",
      "Close CL3 principal mechanism or commissioned conclusion: M6 (Determine what independent NSFA/TDSE central-signal agreement/conflict establishes after accounting for different amplitudes, dimensional/model conventions and limited long-range dynamics, without claiming pointwise equality.).",
      "Close CL4 principal mechanism or commissioned conclusion: M7 (Synthesize timing, compact-to-separated mechanism, orientation, cross-model adequacy and limitations into the strongest conclusion supported by reconstructible calculation.).",
      "Close CL4 material validation/scope: V2 (When extraction, lobe identity, field convention, state, projection, model comparison, anomaly or claim raises a concrete conclusion-changing alternative, provide discriminating evidence or proportionately narrow the claim; otherwise record N/A.).",
      "Supporting claim CL5 is separately scored but does not determine overall closure: Restrict conclusions to fixed nuclei, one-photon XUV, declared effective-dimensional TDSE and NSFA/molecular-state approximations; a model-dependent central shift is not a universal experimental clock."
    ]
  },
  "references": [
    {
      "citation": "Zhao-Han Zhang and Feng He. 2021. *Photoionization of H₂⁺ beyond the dipole approximation with zeptosecond time resolution*. *Physical Review A*, 103, 033112.",
      "url": "https://doi.org/10.1103/PhysRevA.103.033112",
      "scientific_scope": "Photoionization of H₂⁺ beyond the dipole approximation with zeptosecond time resolution",
      "anchors": [
        "Zhang and He (2021), article pp.033112-2-3, Eqs.(1),(4)-(9): light-cone nondipole amplitude, gerade initial molecular state and weak-field LCAO limit with field-free Ip matching.",
        "Zhang and He (2021), article p.033112-2, Eqs.(2),(3) and 2D soft-core/energy-matching paragraphs: independent fixed-nuclei TDSE. Article p.033112-4 Fig.3 caption explicitly uses A0=1.0 for TDSE and 0.01 for NSFA.",
        "Zhang and He (2021), article p.033112-3, longitudinal-marginal paragraphs and stationary central-peak definition; Eq.(9),(10) for angular branch. The central maximum is not generally a mean.",
        "Zhang and He (2021), article pp.033112-2-3, Eqs.(4)-(12), and p.033112-4 bound-state phase paragraph: light-front interference phase includes photon momentum and Ip, with separated asymptote (Ek+Ip)/c.",
        "Zhang and He (2021), article pp.033112-3-4, Fig.2(a,b), Eq.(9), compact-density/diffraction discussion: broad compact R=2 signal versus dense R=10 two-centre fringes and propagation-direction displacement.",
        "Zhang and He (2021), article pp.033112-3-5, Eqs.(10)-(12), Fig.3 and compact/separated interpretation: stable central branch approaches omega/c at large separation; a hidden switch to another lobe does not establish timing.",
        "Zhang and He (2021), article p.033112-5, Fig.5, caption and projected R*cos(beta) paragraph: orientation-dependent central angular signal at R=2 and 10. Orientation may use the weak-field branch; an off-axis TDSE must rotate the geometry consistently.",
        "Zhang and He (2021), article p.033112-4, Fig.3 caption and NSFA/TDSE comparison paragraph: distinct-amplitude models agree in structural single-photon central shift, not pointwise matched-intensity spectra.",
        "Zhang and He (2021), article pp.033112-2-5, effective-dimensional fixed-nuclei model, compact/separated discussion and Sec.IV: relative timing remains molecular-state/branch dependent. Extraction alternatives and claim limits are task-defined; no universal absolute clock or source transition coordinate is compulsory."
      ]
    }
  ]
}