cases/case17/grading_rubric.json

{
  "case_id": "Case17",
  "title": "Case17 — Unconventional gap dependence of high-order harmonic generation in the extremely strong light-matter-coupling regime",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Derive and implement the dissipative two-level density-matrix dynamics from the specified Hamiltonian, lower-state initial condition, pulse and distinct longitudinal/transverse relaxation roles with consistent units, signs and polarization convention.",
      "award_conditions": [
        "The TLS Hamiltonian yields correct population/coherence equations with lower-state initial condition, specified pulse and distinct longitudinal/transverse relaxation roles."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F2, F3, F4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article p.023521-2, Eqs.(1)-(5): driven TLS Hamiltonian, population difference x, complex coherence y, distinct longitudinal/transverse damping and p=y+y*."
      ],
      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Derive and implement a consistent semiconductor Bloch realization of the specified Nambu Hamiltonian and initial state, including populations, one complex interband polarization, distinct damping roles, momentum aggregation and macroscopic polarization conjugate to the drive.",
      "award_conditions": [
        "The specified Nambu branch yields consistent occupations, one complex interband polarization, damping, momentum aggregation and the drive-conjugate macroscopic polarization."
      ],
      "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, O1, O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article p.023521-7, Appendix Eqs.(A1)-(A4): semiconductor Nambu Hamiltonian, electron/hole occupations, complex Pk and drive-conjugate macroscopic polarization. Printed yk in Eq.(A4) denotes the propagated Pk, not an extra variable."
      ],
      "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 polarization-spectrum construction and valid common fifth-harmonic intensity estimator in both branches, declaring finite-record, harmonic-bin, normalization and comparison conventions.",
      "award_conditions": [
        "Both branches use a reconstructible polarization fifth-harmonic estimator with declared record, harmonic-bin, normalization and comparison conventions."
      ],
      "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": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-2-4, Eq.(4), Figs.1-3 and Eqs.(8),(9); Appendix p.023521-7 Fig.8: polarization-spectrum fifth-harmonic and optional time-local diagnostic. Reconstructible estimators and common scaling are task-defined; no fixed record/window is compulsory."
      ],
      "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": "Define every response summary, state/emission diagnostic, gap-drive comparison, transfer test and control actually used precisely enough to reconstruct it from submitted data under common case scaling.",
      "award_conditions": [
        "Every response/state/emission/transfer diagnostic actually used is mathematically defined and reconstructible under common case scaling."
      ],
      "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": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-2-4, Eq.(4), Figs.1-3 and Eqs.(8),(9); Appendix p.023521-7 Fig.8: polarization-spectrum fifth-harmonic and optional time-local diagnostic. Reconstructible estimators and common scaling are task-defined; no fixed record/window 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": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present valid, reconstructible two-level fifth-harmonic evidence over enough off-resonant gap/drive variation to expose joint response, strong-coupling nontrivial regime, turnover and supported boundaries under one common scale.",
      "award_conditions": [
        "Off-resonant TLS gap/drive evidence resolves a strong-coupling gap-increase region, joint organization, fixed-drive turnover and actual claim boundaries under common scale.",
        "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": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-3-4, Figs.2-3 and Sec.III.A: strong-drive gap-increase domain, joint gap/drive organization and fixed-drive turnover. Ridge near Omega0/Delta=6 and maximum near Delta=4 are illustrative, not exact coordinates."
      ],
      "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 state/emission evidence with sufficient temporal/dynamical resolution to distinguish gap-regime mechanisms and connect population/coherence evolution to integrated fifth-harmonic response.",
      "award_conditions": [
        "State/emission data resolve gap-regime dynamical differences and connect population/coherence evolution to integrated fifth-harmonic 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: 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": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-4-5, Figs.4-5, Eqs.(2)-(4),(8),(9): small-gap rapid excitation/early saturation and wing emission; intermediate sustained central polarization; large-gap slow pulse-centred excitation, linking time dynamics to nonmonotonic integrated response."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. 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 semiconductor fifth-harmonic evidence with correct momentum/model binding over a sufficient domain for material gap-drive transfer, under declared common comparison conventions.",
      "award_conditions": [
        "The semiconductor fifth-harmonic output has correct momentum/model identity and sufficient domain to assess material gap-drive transfer.",
        "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, M1, M2, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-7-8, Appendix Eqs.(A1)-(A4), Figs.9-10 and dispersion discussion: semiconductor transfer of gap-drive organization with momentum aggregation, not generic model equivalence."
      ],
      "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 auditable evidence distinguishing claimed gap/dynamics/transfer interpretation from concrete alternatives raised by the method/data, accepting any genuinely discriminating control or dual-purpose evidence.",
      "award_conditions": [
        "Auditable, genuinely discriminating control or dual-purpose evidence distinguishes the claimed dynamics/transfer account from concrete alternatives raised by the calculation.",
        "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, I1, I2, I3, M1, M2, M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-5-6, Sec.III.B and Fig.6: relaxation smooths response but does not generate unconventional gap dependence. This is an optional canonical discriminator; task accepts another genuinely capable alternative test or dual-purpose evidence."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from submitted two-level evidence joint gap-drive organization, including a supported strong-coupling gap-increase domain, nonmonotonic fixed-drive behavior, turnover and domains of validity, without importing a fixed reference ridge coordinate.",
      "award_conditions": [
        "The candidate identifies joint TLS gap-drive structure, a supported gap-increase domain and nonmonotonic turnover without importing fixed reference coordinates."
      ],
      "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 two-level fifth-harmonic evidence over enough off-resonant gap/drive variation to expose joint response, strong-coupling nontrivial regime, turnover and supported boundaries under one common scale.)",
        "Preserve independently valid work in I2, I3, M1, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-3-4, Figs.2-3 and Sec.III.A: strong-drive gap-increase domain, joint gap/drive organization and fixed-drive turnover. Ridge near Omega0/Delta=6 and maximum near Delta=4 are illustrative, not exact coordinates."
      ],
      "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 material gap-regime differences in population difference, coherence buildup/saturation and pulse-local emission relevant to the integrated response.",
      "award_conditions": [
        "The candidate identifies population-difference, coherence saturation/buildup and pulse-local emission differences relevant to integrated response."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O2 (Present valid, reconstructible state/emission evidence with sufficient temporal/dynamical resolution to distinguish gap-regime mechanisms and connect population/coherence evolution to integrated fifth-harmonic response.)",
        "Preserve independently valid work in I1, I3, M1, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-4-5, Figs.4-5, Eqs.(2)-(4),(8),(9): small-gap rapid excitation/early saturation and wing emission; intermediate sustained central polarization; large-gap slow pulse-centred excitation, linking time dynamics to nonmonotonic integrated response."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from the submitted semiconductor calculation which gap-drive organization transfers or fails to transfer under declared momentum/normalization conventions.",
      "award_conditions": [
        "The candidate identifies which organization transfers or fails in the submitted semiconductor evidence under declared aggregation/normalization."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O3 (Present valid, reconstructible semiconductor fifth-harmonic evidence with correct momentum/model binding over a sufficient domain for material gap-drive transfer, under declared common comparison conventions.)",
        "Preserve independently valid work in I1, I2, M1, M2, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-7-8, Appendix Eqs.(A1)-(A4), Figs.9-10 and dispersion discussion: semiconductor transfer of gap-drive organization with momentum aggregation, not generic model equivalence."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain how driven population difference and coherence determine radiating polarization, including excitation/saturation redistribution of emission within the pulse.",
      "award_conditions": [
        "Driven population difference and coherence explain radiating polarization and excitation/saturation redistribution within the pulse."
      ],
      "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 (Derive and implement the dissipative two-level density-matrix dynamics from the specified Hamiltonian, lower-state initial condition, pulse and distinct longitudinal/transverse relaxation roles with consistent units, signs and polarization convention.)",
        "Preserve independently valid work in M2, 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": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-4-5, Figs.4-5, Eqs.(2)-(4),(8),(9): small-gap rapid excitation/early saturation and wing emission; intermediate sustained central polarization; large-gap slow pulse-centred excitation, linking time dynamics to nonmonotonic integrated response."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use identified dynamics to explain the progression from early saturation/wing-weighted emission through sustained central response to slower pulse-centred emission as the off-resonant gap changes.",
      "award_conditions": [
        "Identified dynamics explain early saturation/wing emission, sustained intermediate central response and slow large-gap pulse-centred emission."
      ],
      "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 material gap-regime differences in population difference, coherence buildup/saturation and pulse-local emission relevant to the integrated response.)",
        "Preserve independently valid work in M1, 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": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-4-5, Figs.4-5, Eqs.(2)-(4),(8),(9): small-gap rapid excitation/early saturation and wing emission; intermediate sustained central polarization; large-gap slow pulse-centred excitation, linking time dynamics to nonmonotonic integrated response."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect pulse-local state/emission dynamics to the integrated nonmonotonic fifth-harmonic gap-drive response rather than invoking a static gap-only or dissipation-generated rule.",
      "award_conditions": [
        "Actual time-local state/emission evidence explains integrated nonmonotonic gap-drive response rather than a static gap rule or dissipation-generated mechanism."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: I1 (Identify from submitted two-level evidence joint gap-drive organization, including a supported strong-coupling gap-increase domain, nonmonotonic fixed-drive behavior, turnover and domains of validity, without importing a fixed reference ridge coordinate.); I2 (Identify material gap-regime differences in population difference, coherence buildup/saturation and pulse-local emission relevant to the integrated response.)",
        "Preserve independently valid work in M1, M2, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-4-5, Figs.4-5, Eqs.(2)-(4),(8),(9): small-gap rapid excitation/early saturation and wing emission; intermediate sustained central polarization; large-gap slow pulse-centred excitation, linking time dynamics to nonmonotonic integrated response."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Integrate state-polarization identity, temporal-regime mechanism and time-spectrum linkage into the principal explanation of joint gap-drive response and turnover.",
      "award_conditions": [
        "State-polarization identity, dynamical regimes and time-spectrum linkage form one principal explanation of joint organization and turnover."
      ],
      "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 driven population difference and coherence determine radiating polarization, including excitation/saturation redistribution of emission within the pulse.); M2 (Use identified dynamics to explain the progression from early saturation/wing-weighted emission through sustained central response to slower pulse-centred emission as the off-resonant gap changes.); M3 (Connect pulse-local state/emission dynamics to the integrated nonmonotonic fifth-harmonic gap-drive response rather than invoking a static gap-only or dissipation-generated rule.)",
        "Preserve independently valid work in M5, 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": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-4-5, Figs.4-5, Eqs.(2)-(4),(8),(9): small-gap rapid excitation/early saturation and wing emission; intermediate sustained central polarization; large-gap slow pulse-centred excitation, linking time dynamics to nonmonotonic integrated response."
      ],
      "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 semiconductor evidence to determine what organization transfers, accepting a supported qualified negative result; visual resemblance alone is insufficient.",
      "award_conditions": [
        "Semiconductor evidence supports the transfer decision, including a genuinely supported qualified negative result rather than resemblance alone."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I3 (Identify from the submitted semiconductor calculation which gap-drive organization transfers or fails to transfer under declared momentum/normalization conventions.)",
        "Preserve independently valid work in M1, 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": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-7-8, Appendix Eqs.(A1)-(A4), Figs.9-10 and dispersion discussion: semiconductor transfer of gap-drive organization with momentum aggregation, not generic model equivalence."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain why dispersion, momentum aggregation and omitted intraband/multiband physics bound transfer from the two-level result, distinguishing bounded organization from generic model equivalence.",
      "award_conditions": [
        "Dispersion, momentum summation and omitted realistic intraband/multiband physics bound transfer and preclude generic TLS/semiconductor equivalence."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: F2 (Derive and implement a consistent semiconductor Bloch realization of the specified Nambu Hamiltonian and initial state, including populations, one complex interband polarization, distinct damping roles, momentum aggregation and macroscopic polarization conjugate to the drive.); M5 (Use semiconductor evidence to determine what organization transfers, accepting a supported qualified negative result; visual resemblance alone is insufficient.)",
        "Preserve independently valid work in M1, M2, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-7-8, Appendix Eqs.(A1)-(A4), Figs.9-10 and dispersion discussion: semiconductor transfer of gap-drive organization with momentum aggregation, not generic model equivalence."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Synthesize two-level response, principal dynamics, semiconductor transfer, alternative discrimination and scope into the strongest mutually consistent evidence-supported conclusion.",
      "award_conditions": [
        "TLS response, central dynamics, semiconductor transfer, alternatives and scope support the strongest mutually consistent evidence-based 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: M4 (Integrate state-polarization identity, temporal-regime mechanism and time-spectrum linkage into the principal explanation of joint gap-drive response and turnover.); M6 (Explain why dispersion, momentum aggregation and omitted intraband/multiband physics bound transfer from the two-level result, distinguishing bounded organization from generic model equivalence.); O4 (Present auditable evidence distinguishing claimed gap/dynamics/transfer interpretation from concrete alternatives raised by the method/data, accepting any genuinely discriminating control or dual-purpose evidence.)",
        "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": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-2,6-8, TLS omissions, Sec.IV and Appendix scope: limited transfer with dispersion and momentum-dependent coupling. Synthesis and triggered sampling/normalization/relaxation controls are task duties, not a required universal-scaling study."
      ],
      "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 the specified dissipative two-level/restrictive two-band semiconductor models, computed off-resonant domain and polarization fifth-harmonic evidence; do not claim generic equivalence or omitted realistic intraband, multiband or experimental behavior.",
      "award_conditions": [
        "The conclusion stays within the specified dissipative TLS/restrictive semiconductor, computed off-resonant range and polarization fifth-harmonic observable."
      ],
      "applicability_and_na": [
        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-2,6-8, TLS omissions, Sec.IV and Appendix scope: limited transfer with dispersion and momentum-dependent coupling. Synthesis and triggered sampling/normalization/relaxation controls are task duties, not a required universal-scaling study."
      ],
      "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 sampling, normalization, transform, momentum aggregation, relaxation interpretation, anomaly or claim creates a concrete conclusion-changing alternative, provide discriminating evidence or proportionately narrow the claim; otherwise record N/A.",
      "award_conditions": [
        "Only a concrete triggered sampling, transform, scaling, aggregation, relaxation or claim risk requires discriminating evidence or narrower claims; otherwise N/A."
      ],
      "applicability_and_na": [
        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve 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": [
        "Global basis phases, Fourier, one common intensity factor, Brillouin-zone sum normalization and harmless time origins are accepted after mapping.",
        "Fifth-harmonic power |p(5 omega0)|^2, the corresponding squared polarization transform and an explicitly equivalent narrow-bin finite-pulse estimator are accepted; another harmonic/observable requires a supported conversion.",
        "Converged ODE/SBE solvers, records, quadratures, transforms, windows, parameter samples and layouts are accepted; maps, lineouts, regimes, boundaries, state histories, local spectra and controlled perturbations qualify by their causal discriminating function.",
        "Relaxation variation, cross-frequency scaling, another harmonic or a different control may supply robustness evidence when it tests the actual causal claim; no Gaussian-window plot, relaxation sweep or fixed gap triplet is compulsory."
      ],
      "source_support": [
        "Kofuji and Peters (2023), article pp.023521-2,6-8, TLS omissions, Sec.IV and Appendix scope: limited transfer with dispersion and momentum-dependent coupling. Synthesis and triggered sampling/normalization/relaxation controls are task duties, not a required universal-scaling study."
      ],
      "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 semiconductor macroscopic polarization is conjugate to the drive in the Nambu Hamiltonian. The isolated printed y_k is an alias/notation error for propagated P_k, not a second dynamical variable or alternative model.",
    "Strong drive contains a gap-increase domain and nonmonotonic fixed-drive response, followed by decline at larger gap. A uniformly decreasing gap law across the entire strong-drive study is materially wrong.",
    "At small gap rapid excitation suppresses population difference early and weights emission toward pulse wings; intermediate gap sustains polarization centrally; larger gap slows excitation and confines emission near the centre before decline.",
    "The source TLS ridge near Omega0/Delta=6 and fixed-drive maximum near Delta=4 at Omega0=22.7, and semiconductor ridge near ratio 7/maximum near Delta=4 at drive 27, are recognition landmarks rather than exact coordinates or tolerances.",
    "Relaxation smooths/exposes fine structure but does not generate the unconventional dependence. The transfer supports bounded gap-drive organization, not generic equivalence of a TLS with a semiconductor.",
    "Independent case scaling, resonance-only slices presented as global off-resonant laws, omitted semiconductor diagonal/interband roles and unrelated polarization objects are not equivalent.",
    "Source/model data must be consulted when a material decision depends on regime resolution or transfer identity; numerical convergence and smooth maps alone cannot supply the physical check or missing candidate reasoning.",
    "For the two-level branch, the canonical route evolves the lower-state initial density matrix under the visible Hamiltonian with longitudinal relaxation and transverse decoherence. In the source notation, the population difference \\(x=\\rho_{11}-\\rho_{22}\\) and coherence \\(y=\\rho_{21}\\) obey the source density-matrix equations, and \\(p(t)=y+y^*\\). The fifth-harmonic reference is \\(\\lvert p(5\\omega_0)\\rvert^2\\), up to one declared common scale.",
    "The source does not fix a finite-record normalization, momentum-sum normalization, quadrature, propagator, step, window outside its optional local transform, or convergence tolerance. These are not student duties. Grade the mathematical observable and invariant structures, not absolute colorbar agreement.",
    "The canonical evidence is the source fifth-harmonic gap-drive map and its fixed-drive discussion on pp. 3-4, together with the structural reproduction.",
    "In the sufficiently strong-coupling region, the response contains a domain where increasing the gap increases the fifth-harmonic intensity.",
    "At fixed high drive, the dependence is nonmonotonic: the response rises to a maximum region and then decreases for larger gaps.",
    "The map is jointly organized by gap and drive. The canonical ridge lies near \\(\\Omega_0/\\Delta\\approx6\\), and the source fixed-drive case \\(\\Omega_0=22.7\\) has its maximum near \\(\\Delta=4\\).",
    "These locations are recognition anchors, not exact-coordinate requirements. A different sufficiently broad, converged sampling is accepted. A claim that the response decreases uniformly with gap across the entire strong-drive study is materially wrong.",
    "The canonical mechanism evidence is the source population/coherence evolution and local Gaussian-window spectrum on pp. 4-6, plus the sensitivity-tested Gabor reproduction.",
    "At small gap and fixed strong drive, rapid excitation reduces the population difference early, the polarization saturates and may weaken near the pulse centre, and high-harmonic emission is weighted toward the pulse wings.",
    "In the intermediate regime where the integrated response is largest, the polarization and harmonic emission remain substantial over a longer central part of the pulse.",
    "At large gap, excitation is slower and the dominant emission is confined more closely to the pulse centre before the integrated response enters the conventional decreasing regime.",
    "Thus the nontrivial integrated gap dependence is connected to where the driven coherence can build and emit during the pulse, not to a static gap-only rule.",
    "Students need not use a Gaussian-window spectrum or these three gap values. Population/coherence histories, alternative time-local transforms, interventions on state variables, pulse-segment reconstructions, or another auditable diagnostic receive full credit when they establish the same causal distinction without building it into the analysis.",
    "The source relaxation study on pp. 5-6 shows that reduced relaxation exposes fine structure, while larger relaxation smooths the response and makes the gap dependence more visible. The unconventional dependence persists across the tested rates, so relaxation is not its generating mechanism. This is an accepted robustness/control route, not a mandatory separate output.",
    "The source semiconductor results on pp. 7-8 and the structural reproduction support the following transfer boundary:",
    "the semiconductor fifth-harmonic response contains a qualitatively similar strong-drive gap-increase region and a nonmonotonic fixed-drive dependence;",
    "the canonical ridge is near \\(\\Omega_0/\\Delta\\approx7\\), and the source \\(\\Omega_0=27\\) line peaks near \\(\\Delta=4\\);",
    "the agreement supports bounded transfer of the gap-drive organization, not generic equivalence between a two-level system and a semiconductor.",
    "The two-level model omits realistic intraband currents and multiband effects, while the specified semiconductor model retains dispersion and momentum aggregation under restrictive assumptions. A transfer claim must state this scope. Cross-frequency enhancement scaling is also source-supported and may serve as additional generality evidence, but it is not a required hidden anchor because no dedicated current reproduction result was supplied.",
    "fifth-harmonic power written as \\(\\lvert p(5\\omega_0)\\rvert^2\\), the squared magnitude of the polarization spectrum at \\(5\\omega_0\\), or an explicitly equivalent narrow-bin finite-pulse estimator;",
    "one global arbitrary intensity factor and consistent thermodynamic or finite-grid momentum-sum conventions;",
    "any converged ODE/SBE solver, time record, quadrature, transform, window, parameter sampling, or plot layout;",
    "lineouts, maps, regime diagrams, fitted response boundaries, time-domain state evidence, local spectra, controlled perturbations, or other evidence packages with the same physical discriminating function;",
    "relaxation variation, cross-frequency scaling, another harmonic order, or another control when it genuinely tests the submitted causal claim.",
    "Not equivalent: a different harmonic or radiating observable presented as the common fifth- harmonic target without a supported conversion;",
    "Not equivalent: independently rescaled cases that erase relative gap, drive, time, or model information used in the claim;",
    "Not equivalent: a resonance-only slice presented as a global off-resonant gap law;",
    "Not equivalent: semiconductor dynamics that omit the specified diagonal/interband roles or use an unrelated polarization object;",
    "Not equivalent: a generic statement that the two models are equivalent;",
    "Not equivalent: a visually smooth map or local spectrum whose material structures are numerical, windowing, or normalization artefacts.",
    "For F1/M1-M4, article p.023521-2, Eqs.(2)-(4),\n$$\\dot x=2i\\Omega(t)(y-y^*)-\\gamma_L(x-1),\\quad\n\\dot y=-(i\\Delta+\\gamma_T)y+i\\Omega(t)x,\\quad p(t)=2\\Re y(t),\\quad (x,y)_{t_0}=(1,0).$$\nFor F2/O3/M5-M6, article p.023521-7, Eqs.(A2)-(A4),\n$$\\dot f_k^{e/h}=2\\Omega\\sin\\theta_k\\Re P_k-\\gamma_L f_k^{e/h},$$\n$$\\dot P_k=-[i(\\varepsilon_k^e+\\varepsilon_k^h)+\\gamma_T]P_k+\\Omega\\sin\\theta_k(1-f_k^e-f_k^h),$$\n$$p(t)=\\sum_k\\{\\cos\\theta_k(1-f_k^e-f_k^h)-2\\sin\\theta_k\\Im P_k\\}.$$\nHere $\\varepsilon_k^{e/h}=E_k^{e/h}+\\Omega\\cos\\theta_k$. The printed yk in Eq.(A4) is the same propagated Pk. Both branches grade $|\\widetilde p(5\\omega_0)|^2$ or an explicitly equivalent narrow-bin estimator under one consistent scale, not a derivative spectrum without conversion or independently normalized map slices."
  ],
  "closure_requirements": {
    "RC0": [
      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
      "Required indispensable claim CL1, central physical object: all of: F1 (Derive and implement the dissipative two-level density-matrix dynamics from the specified Hamiltonian, lower-state initial condition, pulse and distinct longitudinal/transverse relaxation roles with consistent units, signs and polarization convention.); F3 (Define a reconstructible polarization-spectrum construction and valid common fifth-harmonic intensity estimator in both branches, declaring finite-record, harmonic-bin, normalization and comparison conventions.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC1": [
      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
      "Required co primary claim CL2, indispensable material component: O1 (Present valid, reconstructible two-level fifth-harmonic evidence over enough off-resonant gap/drive variation to expose joint response, strong-coupling nontrivial regime, turnover and supported boundaries under one common scale.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL3, indispensable material component: O3 (Present valid, reconstructible semiconductor fifth-harmonic evidence with correct momentum/model binding over a sufficient domain for material gap-drive transfer, under declared common comparison conventions.). 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: M4 (Integrate state-polarization identity, temporal-regime mechanism and time-spectrum linkage into the principal explanation of joint gap-drive response and turnover.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL3, principal mechanism or commissioned conclusion: M6 (Explain why dispersion, momentum aggregation and omitted intraband/multiband physics bound transfer from the two-level result, distinguishing bounded organization from generic model equivalence.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL4, principal mechanism or commissioned conclusion: M7 (Synthesize two-level response, principal dynamics, semiconductor transfer, alternative discrimination and scope into the strongest mutually consistent evidence-supported conclusion.). 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 sampling, normalization, transform, momentum aggregation, relaxation interpretation, anomaly or claim creates 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: F1 (Derive and implement the dissipative two-level density-matrix dynamics from the specified Hamiltonian, lower-state initial condition, pulse and distinct longitudinal/transverse relaxation roles with consistent units, signs and polarization convention.); F3 (Define a reconstructible polarization-spectrum construction and valid common fifth-harmonic intensity estimator in both branches, declaring finite-record, harmonic-bin, normalization and comparison conventions.).",
      "Close CL2 indispensable material component: O1 (Present valid, reconstructible two-level fifth-harmonic evidence over enough off-resonant gap/drive variation to expose joint response, strong-coupling nontrivial regime, turnover and supported boundaries under one common scale.).",
      "Close CL2 principal mechanism or commissioned conclusion: M4 (Integrate state-polarization identity, temporal-regime mechanism and time-spectrum linkage into the principal explanation of joint gap-drive response and turnover.).",
      "Close CL3 indispensable material component: O3 (Present valid, reconstructible semiconductor fifth-harmonic evidence with correct momentum/model binding over a sufficient domain for material gap-drive transfer, under declared common comparison conventions.).",
      "Close CL3 principal mechanism or commissioned conclusion: M6 (Explain why dispersion, momentum aggregation and omitted intraband/multiband physics bound transfer from the two-level result, distinguishing bounded organization from generic model equivalence.).",
      "Close CL4 principal mechanism or commissioned conclusion: M7 (Synthesize two-level response, principal dynamics, semiconductor transfer, alternative discrimination and scope into the strongest mutually consistent evidence-supported conclusion.).",
      "Close CL4 material validation/scope: V2 (When sampling, normalization, transform, momentum aggregation, relaxation interpretation, anomaly or claim creates 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 the specified dissipative two-level/restrictive two-band semiconductor models, computed off-resonant domain and polarization fifth-harmonic evidence; do not claim generic equivalence or omitted realistic intraband, multiband or experimental behavior."
    ]
  },
  "references": [
    {
      "citation": "Akira Kofuji and Robert Peters. 2023. *Unconventional gap dependence of high-order harmonic generation in the extremely strong light-matter-coupling regime*. *Physical Review A*, 108, 023521.",
      "url": "https://doi.org/10.1103/PhysRevA.108.023521",
      "scientific_scope": "Unconventional gap dependence of high-order harmonic generation in the extremely strong light-matter-coupling regime",
      "anchors": [
        "Kofuji and Peters (2023), article p.023521-2, Eqs.(1)-(5): driven TLS Hamiltonian, population difference x, complex coherence y, distinct longitudinal/transverse damping and p=y+y*.",
        "Kofuji and Peters (2023), article p.023521-7, Appendix Eqs.(A1)-(A4): semiconductor Nambu Hamiltonian, electron/hole occupations, complex Pk and drive-conjugate macroscopic polarization. Printed yk in Eq.(A4) denotes the propagated Pk, not an extra variable.",
        "Kofuji and Peters (2023), article pp.023521-2-4, Eq.(4), Figs.1-3 and Eqs.(8),(9); Appendix p.023521-7 Fig.8: polarization-spectrum fifth-harmonic and optional time-local diagnostic. Reconstructible estimators and common scaling are task-defined; no fixed record/window is compulsory.",
        "Kofuji and Peters (2023), article pp.023521-3-4, Figs.2-3 and Sec.III.A: strong-drive gap-increase domain, joint gap/drive organization and fixed-drive turnover. Ridge near Omega0/Delta=6 and maximum near Delta=4 are illustrative, not exact coordinates.",
        "Kofuji and Peters (2023), article pp.023521-4-5, Figs.4-5, Eqs.(2)-(4),(8),(9): small-gap rapid excitation/early saturation and wing emission; intermediate sustained central polarization; large-gap slow pulse-centred excitation, linking time dynamics to nonmonotonic integrated response.",
        "Kofuji and Peters (2023), article pp.023521-7-8, Appendix Eqs.(A1)-(A4), Figs.9-10 and dispersion discussion: semiconductor transfer of gap-drive organization with momentum aggregation, not generic model equivalence.",
        "Kofuji and Peters (2023), article pp.023521-5-6, Sec.III.B and Fig.6: relaxation smooths response but does not generate unconventional gap dependence. This is an optional canonical discriminator; task accepts another genuinely capable alternative test or dual-purpose evidence.",
        "Kofuji and Peters (2023), article pp.023521-2,6-8, TLS omissions, Sec.IV and Appendix scope: limited transfer with dispersion and momentum-dependent coupling. Synthesis and triggered sampling/normalization/relaxation controls are task duties, not a required universal-scaling study."
      ]
    }
  ]
}