cases/case12/grading_rubric.json

{
  "case_id": "Case12",
  "title": "Case12 — Enhanced high-order harmonic generation from periodic potentials in inhomogeneous laser fields",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Establish the specified one-dimensional single-active-electron periodic model with the field-free k=0 valence-band-top physical initial state.",
      "award_conditions": [
        "The specified 1D SAE periodic Hamiltonian and physical k=0 valence-band-top initial state are correctly established."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article pp.023419-1-2, Eqs.(1)-(7), paragraph choosing the k=0 valence-top state: specified periodic SAE model and xE+epsilon*x^2*E interaction. Inhomogeneity is the stated interaction, not a separately substituted force law."
      ],
      "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": "Implement xE(t)+epsilon x^2 E(t), the specified finite pulse and epsilon=0,0.0002,0.0005 under one unit, time-origin and sign convention.",
      "award_conditions": [
        "All three epsilon values use the specified finite pulse and interaction xE+epsilon*x^2*E with a consistent field, charge, unit and time convention."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article pp.023419-1-2, Eqs.(1)-(7), paragraph choosing the k=0 valence-top state: specified periodic SAE model and xE+epsilon*x^2*E interaction. Inhomogeneity is the stated interaction, not a separately substituted force law."
      ],
      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Derive a physically consistent radiation observable from the propagated state with gauge/sign, frequency weighting and boundary terms sufficient to define the harmonic response.",
      "award_conditions": [
        "The propagated state yields a consistent harmonic radiation observable with gauge/sign, frequency factors and relevant boundary terms explicit."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article p.023419-2, Eq.(8) and following Fourier paragraph: current-derived harmonic spectrum. Equivalent radiation forms require consistent frequency/boundary mapping."
      ],
      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present auditable total harmonic response for epsilon=0,0.0002,0.0005 under common comparison conventions with correct three-case binding.",
      "award_conditions": [
        "All three total harmonic responses are auditable, correctly case-bound and comparable under common scale/conventions.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article p.023419-2, Fig.2(a-c), caption and two-plateau paragraph: matched epsilon=0,0.0002,0.0005 total spectra and selective high-energy enhancement rather than common scaling."
      ],
      "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": "Resolve both material plateau families and selective high-energy change in matched total spectra, showing comparable low-energy response rather than uniform vertical rescaling.",
      "award_conditions": [
        "Matched spectra resolve both plateaus and selective higher-energy change while lower-energy response remains comparable, not merely globally rescaled.",
        "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 all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article p.023419-2, Fig.2(a-c), caption and two-plateau paragraph: matched epsilon=0,0.0002,0.0005 total spectra and selective high-energy enhancement rather than common scaling."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present reconstructible causal evidence distinguishing driven lower/higher conduction-band participation and testing whether altered higher-band access causes the high-energy change.",
      "award_conditions": [
        "Driven causal evidence distinguishes lower/higher conduction-band participation and tests its relation to the high-energy change.",
        "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 all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article pp.023419-3-4, Fig.3, Fig.5(c,d), Fig.6 and transition-probability paragraphs: small lower-band versus much larger higher-band change and coupling to the valence state. The article does not define a unique projected-current cross-term allocation; task accepts functionally equivalent causal 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": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present time-resolved, intervention-based or equivalent evidence consistent with the total spectrum that distinguishes changed pathway/dynamical structure from uniform amplification of unchanged pathways.",
      "award_conditions": [
        "Valid time-resolved, intervention or equivalent evidence distinguishes changed dynamical/pathway structure from uniform brightening along unchanged paths.",
        "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 all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article p.023419-3, Fig.4(a,b) full response and Fig.4(c,d) interband illustrations: inhomogeneity changes emission/pathway structure. The caption does not assign the nonzero map an unambiguous epsilon from the two scan values; grade a candidate-declared case, not guessed panel identity."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Explicitly identify low/high plateaus and the affected high-energy region in submitted matched spectra, distinguishing the change from common rescaling.",
      "award_conditions": [
        "The candidate identifies low/high plateaus and the selectively affected high-energy region from matched total spectra."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: at least one of: O1 (Present auditable total harmonic response for epsilon=0,0.0002,0.0005 under common comparison conventions with correct three-case binding.); O2 (Resolve both material plateau families and selective high-energy change in matched total spectra, showing comparable low-energy response rather than uniform vertical rescaling.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article p.023419-2, Fig.2(a-c), caption and two-plateau paragraph: matched epsilon=0,0.0002,0.0005 total spectra and selective high-energy enhancement rather than common scaling."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify the material sector difference of smaller lower-band and stronger higher-band participation changes from submitted causal evidence.",
      "award_conditions": [
        "The candidate identifies smaller lower-band and stronger higher-band participation changes from their own causal evidence."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O3 (Present reconstructible causal evidence distinguishing driven lower/higher conduction-band participation and testing whether altered higher-band access causes the high-energy change.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article pp.023419-3-4, Fig.3, Fig.5(c,d), Fig.6 and transition-probability paragraphs: small lower-band versus much larger higher-band change and coupling to the valence state. The article does not define a unique projected-current cross-term allocation; task accepts functionally equivalent causal 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."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from discriminating evidence whether pathway/emission structure changes or only brightness increases, declaring reconstructible binding of the chosen nonzero-epsilon case.",
      "award_conditions": [
        "The candidate identifies changed emission/pathway structure versus brightness-only change with the chosen nonzero-epsilon case explicitly bound."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O4 (Present time-resolved, intervention-based or equivalent evidence consistent with the total spectrum that distinguishes changed pathway/dynamical structure from uniform amplification of unchanged pathways.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article p.023419-3, Fig.4(a,b) full response and Fig.4(c,d) interband illustrations: inhomogeneity changes emission/pathway structure. The caption does not assign the nonzero map an unambiguous epsilon from the two scan values; grade a candidate-declared case, not guessed panel identity."
      ],
      "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": "Reach an evidence-grounded material decision on whether the response change is selective from the identified plateaus.",
      "award_conditions": [
        "The identified plateau evidence supports a material decision about response selectivity."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I1 (Explicitly identify low/high plateaus and the affected high-energy region in submitted matched spectra, distinguishing the change from common rescaling.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article p.023419-2, Fig.2(a-c), caption and two-plateau paragraph: matched epsilon=0,0.0002,0.0005 total spectra and selective high-energy enhancement rather than common scaling."
      ],
      "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": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain why case-matched relative changes exclude uniform vertical rescaling rather than merely citing a brighter high-energy spectrum.",
      "award_conditions": [
        "Case-matched relative changes are used to exclude common vertical rescaling, not only to describe a brighter spectrum."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I1 (Explicitly identify low/high plateaus and the affected high-energy region in submitted matched spectra, distinguishing the change from common rescaling.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article p.023419-2, Fig.2(a-c), caption and two-plateau paragraph: matched epsilon=0,0.0002,0.0005 total spectra and selective high-energy enhancement rather than common scaling."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Establish the causal connection between the spatially nonuniform interaction and materially altered access to higher conduction bands.",
      "award_conditions": [
        "The spatially nonuniform interaction is causally connected to altered access to higher conduction bands."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I2 (Identify the material sector difference of smaller lower-band and stronger higher-band participation changes from submitted causal evidence.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article pp.023419-3-4, Fig.3, Fig.5(c,d), Fig.6 and transition-probability paragraphs: small lower-band versus much larger higher-band change and coupling to the valence state. The article does not define a unique projected-current cross-term allocation; task accepts functionally equivalent causal evidence."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect enhanced higher-band access to selective high-energy plateau response with consistent output/energy-region correspondence.",
      "award_conditions": [
        "Enhanced higher-band participation and the selectively changed higher plateau are connected over corresponding energy/output ranges."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I2 (Identify the material sector difference of smaller lower-band and stronger higher-band participation changes from submitted causal evidence.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article pp.023419-3-4, Fig.3, Fig.5(c,d), Fig.6 and transition-probability paragraphs: small lower-band versus much larger higher-band change and coupling to the valence state. The article does not define a unique projected-current cross-term allocation; task accepts functionally equivalent causal evidence."
      ],
      "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": "Complete the selectivity mechanism with relatively stable lower-band/first-plateau evidence rather than stating only higher-band enhancement.",
      "award_conditions": [
        "Relatively stable lower-band/first-plateau evidence completes the selectivity explanation."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I2 (Identify the material sector difference of smaller lower-band and stronger higher-band participation changes from submitted causal evidence.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article pp.023419-3-4, Fig.3, Fig.5(c,d), Fig.6 and transition-probability paragraphs: small lower-band versus much larger higher-band change and coupling to the valence state. The article does not define a unique projected-current cross-term allocation; task accepts functionally equivalent causal evidence."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use submitted discriminating evidence to argue that emission pathway/time structure changes rather than uniformly amplifying unchanged paths.",
      "award_conditions": [
        "Discriminating evidence supports actual emission/pathway-time changes rather than only uniform amplification."
      ],
      "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 discriminating evidence whether pathway/emission structure changes or only brightness increases, declaring reconstructible binding of the chosen nonzero-epsilon case.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article p.023419-3, Fig.4(a,b) full response and Fig.4(c,d) interband illustrations: inhomogeneity changes emission/pathway structure. The caption does not assign the nonzero map an unambiguous epsilon from the two scan values; grade a candidate-declared case, not guessed panel identity."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Reconcile dynamics with plateau behavior and odd/even structures permitted by broken spatial symmetry, without interpreting every intensity change as a new pathway.",
      "award_conditions": [
        "The candidate reconciles dynamical evidence with plateaus and symmetry-permitted odd/even structures without equating every intensity change to a new pathway."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: I1 (Explicitly identify low/high plateaus and the affected high-energy region in submitted matched spectra, distinguishing the change from common rescaling.); I3 (Identify from discriminating evidence whether pathway/emission structure changes or only brightness increases, declaring reconstructible binding of the chosen nonzero-epsilon case.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article pp.023419-2-3, Fig.2(b,c) odd/even spectra, broken-symmetry paragraph and Fig.4 time-frequency discussion: pathway changes and parity-permitted supporting structure."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M8",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Address a material alternative exposed by the submitted calculation in proportion to the evidence and form a final model-bounded scientific conclusion.",
      "award_conditions": [
        "A material alternative raised by the calculation is handled in proportion to evidence and the final conclusion is restricted to the actual model/domain."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: 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": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article pp.023419-1,4-5, one-dimensional SAE model and summary; bounded selectivity and triggered numerical/physical-alternative treatment are task obligations, not absolute-yield or universal experimental-efficiency requirements."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "V1",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "When the method, data, anomaly or claim triggers a concrete material risk, supply evidence capable of exposing/excluding it or preserve an explicit unresolved adjudication.",
      "award_conditions": [
        "A concrete triggered conclusion-threatening numerical or physical risk receives capable evidence or remains explicitly unresolved; otherwise N/A."
      ],
      "applicability_and_na": [
        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article pp.023419-1,4-5, one-dimensional SAE model and summary; bounded selectivity and triggered numerical/physical-alternative treatment are task obligations, not absolute-yield or universal experimental-efficiency requirements."
      ],
      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Restrict conclusions to the one-dimensional single-active-electron model, actually established epsilon cases and evidence domain, without absolute-yield or universal material/experimental-efficiency extrapolation; honestly state uncovered ranges.",
      "award_conditions": [
        "Conclusions remain within the specified 1D SAE model, established epsilon cases and covered range, without absolute-yield or universal experimental-efficiency claims."
      ],
      "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": [
        "Converged Bloch, grid, basis, gauge and propagator equivalents are accepted when they preserve the same physical initial state and xE+epsilon x^2 E interaction; charge/field/current sign changes must transform the full construction consistently.",
        "Band populations in declared projectors, interaction-linked transition/coupling evidence, rigorous current decompositions with cross terms/additivity limits, and equivalent interventions may distinguish lower/higher-band pathways; no unique source band-projected current exists.",
        "Any documented stable time-frequency, time-resolved or intervention representation exposing the same dynamical distinction is accepted; no wavelet, STFT kernel, width, floor or sampling rule is canonical.",
        "Current/velocity/acceleration forms require treatment of frequency factors and boundary terms before comparison. Common scale is accepted; absolute yield is not a target."
      ],
      "source_support": [
        "Du et al. (2016), article pp.023419-1,4-5, one-dimensional SAE model and summary; bounded selectivity and triggered numerical/physical-alternative treatment are task obligations, not absolute-yield or universal experimental-efficiency requirements."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    }
  ],
  "case_scientific_rules": [
    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
    "The higher plateau changes selectively by roughly two to three orders in the source, while the first remains comparable. Exact enhancement is not a threshold: supported reproductions establish the same selective relation with smaller integrated enhancement.",
    "Broken spatial symmetry allows even and odd harmonics, but this supporting consequence cannot replace selective high-energy evidence.",
    "The first plateau is associated mainly with valence-to-first-conduction transitions, the higher plateau with higher conduction bands. Static band labels without driven causal evidence do not establish this assignment.",
    "Do not force component powers to sum to the coherent total unless the mathematical decomposition actually warrants it.",
    "The source nonzero time-frequency map is not bound to epsilon=0.0002 or 0.0005. Judge the candidate-declared nonzero case and coarse structural change; neither hidden panel identity nor exact ridge times are duties.",
    "The zero-CEP finite-support pulse convention defines the time-resolved task. Finer time-frequency comparisons require applicable source and submitted data or bounded review, not an invented transform tolerance.",
    "The source model is a one-dimensional single-active-electron TDSE with the specified Mathieu-type periodic potential and the length-gauge interaction $xE(t)+\\epsilon x^2E(t)$. The physical initial state is the field-free $k=0$ state at the top of the valence band, where the gap is minimal. Changing the sign convention for charge, field or current is acceptable only when the entire Hamiltonian, observable and interpretation are transformed consistently.",
    "The source used a coordinate-space B-spline basis, a symmetric split operator, a finite box, an absorber and a Hanning window. Those details are reproduction evidence, not student requirements. Converged Bloch-, grid-, basis-, gauge- and propagation-equivalent realizations are accepted. A smooth spectrum or shared code path alone does not establish equivalence.",
    "The matched current-derived spectra for $\\epsilon=0$, $0.0002$ and $0.0005$ contain two plateau families. The larger nonzero case produces a selective change of the higher plateau by roughly two to three orders of magnitude, while the first plateau remains of comparable scale. The result is not a common vertical rescaling.",
    "Broken spatial symmetry in the nonzero-$\\epsilon$ model permits even as well as odd harmonic orders. This is a supporting structural consequence, not a substitute for establishing the selective high-energy response.",
    "In the source interpretation, the first plateau is associated principally with transitions between the valence band and the first conduction band, whereas the higher plateau is associated with the higher conduction-band group. The nonzero interaction changes access to the higher bands much more strongly than it changes the first-band response.",
    "Source band populations show a small change in the first conduction-band population and a much larger change in the higher-band population. Source transition-matrix evidence likewise shows little change in the low-energy first-band range and a substantial increase over higher-band energies. These are accepted causal anchors for the selective enhancement.",
    "The source full-response time-frequency comparison changes branch structure under spatial inhomogeneity rather than merely increasing brightness along unchanged branches. The article does not bind that displayed nonzero map to $\\epsilon=0.0002$ or $0.0005$; do not use hidden panel identity to require either one. Grade a student's declared nonzero case against its own reconstructible signal and the robust source-supported structural claim.",
    "The article labels full, first-conduction-band and combined higher-band spectra, but does not define an exact band-projected current or cross-term allocation. Therefore that particular split is not required and no uniquely prescribed projection convention is required for scoring. Accept, among other physically adequate routes:",
    "populations in declared field-free or time-dependent band projectors;",
    "transition-matrix or coupling evidence tied to the stated interaction;",
    "a rigorously defined current decomposition whose cross terms and additivity limits are stated; or",
    "another intervention or representation that distinguishes lower- and higher-band pathways and excludes common rescaling.",
    "A component spectrum cannot be forced arithmetically to add to the coherent total unless the student's mathematical decomposition warrants that identity. Static band labels without driven causal evidence are insufficient for full mechanism credit.",
    "No wavelet, short-time Fourier kernel, window width, range, floor or sampling rule is canonical. Accept any documented representation that resolves the claim-relevant emission structure and is stable enough for the claim made. Current, velocity and acceleration forms may differ by standard frequency factors and boundary terms; compare them only after the student's conventions and physical equivalence have been established. Absolute yield is ungraded when only a common display scale is fixed.",
    "For F2-F3/M3-M5, article pp.023419-1-2, Eqs.(1)-(3),(8),\n$$H(t)=\\frac{p^2}{2}-0.37[1+\\cos(2\\pi x/8)]+E(t)(x+\\epsilon x^2),\\quad j(t)=-\\langle p\\rangle.$$\nIf acceleration is used, Ehrenfest evolution for this stated Hamiltonian gives $\\dot{\\langle p\\rangle}=-\\langle V'(x)\\rangle-E(t)[1+2\\epsilon\\langle x\\rangle]$ (subject to any separately accounted boundary/mask effects). Substituting $1+\\epsilon x$ as the force while retaining this Hamiltonian is not equivalent. Band population evidence may use $n_b(t)=\\langle\\psi(t)|P_b|\\psi(t)\\rangle$ with declared projectors. Source Fig.6 compares $|\\langle\\varphi_{n_0}|x|\\varphi_n\\rangle|^2$ and $|\\langle\\varphi_{n_0}|x^2|\\varphi_n\\rangle|^2$; these illustrate a mechanism, not a mandatory decomposition or permission to add component spectral powers."
  ],
  "closure_requirements": {
    "RC0": [
      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
      "Required indispensable claim CL1, central physical object: all of: F1 (Establish the specified one-dimensional single-active-electron periodic model with the field-free k=0 valence-band-top physical initial state.); F2 (Implement xE(t)+epsilon x^2 E(t), the specified finite pulse and epsilon=0,0.0002,0.0005 under one unit, time-origin and sign convention.); F3 (Derive a physically consistent radiation observable from the propagated state with gauge/sign, frequency weighting and boundary terms sufficient to define the harmonic response.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC1": [
      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
      "Required indispensable claim CL1, indispensable material component: all of: O1 (Present auditable total harmonic response for epsilon=0,0.0002,0.0005 under common comparison conventions with correct three-case binding.); O2 (Resolve both material plateau families and selective high-energy change in matched total spectra, showing comparable low-energy response rather than uniform vertical rescaling.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC2": [
      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
      "Required indispensable claim CL1, principal mechanism or commissioned conclusion: all of: M1 (Reach an evidence-grounded material decision on whether the response change is selective from the identified plateaus.); M2 (Explain why case-matched relative changes exclude uniform vertical rescaling rather than merely citing a brighter high-energy spectrum.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M3 (Establish the causal connection between the spatially nonuniform interaction and materially altered access to higher conduction bands.); M4 (Connect enhanced higher-band access to selective high-energy plateau response with consistent output/energy-region correspondence.); M5 (Complete the selectivity mechanism with relatively stable lower-band/first-plateau evidence rather than stating only higher-band enhancement.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL3, principal mechanism or commissioned conclusion: all of: M6 (Use submitted discriminating evidence to argue that emission pathway/time structure changes rather than uniformly amplifying unchanged paths.); M7 (Reconcile dynamics with plateau behavior and odd/even structures permitted by broken spatial symmetry, without interpreting every intensity change as a new pathway.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL4, principal mechanism or commissioned conclusion: M8 (Address a material alternative exposed by the submitted calculation in proportion to the evidence and form a final model-bounded scientific 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: V1 (When the method, data, anomaly or claim triggers a concrete material risk, supply evidence capable of exposing/excluding it or preserve an explicit unresolved adjudication.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC4": [
      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
      "Close CL1 central physical object: all of: F1 (Establish the specified one-dimensional single-active-electron periodic model with the field-free k=0 valence-band-top physical initial state.); F2 (Implement xE(t)+epsilon x^2 E(t), the specified finite pulse and epsilon=0,0.0002,0.0005 under one unit, time-origin and sign convention.); F3 (Derive a physically consistent radiation observable from the propagated state with gauge/sign, frequency weighting and boundary terms sufficient to define the harmonic response.).",
      "Close CL1 indispensable material component: all of: O1 (Present auditable total harmonic response for epsilon=0,0.0002,0.0005 under common comparison conventions with correct three-case binding.); O2 (Resolve both material plateau families and selective high-energy change in matched total spectra, showing comparable low-energy response rather than uniform vertical rescaling.).",
      "Close CL1 principal mechanism or commissioned conclusion: all of: M1 (Reach an evidence-grounded material decision on whether the response change is selective from the identified plateaus.); M2 (Explain why case-matched relative changes exclude uniform vertical rescaling rather than merely citing a brighter high-energy spectrum.).",
      "Close CL2 principal mechanism or commissioned conclusion: all of: M3 (Establish the causal connection between the spatially nonuniform interaction and materially altered access to higher conduction bands.); M4 (Connect enhanced higher-band access to selective high-energy plateau response with consistent output/energy-region correspondence.); M5 (Complete the selectivity mechanism with relatively stable lower-band/first-plateau evidence rather than stating only higher-band enhancement.).",
      "Close CL3 principal mechanism or commissioned conclusion: all of: M6 (Use submitted discriminating evidence to argue that emission pathway/time structure changes rather than uniformly amplifying unchanged paths.); M7 (Reconcile dynamics with plateau behavior and odd/even structures permitted by broken spatial symmetry, without interpreting every intensity change as a new pathway.).",
      "Close CL4 principal mechanism or commissioned conclusion: M8 (Address a material alternative exposed by the submitted calculation in proportion to the evidence and form a final model-bounded scientific conclusion.).",
      "Close CL4 material validation/scope: V1 (When the method, data, anomaly or claim triggers a concrete material risk, supply evidence capable of exposing/excluding it or preserve an explicit unresolved adjudication.)."
    ]
  },
  "references": [
    {
      "citation": "Tao-Yuan Du, Zhong Guan, Xiao-Xin Zhou, and Xue-Bin Bian. 2016. *Enhanced high-order harmonic generation from periodic potentials in inhomogeneous laser fields*. *Physical Review A*, 94, 023419.",
      "url": "https://doi.org/10.1103/PhysRevA.94.023419",
      "scientific_scope": "Enhanced high-order harmonic generation from periodic potentials in inhomogeneous laser fields",
      "anchors": [
        "Du et al. (2016), article pp.023419-1-2, Eqs.(1)-(7), paragraph choosing the k=0 valence-top state: specified periodic SAE model and xE+epsilon*x^2*E interaction. Inhomogeneity is the stated interaction, not a separately substituted force law.",
        "Du et al. (2016), article p.023419-2, Eq.(8) and following Fourier paragraph: current-derived harmonic spectrum. Equivalent radiation forms require consistent frequency/boundary mapping.",
        "Du et al. (2016), article p.023419-2, Fig.2(a-c), caption and two-plateau paragraph: matched epsilon=0,0.0002,0.0005 total spectra and selective high-energy enhancement rather than common scaling.",
        "Du et al. (2016), article pp.023419-3-4, Fig.3, Fig.5(c,d), Fig.6 and transition-probability paragraphs: small lower-band versus much larger higher-band change and coupling to the valence state. The article does not define a unique projected-current cross-term allocation; task accepts functionally equivalent causal evidence.",
        "Du et al. (2016), article p.023419-3, Fig.4(a,b) full response and Fig.4(c,d) interband illustrations: inhomogeneity changes emission/pathway structure. The caption does not assign the nonzero map an unambiguous epsilon from the two scan values; grade a candidate-declared case, not guessed panel identity.",
        "Du et al. (2016), article pp.023419-2-3, Fig.2(b,c) odd/even spectra, broken-symmetry paragraph and Fig.4 time-frequency discussion: pathway changes and parity-permitted supporting structure.",
        "Du et al. (2016), article pp.023419-1,4-5, one-dimensional SAE model and summary; bounded selectivity and triggered numerical/physical-alternative treatment are task obligations, not absolute-yield or universal experimental-efficiency requirements."
      ]
    }
  ]
}