cases/case35/grading_rubric.json

{
  "case_id": "Case35",
  "title": "Photon-state dependence and coherent-overlap effects in quantum-light high-harmonic generation",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Correctly instantiate the stated soft-core matter Hamiltonian, normalized field-free electronic ground state, squeezed/Fock/two-colour optical cases, carrier/intensity/phase/common-envelope bindings and matched classical controls.",
      "award_conditions": [
        "Correctly instantiate the stated soft-core matter Hamiltonian, normalized field-free electronic ground state, squeezed/Fock/two-colour optical cases, carrier/intensity/phase/common-envelope bindings and matched classical controls."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Wang and Bian (2025), article pp. 043111-6–7, Fig. 3(a,b), Fig. 4(a), Eq. (26); Appendices E–F, pp. 043111-10–11, Eqs. (E1)–(E2), (F1)–(F4). Matter ground state, field-amplitude calibration, single-mode state cases and two-colour frequency/phase controls; Fig. 4(b) is a different, unrequired two-mode squeezed case."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Construct state-specific optical coefficients and the Gram metric on the generalized von Neumann lattice, with C†GC=1; compute component complex HHG responses from the common electronic initial state and retain all full cross terms in a form equivalent to u†Gu.",
      "award_conditions": [
        "State-specific coefficients solve or demonstrably represent the projection problem with the Gram metric and normalized optical state.",
        "Component complex responses use the common electronic initial state and retain all cross terms in the declared full quadratic form; a formula recital or diagonal mixture is insufficient."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for F1, F3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.",
        "Judge this full construction independently of F1 case binding and F3 estimator mapping; unrelated weaknesses do not erase its valid coefficients, metric or full-cross-term work."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article pp. 043111-2–4, Eqs. (7)–(11), (18)–(22); Fig. 2(c,d), p. 043111-5. Nonorthogonal coefficients, overlap metric, normalization and full complex response. The task uses the explicitly declared equivalent quadratic-form convention."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Define the HHG estimator, full branch, same-quadratic-form off-diagonal-deletion comparator, matched classical branch, common normalization, case mapping and reconstructible data products.",
      "award_conditions": [
        "Full, same-form diagonal-deletion and matched-classical branches have explicit estimator, normalization and physical-case mappings.",
        "Underlying data products reconstruct that comparison without independently rescaling away its material branch relation."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for F1, F2; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.",
        "Judge the estimator/comparison contract independently; an F1/F2 defect propagates only when it actually damages this case, branch or data-product identity."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article pp. 043111-4–6, Eqs. (22)–(25), Fig. 3(a,b); Appendix G, Fig. 7(a,b), p. 043111-11. Full versus coefficient-diagonal and Husimi approximations; overlap smallness is state-dependent. The task comparator deletes off-diagonal terms from the same form, not from an independently normalized mixture."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present physically valid, reconstructible squeezed-vacuum full/diagonal/matched-classical HHG evidence with global structure sufficient to assess broad harmonic support/envelope, quantum/classical relation and branch identity.",
      "award_conditions": [
        "Present physically valid, reconstructible squeezed-vacuum full/diagonal/matched-classical HHG evidence with global structure sufficient to assess broad harmonic support/envelope, quantum/classical relation and branch identity.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F1 AND F2 AND F3). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for O2, O3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article p. 043111-6, Fig. 3(a) and squeezed-vacuum paragraph; Fig. 2(a,c), p. 043111-5. Extended squeezed harmonic support and altered envelope linked to longitudinal field-amplitude support; spectra are vertically offset, so absolute inter-curve ordinate ratios are not targets."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present physically valid, reconstructible Fock-state full/diagonal/matched-classical HHG evidence with global structure sufficient to assess broad harmonic support/cutoff, quantum/classical relation and branch identity.",
      "award_conditions": [
        "Present physically valid, reconstructible Fock-state full/diagonal/matched-classical HHG evidence with global structure sufficient to assess broad harmonic support/cutoff, quantum/classical relation and branch identity.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F1 AND F2 AND F3). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for O1, O3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article p. 043111-6, Fig. 3(b), Fock-state paragraph; Fig. 2(b,d), p. 043111-5. Closer Fock/coherent broad cutoff and structure, not pointwise identity or an all-state theorem."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present two-colour quantum and matched-classical HHG evidence with correct two-frequency, intensity/phase, common-envelope and electronic-initial-state bindings, including the material even-harmonic family and broad spectral relation.",
      "award_conditions": [
        "Present two-colour quantum and matched-classical HHG evidence with correct two-frequency, intensity/phase, common-envelope and electronic-initial-state bindings, including the material even-harmonic family and broad spectral relation.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F1 AND F2 AND F3). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for O1, O2; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article pp. 043111-6–7, Eq. (26), Fig. 4(a) and its caption and adjacent first-scenario paragraph. 800-nm coherent plus 400-nm squeezed case, phase alignment, even-harmonic family and broad quantum/classical spectral relation. Fig. 4(b) is not this comparison."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present a direct full-metric/diagonal-only comparison, or functionally equivalent evidence with the same discriminating power, showing that finite-lattice or assembly error does not create the major state/case relation.",
      "award_conditions": [
        "Present a direct full-metric/diagonal-only comparison, or functionally equivalent evidence with the same discriminating power, showing that finite-lattice or assembly error does not create the major state/case relation.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F2 AND F3). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for O1, O2, O3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article pp. 043111-4–6, Eqs. (22)–(25), Fig. 3(a,b); Appendix G, Fig. 7(a,b), p. 043111-11. Full versus coefficient-diagonal and Husimi approximations; overlap smallness is state-dependent. The task comparator deletes off-diagonal terms from the same form, not from an independently normalized mixture."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from the candidate's own valid squeezed spectra the substantial broad harmonic-support/envelope difference between full quantum and matched classical responses.",
      "award_conditions": [
        "Identify from the candidate's own valid squeezed spectra the substantial broad harmonic-support/envelope difference between full quantum and matched classical responses."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O1. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for I2, I3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article p. 043111-6, Fig. 3(a) and squeezed-vacuum paragraph; Fig. 2(a,c), p. 043111-5. Extended squeezed harmonic support and altered envelope linked to longitudinal field-amplitude support; spectra are vertically offset, so absolute inter-curve ordinate ratios are not targets."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from the candidate's own valid Fock spectra the closer quantum/classical cutoff and broad-structure relation without claiming pointwise identity.",
      "award_conditions": [
        "Identify from the candidate's own valid Fock spectra the closer quantum/classical cutoff and broad-structure relation without claiming pointwise identity."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O2. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for I1, I3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article p. 043111-6, Fig. 3(b), Fock-state paragraph; Fig. 2(b,d), p. 043111-5. Closer Fock/coherent broad cutoff and structure, not pointwise identity or an all-state theorem."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify the material even-harmonic family and broad quantum/classical spectral-scale relation in the candidate's own two-colour evidence, preserving frequency/phase/case identity.",
      "award_conditions": [
        "Identify the material even-harmonic family and broad quantum/classical spectral-scale relation in the candidate's own two-colour evidence, preserving frequency/phase/case identity."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O3. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for I1, I2; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article pp. 043111-6–7, Eq. (26), Fig. 4(a) and its caption and adjacent first-scenario paragraph. 800-nm coherent plus 400-nm squeezed case, phase alignment, even-harmonic family and broad quantum/classical spectral relation. Fig. 4(b) is not this comparison."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect optical coefficient/amplitude/phase support, nonorthogonal coherent overlap and component complex responses to the full metric HHG response; explain why diagonal deletion is an approximation, not optical-state identity.",
      "award_conditions": [
        "Connect optical coefficient/amplitude/phase support, nonorthogonal coherent overlap and component complex responses to the full metric HHG response; explain why diagonal deletion is an approximation, not optical-state identity."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F2 AND F3). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M6; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article pp. 043111-2–4, Eqs. (7)–(11), (18)–(22); Fig. 2(c,d), p. 043111-5. Nonorthogonal coefficients, overlap metric, normalization and full complex response. The task uses the explicitly declared equivalent quadratic-form convention."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain the candidate's squeezed quantum/classical response difference through squeezed-state field-amplitude/phase support and coherent superposition, not relabelling of the same classical field.",
      "award_conditions": [
        "Explain the candidate's squeezed quantum/classical response difference through squeezed-state field-amplitude/phase support and coherent superposition, not relabelling of the same classical field."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (I1 AND M1). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article p. 043111-6, Fig. 3(a) and squeezed-vacuum paragraph; Fig. 2(a,c), p. 043111-5. Extended squeezed harmonic support and altered envelope linked to longitudinal field-amplitude support; spectra are vertically offset, so absolute inter-curve ordinate ratios are not targets."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain the closer Fock quantum/classical broad response through Fock-state support and coherent representation, without extrapolation to all states.",
      "award_conditions": [
        "Explain the closer Fock quantum/classical broad response through Fock-state support and coherent representation, without extrapolation to all states."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (I2 AND M1). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M2; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article p. 043111-6, Fig. 3(b), Fock-state paragraph; Fig. 2(b,d), p. 043111-5. Closer Fock/coherent broad cutoff and structure, not pointwise identity or an all-state theorem."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Combine both candidate-established single-mode chains to conclude how photon-state structure changes quantum/classical HHG response, restricted to the specified narrow state families.",
      "award_conditions": [
        "Combine both candidate-established single-mode chains to conclude how photon-state structure changes quantum/classical HHG response, restricted to the specified narrow state families."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (I1 AND I2 AND M2 AND M3). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M7; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article pp. 043111-5–6, Figs. 2(a–d), 3(a,b), discussion after Fig. 3. Synthesis of the two separately established single-mode state-response chains; static state distributions alone are insufficient dynamic evidence."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use same-state, same-response full/diagonal evidence to judge where the diagonal approximation preserves overall trends and where it remains approximate; distinguish overlap effects from finite-lattice risk.",
      "award_conditions": [
        "Use same-state, same-response full/diagonal evidence to judge where the diagonal approximation preserves overall trends and where it remains approximate; distinguish overlap effects from finite-lattice risk."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (O4 AND M1). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M4, M7; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article pp. 043111-4–6, Eqs. (22)–(25), Fig. 3(a,b); Appendix G, Fig. 7(a,b), p. 043111-11. Full versus coefficient-diagonal and Husimi approximations; overlap smallness is state-dependent. The task comparator deletes off-diagonal terms from the same form, not from an independently normalized mixture."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect two-colour frequency/phase/quadrature composition to the observed even-harmonic symmetry family, retaining the common envelope and matched controls rather than borrowing a single-mode conclusion.",
      "award_conditions": [
        "Connect two-colour frequency/phase/quadrature composition to the observed even-harmonic symmetry family, retaining the common envelope and matched controls rather than borrowing a single-mode conclusion."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F1 AND I3). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M2, M3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article pp. 043111-6–7, Eq. (26), Fig. 4(a) and its caption and adjacent first-scenario paragraph. 800-nm coherent plus 400-nm squeezed case, phase alignment, even-harmonic family and broad quantum/classical spectral relation. Fig. 4(b) is not this comparison."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use the candidate's two-colour quantum/classical signals and frequency/phase mechanism to establish the broad transfer/symmetry relation without pointwise-equality or universal assertions.",
      "award_conditions": [
        "Use the candidate's two-colour quantum/classical signals and frequency/phase mechanism to establish the broad transfer/symmetry relation without pointwise-equality or universal assertions."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (I3 AND M6). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M4, M5; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article pp. 043111-6–7, Eq. (26), Fig. 4(a) and its caption and adjacent first-scenario paragraph. 800-nm coherent plus 400-nm squeezed case, phase alignment, even-harmonic family and broad quantum/classical spectral relation. Fig. 4(b) is not this comparison."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M8",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Integrate single-mode state dependence, full/diagonal adequacy and two-colour transfer to answer whether a diagonal phase-space description suffices for the specified fields and how adequacy depends on photon-state structure/configuration.",
      "award_conditions": [
        "Integrate single-mode state dependence, full/diagonal adequacy and two-colour transfer to answer whether a diagonal phase-space description suffices for the specified fields and how adequacy depends on photon-state structure/configuration."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (M4 AND M5 AND M7). This identifies facts, not prerequisite half-point awards.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.",
        "Failure of integration preserves independently established single-mode, diagonal-adequacy and two-colour chains; none can replace another required chain."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article p. 043111-6, Eq. (25), Figs. 3(a,b), 4(a); Appendix G, Fig. 7(a,b), p. 043111-11. Evidence-based synthesis of state dependence, diagonal adequacy and two-colour transfer; the final integrated judgment is task-defined."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "V1",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "State the actual one-dimensional single-active-electron, finite-pulse, single-atom, finite-lattice and calculated optical-state evidence domain; distinguish macroscopic propagation, phase matching, experimental yields and all-state universality.",
      "award_conditions": [
        "State the actual one-dimensional single-active-electron, finite-pulse, single-atom, finite-lattice and calculated optical-state evidence domain; distinguish macroscopic propagation, phase matching, experimental yields and all-state universality."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article p. 043111-7, Sec. V; Appendices E–F, pp. 043111-10–11. Single-atom 1D model and theoretical coupling-domain limitations, not macroscopic or universal validation."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "If actual finite-lattice, TDSE/FFT, normalization, mode/phase binding, data anomalies or conclusions create a concrete risk capable of overturning diagonal-sufficiency or state-dependence conclusions, provide discriminating evidence or an evidence-based scope restriction; otherwise record N/A.",
      "award_conditions": [
        "If actual finite-lattice, TDSE/FFT, normalization, mode/phase binding, data anomalies or conclusions create a concrete risk capable of overturning diagonal-sufficiency or state-dependence conclusions, provide discriminating evidence or an evidence-based scope restriction; otherwise record N/A.",
        "When triggered, award only if claim-relevant discriminating evidence resolves the threat or an evidence-based restriction makes it immaterial; merely acknowledging an unresolved material threat is not positive validation credit. With no trigger, record N/A and retain the fixed 0.5 without claiming performed validation."
      ],
      "applicability_and_na": [
        "Applies only when the submitted method, data, anomaly or conclusion creates the concrete material risk described here. If untriggered, record not_applicable and retain the fixed 0.5 contribution; this is not evidence that validation was performed, and does not block RC4."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for V1; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept metric-preserving nonorthogonal coordinates, dual-frame notation, covariant/contravariant coefficients or absorbed-metric amplitudes when the resulting quadratic form and all corresponding cross terms are unchanged. A positive incoherent mixture is not the full response.",
        "Accept physically equivalent gauges, current/dipole/acceleration observables, coefficient solvers, finite lattices, sparse assembly, TDSE propagators and Fourier conventions with consistent physical case and normalization. Separate/grouped figures, reconstructible tables and equivalent displays are acceptable; no fixed panel, colour, crop, absolute intensity or cutoff threshold."
      ],
      "source_support": [
        "Article p. 043111-5, coefficient residual/normalization paragraph; p. 043111-6, Eq. (25); Appendices F–G, pp. 043111-10–11. Potential finite-lattice, response and approximation failure modes; conditional testing is task-defined, with no compulsory residual threshold or source grid."
      ],
      "rc_relation": "Material-validation role: RC3 only for a triggered, unresolved threat to a central conclusion, with all six burden-of-proof elements established. N/A does not block RC4."
    }
  ],
  "case_scientific_rules": [
    "Write |chi>=sum_i C_i|alpha_i>, G_ij=<alpha_i|alpha_j>, C†GC=1, u_i(omega)=C_i j_i*(omega), and S_full(omega) proportional to u†Gu. Obtain the specified diagonal comparator by deleting all off-diagonal terms from this same quadratic form. Coefficient-diagonal and Husimi-positive-weight mixtures are approximations, not interchangeable full-response definitions.",
    "Every coherent component and matched classical control starts from the same normalized field-free electronic ground state of H0=p²/2+V(x). Different component initial states or mismatched quantum/classical envelopes or phases change the physical problem.",
    "At the stated 800-nm single-mode cases, r=4 squeezed vacuum has substantially extended harmonic support relative to its classical control and lacks the usual clear classical plateau envelope; N=10000 Fock quantum/classical cutoffs and broad structures are much closer, not pointwise identical. Overlap corrections may be small for these narrow prominent coefficient distributions, not for every quantum state.",
    "The 800-nm coherent plus 400-nm imaginary-quadrature squeezed case produces a material even-harmonic family in both quantum and matched classical spectra. Compare broad cutoff scale and structure, not exact cutoff differences or pointwise equality. Frequency, phase and common envelope must remain bound.",
    "Static Husimi or coefficient plots cannot replace dynamic spectra. Finite-lattice truncation, coefficient floor, neighbour cutoff, solver, TDSE grid/absorber, FFT/window and display choices matter only through actual damage to an output or claim; no prescribed refinement check or hidden harmonic floor is required.",
    "Risks include wrong electronic/projection/state identity, diagonal-as-full substitution, independent normalization fabricating contrast, finite-lattice/FFT floors fabricating cutoff or parity, wrong mode phase, and global claims from limited support. Address only genuinely triggered material risks.",
    "Score exactly twenty fixed 0/0.5 material-core criteria. Do not import numerical score ranges or RC score caps. A valid run with no assessable scientific work receives score 0 and RC0 before criterion summation; assessable partial work and timeouts are graded on available evidence.",
    "Object existence, candidate presentation, candidate identification, physical inference and validation are different acts. Inspect every candidate-authored claim-bearing figure. A reference, rerender or examiner reconstruction can verify an object but cannot create missing candidate reasoning.",
    "When a material decision depends on feature resolution, fine structure, component relations, formula identity, representation equivalence or suspicious morphology, perform a focused applicable source/reference check. Establish model/observable/case/component, units, basis/gauge, normalization and transformations first; do not turn source-only display choices into new duties. A provisional score at least 9.0 or provisional RC4 requires a focused check of one central output and one principal-mechanism link. Reference verification is examiner-side, not a new candidate deliverable.",
    "Nonorthogonal identity: $|\\chi\\rangle=\\sum_i C_i|\\alpha_i\\rangle$, $G_{ij}=\\langle\\alpha_i|\\alpha_j\\rangle=\\exp[-(|\\alpha_i|^2+|\\alpha_j|^2)/2+\\alpha_i^*\\alpha_j]$, $C^\\dagger GC=1$. The projection system is $GC=Q$, $Q_i=\\langle\\alpha_i|\\chi\\rangle$; $Q_i$ is not itself an expansion coefficient (Eqs. (8)–(11)).",
    "In the task convention $u_i(\\Omega)=C_i j_i^*(\\Omega)$, the full response is $S_{\\rm full}(\\Omega)\\propto u^\\dagger Gu$, and $S_{\\rm diag}(\\Omega)\\propto\\sum_i G_{ii}|u_i|^2$ deletes only off-diagonal terms. Here $j_i$ is the component complex HHG response at emitted frequency $\\Omega$; equivalent conjugation/index conventions must preserve the complete quadratic form. This is not an arbitrary positive Husimi mixture.",
    "The common electronic initial state is the normalized ground state of $H_0=p^2/2-1/\\sqrt{x^2+a^2}$, with the stated $a=1$ a.u.; component propagation may use $H_i=H_0+xE_i(t)$ or the gauge-equivalent velocity form. Optical calibration is $E_{0i}=2g_0\\sqrt{\\omega}|\\alpha_i|$, $\\phi_i=-\\arg\\alpha_i$; $\\langle n\\rangle=\\sinh^2r$ for squeezed vacuum and $N$ for Fock states (Appendices E–F). These relations bind the declared finite-pulse single-atom cases, not realistic macroscopic yields."
  ],
  "closure_requirements": {
    "RC0": [
      "The central physical object is absent or materially invalid. Establish this scientific fact independently of atomic credit; a local notation or presentation weakness is not itself RC0.",
      "(F1 AND F2 AND F3): Correctly instantiate the stated soft-core matter Hamiltonian, normalized field-free electronic ground state, squeezed/Fock/two-colour optical cases, carrier/intensity/phase/common-envelope bindings and matched classical controls. Construct state-specific optical coefficients and the Gram metric on the generalized von Neumann lattice, with C†GC=1; compute component complex HHG responses from the common electronic initial state and retain all full cross terms in a form equivalent to u†Gu. Define the HHG estimator, full branch, same-quadratic-form off-diagonal-deletion comparator, matched classical branch, common normalization, case mapping and reconstructible data products."
    ],
    "RC1": [
      "The central object exists, but a required indispensable component is absent or materially invalid. A failed presentation or overextended claim alone does not establish object absence or invalidity.",
      "(O1 AND O2): Present physically valid, reconstructible squeezed-vacuum full/diagonal/matched-classical HHG evidence with global structure sufficient to assess broad harmonic support/envelope, quantum/classical relation and branch identity. Present physically valid, reconstructible Fock-state full/diagonal/matched-classical HHG evidence with global structure sufficient to assess broad harmonic support/cutoff, quantum/classical relation and branch identity.",
      "O3: Present two-colour quantum and matched-classical HHG evidence with correct two-frequency, intensity/phase, common-envelope and electronic-initial-state bindings, including the material even-harmonic family and broad spectral relation.",
      "O4: Present a direct full-metric/diagonal-only comparison, or functionally equivalent evidence with the same discriminating power, showing that finite-lattice or assembly error does not create the major state/case relation."
    ],
    "RC2": [
      "Required objects are scientifically valid, but a required principal mechanism or state-dependence inference is absent or incorrect. Reference evidence cannot provide omitted candidate reasoning.",
      "M4: Combine both candidate-established single-mode chains to conclude how photon-state structure changes quantum/classical HHG response, restricted to the specified narrow state families.",
      "M7: Use the candidate's two-colour quantum/classical signals and frequency/phase mechanism to establish the broad transfer/symmetry relation without pointwise-equality or universal assertions.",
      "M8: Integrate single-mode state dependence, full/diagonal adequacy and two-colour transfer to answer whether a diagonal phase-space description suffices for the specified fields and how adequacy depends on photon-state structure/configuration."
    ],
    "RC3": [
      "Required objects and principal mechanisms are established, but a concrete material validation or scope threat to a central conclusion remains unresolved.",
      "V2: If actual finite-lattice, TDSE/FFT, normalization, mode/phase binding, data anomalies or conclusions create a concrete risk capable of overturning diagonal-sufficiency or state-dependence conclusions, provide discriminating evidence or an evidence-based scope restriction; otherwise record N/A.",
      "Before assigning RC3, establish all six elements: the concrete failure mode; its origin in the submitted method/data/conclusion; a fair recognizable scientific risk; the affected central conclusion; why the submitted evidence cannot discriminate or exclude it; and functionally equivalent remedies. Evidence-based restriction may remove unsupported breadth, but cannot repair an incorrect signal, absent component or missing mechanism."
    ],
    "RC4": [
      "Every indispensable and co-primary claim has all its nonempty required role slots closed; supporting claims do not independently determine overall RC. Preserve AND/OR branch logic shown above and use scientific gate outcomes, not atomic scores.",
      "No triggered material risk remains unresolved. Untriggered risk criteria recorded N/A do not block RC4 and do not establish validation evidence.",
      "Classify descriptively by the most severe applicable failed required role (lowest RC), without score ceilings or target distributions. A score/RC tension prompts scientific review, not forced adjustment."
    ]
  },
  "references": [
    {
      "citation": "Yi-Ben Wang and Xue-Bin Bian. 2025. *High-order harmonic generation in quantum light by a generalized von Neumann lattice method*. *Physical Review A*, 111, 043111.",
      "url": "https://doi.org/10.1103/PhysRevA.111.043111",
      "scientific_scope": "Full nonorthogonal quantum-light HHG, state-specific single-mode comparisons and coherent-plus-squeezed two-colour transfer. Source-only two-mode and broader-state examples delimit approximations rather than add commissioned calculations.",
      "anchors": [
        "Wang and Bian (2025), article pp. 043111-6–7, Fig. 3(a,b), Fig. 4(a), Eq. (26); Appendices E–F, pp. 043111-10–11, Eqs. (E1)–(E2), (F1)–(F4).",
        "Article pp. 043111-2–4, Eqs. (7)–(11), (18)–(22); Fig. 2(c,d), p. 043111-5.",
        "Article pp. 043111-4–6, Eqs. (22)–(25), Fig. 3(a,b); Appendix G, Fig. 7(a,b), p. 043111-11.",
        "Article p. 043111-6, Fig. 3(a) and squeezed-vacuum paragraph; Fig. 2(a,c), p. 043111-5.",
        "Article p. 043111-6, Fig. 3(b), Fock-state paragraph; Fig. 2(b,d), p. 043111-5.",
        "Article pp. 043111-5–6, Figs. 2(a–d), 3(a,b), discussion after Fig. 3.",
        "Article pp. 043111-6–7, Eq. (26), Fig. 4(a) and its caption and adjacent first-scenario paragraph.",
        "Article p. 043111-6, Eq. (25), Figs. 3(a,b), 4(a); Appendix G, Fig. 7(a,b), p. 043111-11.",
        "Article p. 043111-7, Sec. V; Appendices E–F, pp. 043111-10–11.",
        "Article p. 043111-5, coefficient residual/normalization paragraph; p. 043111-6, Eq. (25); Appendices F–G, pp. 043111-10–11."
      ]
    }
  ]
}