cases/case11/grading_rubric.json

{
  "case_id": "Case11",
  "title": "Case11 — High harmonic generation in solids: Real versus virtual transition channels",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Instantiate both materials, all three specified case families, initially occupied valence band and consistent F=-dA/dt, K_t, Bloch gauge, Brillouin-zone and current conventions.",
      "award_conditions": [
        "Both materials and all three commissioned case families share correct initially occupied valence state, field/vector potential, moving K, Bloch gauge and current conventions."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in O1, O2, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-2-4, Eqs.(1)-(19), Fig.2 caption: moving-K two-band exact density matrix, instantaneous adiabatic diagonalization, second-order expansion and dressed-gap SFAF; exact propagation is distinct from FVB."
      ],
      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Derive a computable second-order instantaneous-adiabatic-basis SFAF retaining the dressed gap and correctly connect it to exact density-matrix propagation and interband/intraband currents.",
      "award_conditions": [
        "The candidate derives a computable second-order adiabatic-basis SFAF with dressed gap and connects its currents to exact density-matrix propagation."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F1 (Instantiate both materials, all three specified case families, initially occupied valence band and consistent F=-dA/dt, K_t, Bloch gauge, Brillouin-zone and current conventions.)",
        "Preserve independently valid work in F3, F4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-2-4, Eqs.(1)-(19), Fig.2 caption: moving-K two-band exact density matrix, instantaneous adiabatic diagonalization, second-order expansion and dressed-gap SFAF; exact propagation is distinct from FVB."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Apply the fixed filter to complex amplitude v, retain the nonresonant population mixed term and construct real/nonreal interband and intraband currents from the corresponding amplitudes.",
      "award_conditions": [
        "The fixed filter acts on complex v, preserving the mixed nonresonant population term and correctly constructing resolved interband/intraband currents."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F2 (Derive a computable second-order instantaneous-adiabatic-basis SFAF retaining the dressed gap and correctly connect it to exact density-matrix propagation and interband/intraband currents.)",
        "Preserve independently valid work in O1, O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-4-5, Eqs.(20)-(25): filtering complex amplitude v into low-frequency resonant and complementary virtual parts; mixed population term belongs to the nonresonant definition."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F4",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Coherently assemble all applicable time-domain interband/intraband components before Fourier transformation and squaring, with common units, normalization, case binding and reconstructible spectral conventions.",
      "award_conditions": [
        "Applicable complex current contributions are assembled coherently before Fourier squaring with common scale, units, case binding and reconstructible reduction."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F1 (Instantiate both materials, all three specified case families, initially occupied valence band and consistent F=-dA/dt, K_t, Bloch gauge, Brillouin-zone and current conventions.)",
        "Preserve independently valid work in F3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-3,5-6, Eqs.(19),(24),(25), Fig.5 and high-field interference discussion: coherent current combination before Fourier power. Candidate spectral-density/fluence equivalents are allowed under common conventions."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present physically valid, reconstructible semiconductor exact and dressed-gap SFAF spectra sufficient to assess their agreement range and principal interband/intraband balance independently.",
      "award_conditions": [
        "Semiconductor exact and dressed-gap SFAF spectra are valid and expose both agreement range and interband/intraband balance.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: F1 (Instantiate both materials, all three specified case families, initially occupied valence band and consistent F=-dA/dt, K_t, Bloch gauge, Brillouin-zone and current conventions.); F2 (Derive a computable second-order instantaneous-adiabatic-basis SFAF retaining the dressed gap and correctly connect it to exact density-matrix propagation and interband/intraband currents.); F4 (Coherently assemble all applicable time-domain interband/intraband components before Fourier transformation and squaring, with common units, normalization, case binding and reconstructible spectral conventions.)",
        "Preserve independently valid work in O2, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article p.075135-4, Fig.2(a) and comparison paragraph: semiconductor exact/SFAF agreement and interband predominance. Fig.3 on p.075135-5 is auxiliary channel evidence, not a substitute for the dielectric family."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present physically valid, reconstructible long-pulse dielectric exact and dressed-gap SFAF spectra sufficient to assess their agreement range and high-order balance differing from the semiconductor independently.",
      "award_conditions": [
        "Long-pulse dielectric exact and dressed-gap SFAF spectra expose agreement range and a material high-order balance distinct from the semiconductor.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: F1 (Instantiate both materials, all three specified case families, initially occupied valence band and consistent F=-dA/dt, K_t, Bloch gauge, Brillouin-zone and current conventions.); F2 (Derive a computable second-order instantaneous-adiabatic-basis SFAF retaining the dressed gap and correctly connect it to exact density-matrix propagation and interband/intraband currents.); F4 (Coherently assemble all applicable time-domain interband/intraband components before Fourier transformation and squaring, with common units, normalization, case binding and reconstructible spectral conventions.)",
        "Preserve independently valid work in O1, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article p.075135-4, Fig.2(b) and following material/Stark discussion: long-pulse dielectric exact/SFAF comparison, changed high-order balance and optional FVB disagreement."
      ],
      "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 low-field short-pulse dielectric real/nonreal interband/intraband currents and coherent total spectrum, preserving amplitude filter, mixed population term, signed cross terms, common scale and reconstructible data.",
      "award_conditions": [
        "The low-field short-pulse dielectric resolved currents and coherent total are reconstructible with correct amplitude filter, mixed population and common normalization.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: F1 (Instantiate both materials, all three specified case families, initially occupied valence band and consistent F=-dA/dt, K_t, Bloch gauge, Brillouin-zone and current conventions.); F3 (Apply the fixed filter to complex amplitude v, retain the nonresonant population mixed term and construct real/nonreal interband and intraband currents from the corresponding amplitudes.); F4 (Coherently assemble all applicable time-domain interband/intraband components before Fourier transformation and squaring, with common units, normalization, case binding and reconstructible spectral conventions.)",
        "Preserve independently valid work in O1, O2, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-5-6, Fig.5(a,b), Eqs.(20)-(25): short-pulse F0=0.005 dielectric, interband-dominated total with small intraband terms."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present high-field short-pulse dielectric real/nonreal interband/intraband currents and coherent total spectrum, preserving amplitude filter, mixed population term, signed cross terms, common scale and reconstructible data.",
      "award_conditions": [
        "The high-field short-pulse dielectric resolved currents and coherent total are reconstructible with correct amplitude filter, mixed population and signed channel relations.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: F1 (Instantiate both materials, all three specified case families, initially occupied valence band and consistent F=-dA/dt, K_t, Bloch gauge, Brillouin-zone and current conventions.); F3 (Apply the fixed filter to complex amplitude v, retain the nonresonant population mixed term and construct real/nonreal interband and intraband currents from the corresponding amplitudes.); F4 (Coherently assemble all applicable time-domain interband/intraband components before Fourier transformation and squaring, with common units, normalization, case binding and reconstructible spectral conventions.)",
        "Preserve independently valid work in O1, O2, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-5-6, Fig.5(c,d): F0=0.012 dielectric, high-order resonant interband dominance and comparable nonresonant intraband contribution suppressing the coherent total. Signed interference follows from amplitudes, not component-power addition."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify the semiconductor exact/SFAF agreement range and predominant interband response over the supported harmonic domain from submitted evidence.",
      "award_conditions": [
        "The candidate identifies the semiconductor exact/SFAF agreement range and predominant interband response from their evidence."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O1 (Present physically valid, reconstructible semiconductor exact and dressed-gap SFAF spectra sufficient to assess their agreement range and principal interband/intraband balance independently.)",
        "Preserve independently valid work in I2, I3, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article p.075135-4, Fig.2(a) and comparison paragraph: semiconductor exact/SFAF agreement and interband predominance. Fig.3 on p.075135-5 is auxiliary channel evidence, not a substitute for the dielectric family."
      ],
      "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 long-pulse dielectric exact/SFAF agreement range and changed high-order interband/intraband balance relative to the semiconductor from submitted evidence.",
      "award_conditions": [
        "The candidate identifies long-pulse dielectric agreement range and its changed high-order balance relative to semiconductor 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: O2 (Present physically valid, reconstructible long-pulse dielectric exact and dressed-gap SFAF spectra sufficient to assess their agreement range and high-order balance differing from the semiconductor independently.)",
        "Preserve independently valid work in I1, I3, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article p.075135-4, Fig.2(b) and following material/Stark discussion: long-pulse dielectric exact/SFAF comparison, changed high-order balance and optional FVB disagreement."
      ],
      "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 predominantly interband low-field dielectric total response and small intraband currents, preserving a coherent-total rather than power-addition interpretation.",
      "award_conditions": [
        "The candidate identifies low-field dielectric interband-dominated total and small intraband terms, not an incoherent power sum."
      ],
      "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 low-field short-pulse dielectric real/nonreal interband/intraband currents and coherent total spectrum, preserving amplitude filter, mixed population term, signed cross terms, common scale and reconstructible data.)",
        "Preserve independently valid work in M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-5-6, Fig.5(a,b), Eqs.(20)-(25): short-pulse F0=0.005 dielectric, interband-dominated total with small intraband terms."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Establish from the high-field dielectric output that high-order resonant interband response dominates, nonresonant intraband response becomes comparable, and signed channel evidence supports interference reducing the physical total.",
      "award_conditions": [
        "The high-field evidence establishes high-order resonant interband dominance, comparable nonresonant intraband response and interference suppressing the physical total."
      ],
      "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 high-field short-pulse dielectric real/nonreal interband/intraband currents and coherent total spectrum, preserving amplitude filter, mixed population term, signed cross terms, common scale and reconstructible data.)",
        "Preserve independently valid work in I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-5-6, Fig.5(c,d): F0=0.012 dielectric, high-order resonant interband dominance and comparable nonresonant intraband contribution suppressing the coherent total. Signed interference follows from amplitudes, not component-power addition."
      ],
      "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": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Assess the semiconductor SFAF credible harmonic range using specific exact/SFAF spectral structure rather than generic agreement language.",
      "award_conditions": [
        "Specific semiconductor spectral structures support a stated credible SFAF harmonic range."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I1 (Identify the semiconductor exact/SFAF agreement range and predominant interband response over the supported harmonic domain from submitted evidence.)",
        "Preserve independently valid work in M2, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article p.075135-4, Fig.2(a) and comparison paragraph: semiconductor exact/SFAF agreement and interband predominance. Fig.3 on p.075135-5 is auxiliary channel evidence, not a substitute for the dielectric family."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Assess the long-pulse dielectric SFAF credible range and explain the relevant material difference from both material datasets; if used, FVB must remain distinct from SFAF.",
      "award_conditions": [
        "Both material datasets support the dielectric credible range/material difference; FVB, if used, remains distinct from SFAF."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: I1 (Identify the semiconductor exact/SFAF agreement range and predominant interband response over the supported harmonic domain from submitted evidence.); I2 (Identify the long-pulse dielectric exact/SFAF agreement range and changed high-order interband/intraband balance relative to the semiconductor from submitted evidence.)",
        "Preserve independently valid work in M1, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article p.075135-4, Fig.2(b) and following material/Stark discussion: long-pulse dielectric exact/SFAF comparison, changed high-order balance and optional FVB disagreement."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use at least one identified valid field-family branch to explain how the amplitude-level real/nonreal filter separates persistent from oscillatory transition behavior and connects channels to observable HHG.",
      "award_conditions": [
        "At least one valid identified field-family branch grounds how amplitude filtering distinguishes persistent and oscillatory transitions and links them to HHG."
      ],
      "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: I3 (Identify predominantly interband low-field dielectric total response and small intraband currents, preserving a coherent-total rather than power-addition interpretation.); M7 (Establish from the high-field dielectric output that high-order resonant interband response dominates, nonresonant intraband response becomes comparable, and signed channel evidence supports interference reducing the physical total.)",
        "Preserve independently valid work in M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-4-5, Eqs.(20)-(25): filtering complex amplitude v into low-frequency resonant and complementary virtual parts; mixed population term belongs to the nonresonant definition."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain with high-field signed channel evidence how coherent nonresonant-intraband/resonant-interband combination can reduce the total, rather than adding component powers.",
      "award_conditions": [
        "High-field signed channel evidence explains reduced total through coherent nonresonant-intraband/resonant-interband interference."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: M7 (Establish from the high-field dielectric output that high-order resonant interband response dominates, nonresonant intraband response becomes comparable, and signed channel evidence supports interference reducing the physical total.)",
        "Preserve independently valid work in M3, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-5-6, Fig.5(c,d): F0=0.012 dielectric, high-order resonant interband dominance and comparable nonresonant intraband contribution suppressing the coherent total. Signed interference follows from amplitudes, not component-power addition."
      ],
      "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": "Compare the identified two-field dielectric signals to explain redistribution of real/nonreal interband/intraband balance, restricting conclusions to supported harmonic orders.",
      "award_conditions": [
        "Both identified dielectric field branches support the explained redistribution of real/virtual interband/intraband balance over supported orders."
      ],
      "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: I3 (Identify predominantly interband low-field dielectric total response and small intraband currents, preserving a coherent-total rather than power-addition interpretation.); M7 (Establish from the high-field dielectric output that high-order resonant interband response dominates, nonresonant intraband response becomes comparable, and signed channel evidence supports interference reducing the physical total.)",
        "Preserve independently valid work in M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-4-6, Fig.2(a,b), Fig.5(a-d) and dynamic-Stark paragraphs: material and field redistribute real/virtual channels. Adequacy conclusions require the actual submitted case/harmonic 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": "Close the research question by connecting dressed-gap changes to material/field changes, real/virtual interband/intraband channels and coherent total HHG, reaching case- and harmonic-range-specific SFAF adequacy conclusions.",
      "award_conditions": [
        "Dressed-gap physics, material/field variation, channel decomposition and coherent total support case-specific and harmonic-specific SFAF adequacy conclusions."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: M1 (Assess the semiconductor SFAF credible harmonic range using specific exact/SFAF spectral structure rather than generic agreement language.); M2 (Assess the long-pulse dielectric SFAF credible range and explain the relevant material difference from both material datasets; if used, FVB must remain distinct from SFAF.); M3 (Use at least one identified valid field-family branch to explain how the amplitude-level real/nonreal filter separates persistent from oscillatory transition behavior and connects channels to observable HHG.); M4 (Explain with high-field signed channel evidence how coherent nonresonant-intraband/resonant-interband combination can reduce the total, rather than adding component powers.); M5 (Compare the identified two-field dielectric signals to explain redistribution of real/nonreal interband/intraband balance, restricting conclusions to supported harmonic orders.)",
        "Preserve independently valid work in V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-4-6, Fig.2(a,b), Fig.5(a-d) and dynamic-Stark paragraphs: material and field redistribute real/virtual channels. Adequacy conclusions require the actual submitted case/harmonic evidence."
      ],
      "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": "Only when the submitted method, data, anomaly or claim exposes a concrete material alternative, exclude it with discriminating evidence or narrow the threatened conclusion to a supported range.",
      "award_conditions": [
        "A concrete triggered material alternative is excluded with capable evidence or the threatened harmonic/case claim is narrowed; otherwise N/A."
      ],
      "applicability_and_na": [
        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-2,6-7, no-electron-hole-interaction premise and Sec.IV scope/dephasing discussion. Positive model boundaries and triggered alternatives are task duties; additional dephasing/real-material simulation is not compulsory."
      ],
      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Positively identify the actual one-dimensional inversion-symmetric two-band, no-electron-hole-interaction, exact/second-order-SFAF and computed material/pulse/field/coherent-total domain.",
      "award_conditions": [
        "The candidate positively declares 1D inversion-symmetric two-band, no electron-hole interaction, exact/second-order SFAF and actual material/pulse/field domain."
      ],
      "applicability_and_na": [
        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Globally equivalent Fourier, current sign, vector potential, Brillouin-zone and common multiplicative display conventions are accepted; independent curve scales cannot erase channel ratios or interference.",
        "An algebraically equivalent second-order instantaneous-basis derivation is accepted when it retains the dressed gap and same currents. FVB, replacing dressed lambda by bare epsilon, and a delta-like K=0 intraband comparator are optional and never required closure components.",
        "Resolved spectral densities, integrated harmonic fluences and other reconstructible reductions are accepted instead of source harmonic bins if they preserve material structures and apply consistently.",
        "Spectra, lineouts, tables, residuals, sweeps and interventions are accepted by physical function, without fixed source panel order."
      ],
      "source_support": [
        "Thorpe et al. (2023), article pp.075135-2,6-7, no-electron-hole-interaction premise and Sec.IV scope/dephasing discussion. Positive model boundaries and triggered alternatives are task duties; additional dephasing/real-material simulation is not compulsory."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    }
  ],
  "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 exact initial density matrix is diag(0,1) in conduction/valence order; propagation and current must use the same K_t=K+A(t), field, Hamiltonian, dipole, band velocities and gauge.",
    "Filtering power, population or harmonic bins is not equivalent to filtering complex v. The nonresonant population includes |v_nr|^2+2 Re(v_nr v_r*) and need not be independently positive.",
    "The physical total is squared only after time-domain current assembly. Summing component powers can create or erase the high-field interference.",
    "At low dielectric field interband terms dominate and intraband terms are small; at high field resonant interband dominates above low order and nonresonant intraband becomes comparable at high order, allowing destructive interference. The canonical onset near order 11 is not an exact bin target.",
    "Weak H15 mismatch and finite-record tails are not pointwise grading targets. Auxiliary semiconductor channel evidence cannot replace the commissioned dielectric field family.",
    "M3 may use any one valid identified dielectric-field branch; failure of the other branch does not erase independently supported filter physics. Cross-field and cross-material conclusions require their own actual evidence.",
    "For each initial $K$, the exact branch propagates the two-band density matrix from $\\rho(K,-\\infty)=\\operatorname{diag}(0,1)$ in the conduction/valence basis. The physical current uses the same $K_t=K+A(t)$, field, Hamiltonian, dipole, band velocities, and gauge convention as the propagation.",
    "The canonical SFAF derivation diagonalizes the instantaneous Hamiltonian, transforms the exact von Neumann equation to that basis, and expands the time-ordered operator through second order. The resulting transition amplitude contains the dressed gap $\\lambda$ and yields interband and intraband currents. An algebraically equivalent second-order construction is accepted. The FVB replacement $\\lambda\\rightarrow\\varepsilon$ is only an optional discriminator of the dressed-gap branch.",
    "The source filter acts on the complex amplitude $v(K,t)$, not on $|v|^2$, a current power spectrum, or harmonic bins. With $v=v_r+v_{nr}$ and $u_i=\\exp[-i\\int^t\\lambda(K_\\tau,\\tau)d\\tau]v_i$, the canonical resolved populations are",
    "$$\nn_c^r(K,t)=|v_r(K,t)|^2,\n$$",
    "$$\nn_c^{nr}(K,t)=|v_{nr}(K,t)|^2\n+2\\operatorname{Re}[v_{nr}(K,t)v_r^*(K,t)].\n$$",
    "The mixed term belongs to the nonresonant population definition. The resolved currents are, up to the stated approximation and equivalent notation,",
    "$$\nj_{er}^{i}(t)=-\\frac{d}{dt}\\int_{\\mathrm{BZ}}dK\\,\nd(K_t)u_i(K,t)+\\mathrm{c.c.},\n$$",
    "$$\nj_{ra}^{i}(t)=\\int_{\\mathrm{BZ}}dK\\,\n[v_c(K_t)-v_v(K_t)]n_c^i(K,t),\n\\qquad i\\in\\{r,nr\\}.\n$$",
    "Equivalent dimensional prefactors and notation are accepted when they preserve the same mathematical objects and relative physical content.",
    "The physical total current is assembled in the time domain from all applicable interband and intraband components, and its Fourier transform is squared only after that coherent assembly. The total spectrum is not the sum of separately squared component transforms. Students need not use the source's harmonic-bin reduction; resolved spectral density, integrated harmonic fluence, or another reconstructible reduction is accepted when it preserves claim-relevant structures and is applied consistently.",
    "In the model semiconductor, exact and dressed-gap SFAF spectra agree closely, with the interband response larger over the displayed harmonic support.",
    "In the long-pulse dielectric case, exact and SFAF remain the relevant validation pair. The optional FVB branch differs substantially and the high-order interband/intraband balance differs from the semiconductor case.",
    "For the short dielectric pulse, lower and higher field strengths produce different channel balances. At lower field, interband contributions account for most of the total and intraband currents are small.",
    "At higher field, the resonant interband contribution dominates above low order, while the nonresonant intraband contribution becomes comparable at high order and can reduce the coherent total through interference. The source places the onset near harmonic order 11; grade the robust high-order structure, not one exact onset bin.",
    "The material contrast is associated with dressed-gap physics. The dielectric coupling and accessible field strength make dynamic Stark dressing more consequential and change the relative role of real and virtual channels.",
    "The semiconductor channel-only figure is auxiliary evidence. It may support an equivalent solution but cannot replace evidence spanning the visibly commissioned dielectric field family.",
    "For F1-F3/M3/M6, article pp.075135-2-5, Eqs.(2)-(4),(18)-(23),\n$$H=\\tfrac12\\begin{pmatrix}\\varepsilon&\\Omega\\\\\\Omega&-\\varepsilon\\end{pmatrix},\\quad\n\\Omega=2Fd(K_t),\\quad\\lambda=\\sqrt{\\varepsilon^2+\\Omega^2},\\quad K_t=K+A(t),$$\n$$u(K,t)=\\frac i2\\int_{-\\infty}^t\\Omega(K_{t'},t')e^{-i\\int_{t'}^t\\lambda(K_\\tau,\\tau)d\\tau}dt'\n=e^{-i\\int^t\\lambda d\\tau}v(K,t).$$\nThe resonant filter is $G_r(\\omega)=1$ for $|\\omega|\\le\\omega_0/2$ and zero otherwise; $v_i=\\mathcal F^{-1}[G_i\\widetilde v]$, $G_{nr}=1-G_r$. Existing mixed-population and current formulas below retain their full signs. Filtering $|v|^2$, current power or harmonic bins is a different object. The dressed gap cannot be replaced by $\\varepsilon$ and still labelled SFAF; that optional replacement is FVB."
  ],
  "closure_requirements": {
    "RC0": [
      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
      "Required indispensable claim CL0, central physical object: F1 (Instantiate both materials, all three specified case families, initially occupied valence band and consistent F=-dA/dt, K_t, Bloch gauge, Brillouin-zone and current conventions.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC1": [
      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
      "Required indispensable claim CL0, indispensable material component: all of: F2 (Derive a computable second-order instantaneous-adiabatic-basis SFAF retaining the dressed gap and correctly connect it to exact density-matrix propagation and interband/intraband currents.); F3 (Apply the fixed filter to complex amplitude v, retain the nonresonant population mixed term and construct real/nonreal interband and intraband currents from the corresponding amplitudes.); F4 (Coherently assemble all applicable time-domain interband/intraband components before Fourier transformation and squaring, with common units, normalization, case binding and reconstructible spectral conventions.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL1, indispensable material component: all of: O1 (Present physically valid, reconstructible semiconductor exact and dressed-gap SFAF spectra sufficient to assess their agreement range and principal interband/intraband balance independently.); O2 (Present physically valid, reconstructible long-pulse dielectric exact and dressed-gap SFAF spectra sufficient to assess their agreement range and high-order balance differing from the semiconductor independently.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL2, indispensable material component: all of: O3 (Present low-field short-pulse dielectric real/nonreal interband/intraband currents and coherent total spectrum, preserving amplitude filter, mixed population term, signed cross terms, common scale and reconstructible data.); O4 (Present high-field short-pulse dielectric real/nonreal interband/intraband currents and coherent total spectrum, preserving amplitude filter, mixed population term, signed cross terms, common scale and reconstructible data.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC2": [
      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
      "Required co primary claim CL1, principal mechanism or commissioned conclusion: all of: M1 (Assess the semiconductor SFAF credible harmonic range using specific exact/SFAF spectral structure rather than generic agreement language.); M2 (Assess the long-pulse dielectric SFAF credible range and explain the relevant material difference from both material datasets; if used, FVB must remain distinct from SFAF.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M7 (Establish from the high-field dielectric output that high-order resonant interband response dominates, nonresonant intraband response becomes comparable, and signed channel evidence supports interference reducing the physical total.); M3 (Use at least one identified valid field-family branch to explain how the amplitude-level real/nonreal filter separates persistent from oscillatory transition behavior and connects channels to observable HHG.); M4 (Explain with high-field signed channel evidence how coherent nonresonant-intraband/resonant-interband combination can reduce the total, rather than adding component powers.); M5 (Compare the identified two-field dielectric signals to explain redistribution of real/nonreal interband/intraband balance, restricting conclusions to supported harmonic orders.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL3, principal mechanism or commissioned conclusion: M6 (Close the research question by connecting dressed-gap changes to material/field changes, real/virtual interband/intraband channels and coherent total HHG, reaching case- and harmonic-range-specific SFAF adequacy conclusions.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC3": [
      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
      "Required co primary claim CL3, material validation/scope: V1 (Only when the submitted method, data, anomaly or claim exposes a concrete material alternative, exclude it with discriminating evidence or narrow the threatened conclusion to a supported range.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC4": [
      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
      "Close CL0 central physical object: F1 (Instantiate both materials, all three specified case families, initially occupied valence band and consistent F=-dA/dt, K_t, Bloch gauge, Brillouin-zone and current conventions.).",
      "Close CL0 indispensable material component: all of: F2 (Derive a computable second-order instantaneous-adiabatic-basis SFAF retaining the dressed gap and correctly connect it to exact density-matrix propagation and interband/intraband currents.); F3 (Apply the fixed filter to complex amplitude v, retain the nonresonant population mixed term and construct real/nonreal interband and intraband currents from the corresponding amplitudes.); F4 (Coherently assemble all applicable time-domain interband/intraband components before Fourier transformation and squaring, with common units, normalization, case binding and reconstructible spectral conventions.).",
      "Close CL1 indispensable material component: all of: O1 (Present physically valid, reconstructible semiconductor exact and dressed-gap SFAF spectra sufficient to assess their agreement range and principal interband/intraband balance independently.); O2 (Present physically valid, reconstructible long-pulse dielectric exact and dressed-gap SFAF spectra sufficient to assess their agreement range and high-order balance differing from the semiconductor independently.).",
      "Close CL1 principal mechanism or commissioned conclusion: all of: M1 (Assess the semiconductor SFAF credible harmonic range using specific exact/SFAF spectral structure rather than generic agreement language.); M2 (Assess the long-pulse dielectric SFAF credible range and explain the relevant material difference from both material datasets; if used, FVB must remain distinct from SFAF.).",
      "Close CL2 indispensable material component: all of: O3 (Present low-field short-pulse dielectric real/nonreal interband/intraband currents and coherent total spectrum, preserving amplitude filter, mixed population term, signed cross terms, common scale and reconstructible data.); O4 (Present high-field short-pulse dielectric real/nonreal interband/intraband currents and coherent total spectrum, preserving amplitude filter, mixed population term, signed cross terms, common scale and reconstructible data.).",
      "Close CL2 principal mechanism or commissioned conclusion: all of: M7 (Establish from the high-field dielectric output that high-order resonant interband response dominates, nonresonant intraband response becomes comparable, and signed channel evidence supports interference reducing the physical total.); M3 (Use at least one identified valid field-family branch to explain how the amplitude-level real/nonreal filter separates persistent from oscillatory transition behavior and connects channels to observable HHG.); M4 (Explain with high-field signed channel evidence how coherent nonresonant-intraband/resonant-interband combination can reduce the total, rather than adding component powers.); M5 (Compare the identified two-field dielectric signals to explain redistribution of real/nonreal interband/intraband balance, restricting conclusions to supported harmonic orders.).",
      "Close CL3 principal mechanism or commissioned conclusion: M6 (Close the research question by connecting dressed-gap changes to material/field changes, real/virtual interband/intraband channels and coherent total HHG, reaching case- and harmonic-range-specific SFAF adequacy conclusions.).",
      "Close CL3 material validation/scope: V1 (Only when the submitted method, data, anomaly or claim exposes a concrete material alternative, exclude it with discriminating evidence or narrow the threatened conclusion to a supported range.)."
    ]
  },
  "references": [
    {
      "citation": "A. Thorpe, N. Boroumand, A. M. Parks, E. Goulielmakis, and T. Brabec. 2023. *High harmonic generation in solids: Real versus virtual transition channels*. *Physical Review B*, 107, 075135.",
      "url": "https://doi.org/10.1103/PhysRevB.107.075135",
      "scientific_scope": "High harmonic generation in solids: Real versus virtual transition channels",
      "anchors": [
        "Thorpe et al. (2023), article pp.075135-2-4, Eqs.(1)-(19), Fig.2 caption: moving-K two-band exact density matrix, instantaneous adiabatic diagonalization, second-order expansion and dressed-gap SFAF; exact propagation is distinct from FVB.",
        "Thorpe et al. (2023), article pp.075135-4-5, Eqs.(20)-(25): filtering complex amplitude v into low-frequency resonant and complementary virtual parts; mixed population term belongs to the nonresonant definition.",
        "Thorpe et al. (2023), article pp.075135-3,5-6, Eqs.(19),(24),(25), Fig.5 and high-field interference discussion: coherent current combination before Fourier power. Candidate spectral-density/fluence equivalents are allowed under common conventions.",
        "Thorpe et al. (2023), article p.075135-4, Fig.2(a) and comparison paragraph: semiconductor exact/SFAF agreement and interband predominance. Fig.3 on p.075135-5 is auxiliary channel evidence, not a substitute for the dielectric family.",
        "Thorpe et al. (2023), article p.075135-4, Fig.2(b) and following material/Stark discussion: long-pulse dielectric exact/SFAF comparison, changed high-order balance and optional FVB disagreement.",
        "Thorpe et al. (2023), article pp.075135-5-6, Fig.5(a,b), Eqs.(20)-(25): short-pulse F0=0.005 dielectric, interband-dominated total with small intraband terms.",
        "Thorpe et al. (2023), article pp.075135-5-6, Fig.5(c,d): F0=0.012 dielectric, high-order resonant interband dominance and comparable nonresonant intraband contribution suppressing the coherent total. Signed interference follows from amplitudes, not component-power addition.",
        "Thorpe et al. (2023), article pp.075135-4-6, Fig.2(a,b), Fig.5(a-d) and dynamic-Stark paragraphs: material and field redistribute real/virtual channels. Adequacy conclusions require the actual submitted case/harmonic evidence.",
        "Thorpe et al. (2023), article pp.075135-2,6-7, no-electron-hole-interaction premise and Sec.IV scope/dephasing discussion. Positive model boundaries and triggered alternatives are task duties; additional dephasing/real-material simulation is not compulsory."
      ]
    }
  ]
}