cases/case26/grading_rubric.json

{
  "case_id": "Case26",
  "title": "Driving-laser ellipticity dependence of high-order harmonic generation in graphene",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Derive the two bands and gauge-consistent transition-dipole/current matrices from the supplied nearest-neighbor Hamiltonian, including complete reciprocal-cell identity.",
      "award_conditions": [
        "Bands, optical dipole and current matrices come from the supplied lattice Hamiltonian with one gauge-consistent eigenbasis and complete reciprocal cell."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article pp. 063412-2-3, Eqs. (1)-(3), (5)-(6), (10)-(11), Fig. 1(a,b): Bands and current/dipole matrices derive from the same nearest-neighbor Hamiltonian and complete reciprocal cell."
      ],
      "rc_relation": "RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Instantiate the Houston density-matrix dynamics, initial state, fixed field normalization across ellipticity and off-diagonal dephasing for the supplied physical case.",
      "award_conditions": [
        "Houston dynamics uses the supplied initial state, off-diagonal T2 and fixed ellipticity-normalized drive; populations are not artificially dephased."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article pp. 063412-2-4, Eq. (4), Eqs. (12)-(13) and supplied-case paragraph: Houston dynamics shifts momentum by A; dephasing acts off diagonal, and the ellipticity normalization preserves the physical drive comparison."
      ],
      "rc_relation": "RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Construct the coherent vector total current as the time-domain sum of intra- and interband amplitudes; an incoherent sum of channel powers is not equivalent.",
      "award_conditions": [
        "The time-domain vector interband and intraband currents are added before Fourier transformation and squaring; channel interference is retained."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-3, Eqs. (7)-(11) and following spectrum definition; p. 063412-4, yield definition: Total current is the coherent sum before squaring, and harmonic yield integrates a peak. Component comparisons preserve a common scale."
      ],
      "rc_relation": "RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "F4",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Define reconstructible spectra, harmonic-peak-integrated yields, normalization and component/projection branch labels.",
      "award_conditions": [
        "Spectrum, integrated harmonic bands, normalization and component/projection labels define reconstructible physical quantities."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-3, Eqs. (7)-(11) and following spectrum definition; p. 063412-4, yield definition: Total current is the coherent sum before squaring, and harmonic yield integrates a peak. Component comparisons preserve a common scale."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide the fifth-harmonic ellipticity response with its linear-driving maximum and suppression toward circular driving.",
      "award_conditions": [
        "The fifth-harmonic ellipticity data show a linear-driving maximum and suppression toward circular driving in the correct case.",
        "The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge each harmonic locally. The exact ninth-order coherent-total maximum is excluded; robust finite-ellipticity enhancement and circular suppression remain required. A local weak high-order branch does not erase correct fifth/seventh evidence."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-4, Fig. 2(a), HH5 branch, and adjacent text: Fifth-order yield is largest for linear driving and is suppressed toward circular driving."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide the seventh-harmonic ellipticity response with a robust finite-ellipticity maximum and suppression toward circular driving.",
      "award_conditions": [
        "The seventh-harmonic data resolve a robust finite-ellipticity maximum and circular suppression.",
        "The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge each harmonic locally. The exact ninth-order coherent-total maximum is excluded; robust finite-ellipticity enhancement and circular suppression remain required. A local weak high-order branch does not erase correct fifth/seventh evidence."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-4, Fig. 2(a), HH7/HH9 branches: Higher orders show finite-ellipticity enhancement and circular suppression. The exact ninth-order coherent-total optimum is not a scoring target; source peak coordinates are canonical examples only."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide strong finite-ellipticity ninth-harmonic enhancement and circular suppression; its exact total-current optimum is expressly not a required target.",
      "award_conditions": [
        "The ninth-harmonic data resolve strong finite-ellipticity enhancement and circular suppression without requiring the source exact optimum.",
        "The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge each harmonic locally. The exact ninth-order coherent-total maximum is excluded; robust finite-ellipticity enhancement and circular suppression remain required. A local weak high-order branch does not erase correct fifth/seventh evidence."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-4, Fig. 2(a), HH7/HH9 branches: Higher orders show finite-ellipticity enhancement and circular suppression. The exact ninth-order coherent-total optimum is not a scoring target; source peak coordinates are canonical examples only."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide discriminating channel or momentum-space optical-coupling evidence for the mechanism, preserving the physical case and common component scale.",
      "award_conditions": [
        "A same-case channel or momentum-local optical-coupling output has discriminating force for the mechanism and preserves meaningful component scale.",
        "The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "A channel or momentum-local mechanism discriminator needs the same physical case and common scale, but no unique decomposition or local-radius control is required."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-4, Fig. 3 and interband/intraband discussion: The seventh-order interband response carries the robust finite-ellipticity maximum on the stated common scale; equivalent momentum-local discriminators can replace channel plots."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify the fifth-order trend from the candidate's computed ellipticity curve.",
      "award_conditions": [
        "The candidate explicitly identifies the fifth-order trend from their ellipticity curve.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "O1: Provide the fifth-harmonic ellipticity response with its linear-driving maximum and suppression toward circular driving. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge each harmonic locally. The exact ninth-order coherent-total maximum is excluded; robust finite-ellipticity enhancement and circular suppression remain required. A local weak high-order branch does not erase correct fifth/seventh evidence."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-4, Fig. 2(a), HH5 branch, and adjacent text: Fifth-order yield is largest for linear driving and is suppressed toward circular driving."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify robust seventh/ninth finite-ellipticity structure while bounding uncertain or method-sensitive peak details.",
      "award_conditions": [
        "The candidate identifies robust seventh/ninth finite-ellipticity structure while bounding uncertain quantitative peak details.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [O2: Provide the seventh-harmonic ellipticity response with a robust finite-ellipticity maximum and suppression toward circular driving.; O3: Provide strong finite-ellipticity ninth-harmonic enhancement and circular suppression; its exact total-current optimum is expressly not a required target.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge each harmonic locally. The exact ninth-order coherent-total maximum is excluded; robust finite-ellipticity enhancement and circular suppression remain required. A local weak high-order branch does not erase correct fifth/seventh evidence."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-4, Fig. 2(a), HH7/HH9 branches: Higher orders show finite-ellipticity enhancement and circular suppression. The exact ninth-order coherent-total optimum is not a scoring target; source peak coordinates are canonical examples only."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify an interband/current or momentum-local signal in the candidate's evidence supporting the mechanism attribution.",
      "award_conditions": [
        "The candidate identifies the interband/current or momentum-local feature that supports their mechanism attribution.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "O4: Provide discriminating channel or momentum-space optical-coupling evidence for the mechanism, preserving the physical case and common component scale. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "A channel or momentum-local mechanism discriminator needs the same physical case and common scale, but no unique decomposition or local-radius control is required."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-4, Fig. 3 and interband/intraband discussion: The seventh-order interband response carries the robust finite-ellipticity maximum on the stated common scale; equivalent momentum-local discriminators can replace channel plots."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Synthesize the order-dependent physical conclusion about how ellipticity changes the modeled HHG response.",
      "award_conditions": [
        "The research answer synthesizes the different order responses rather than asserting one monotonic ellipticity law.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [I1: Identify the fifth-order trend from the candidate's computed ellipticity curve.; I2: Identify robust seventh/ninth finite-ellipticity structure while bounding uncertain or method-sensitive peak details.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge each harmonic locally. The exact ninth-order coherent-total maximum is excluded; robust finite-ellipticity enhancement and circular suppression remain required. A local weak high-order branch does not erase correct fifth/seventh evidence."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-4, Fig. 2(a), HH7/HH9 branches: Higher orders show finite-ellipticity enhancement and circular suppression. The exact ninth-order coherent-total optimum is not a scoring target; source peak coordinates are canonical examples only."
      ],
      "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect the nontrivial ellipticity response to interband versus intraband emission using the candidate's discriminating evidence.",
      "award_conditions": [
        "The candidate connects the unusual response to interband versus intraband emission using their discriminating output.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "I3: Identify an interband/current or momentum-local signal in the candidate's evidence supporting the mechanism attribution. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "A channel or momentum-local mechanism discriminator needs the same physical case and common scale, but no unique decomposition or local-radius control is required."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-4, Fig. 3 and interband/intraband discussion: The seventh-order interband response carries the robust finite-ellipticity maximum on the stated common scale; equivalent momentum-local discriminators can replace channel plots."
      ],
      "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect the response to the momentum-space optical transition-dipole structure near band-touching points.",
      "award_conditions": [
        "The microscopic explanation connects the response to optical transition-dipole magnitude/direction near the band-touching points.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "I3: Identify an interband/current or momentum-local signal in the candidate's evidence supporting the mechanism attribution. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "A channel or momentum-local mechanism discriminator needs the same physical case and common scale, but no unique decomposition or local-radius control is required."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-5, Fig. 4, Eq. (6), and Figs. 5-6 intervention discussion: Transition-dipole magnitude/direction near Dirac points gives a microscopic mechanism and intervention examples. No fixed local radius, rotation or source control is required."
      ],
      "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain why the selected evidence discriminates plausible microscopic alternatives rather than merely naming a mechanism.",
      "award_conditions": [
        "The candidate explains why their evidence distinguishes a plausible microscopic alternative rather than merely naming the source mechanism.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [O4: Provide discriminating channel or momentum-space optical-coupling evidence for the mechanism, preserving the physical case and common component scale.; I3: Identify an interband/current or momentum-local signal in the candidate's evidence supporting the mechanism attribution.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "A channel or momentum-local mechanism discriminator needs the same physical case and common scale, but no unique decomposition or local-radius control is required."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-5, Fig. 4, Eq. (6), and Figs. 5-6 intervention discussion: Transition-dipole magnitude/direction near Dirac points gives a microscopic mechanism and intervention examples. No fixed local radius, rotation or source control is required."
      ],
      "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Preserve and explain the distinction between coherent total-current emission and an incoherent channel-power sum.",
      "award_conditions": [
        "The coherent total-power cross term is retained and its distinction from an incoherent channel sum is correctly explained.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "F3: Construct the coherent vector total current as the time-domain sum of intra- and interband amplitudes; an incoherent sum of channel powers is not equivalent. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article p. 063412-3, Eqs. (7)-(11) and following spectrum definition; p. 063412-4, yield definition: Total current is the coherent sum before squaring, and harmonic yield integrates a peak. Component comparisons preserve a common scale."
      ],
      "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Keep the mechanism attribution local to the specified two-band model and pulse, not a universal graphene or solid-HHG law.",
      "award_conditions": [
        "The causal attribution remains local to the specified two-band pulse/dephasing model rather than a universal graphene law.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article pp. 063412-4-6, model/case discussion, Figs. 2-7; stated task comparison and scope: Model-specific robust trends must be separated from representation-sensitive peak/component details. Reliability and triggered-risk treatment do not impose source grids or an exact ninth-order optimum."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Distinguish robust physical structures from method-sensitive quantitative details.",
      "award_conditions": [
        "The conclusion distinguishes robust enhancement/suppression from method-sensitive extrema or component heights.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "I2: Identify robust seventh/ninth finite-ellipticity structure while bounding uncertain or method-sensitive peak details. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge each harmonic locally. The exact ninth-order coherent-total maximum is excluded; robust finite-ellipticity enhancement and circular suppression remain required. A local weak high-order branch does not erase correct fifth/seventh evidence."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article pp. 063412-4-6, model/case discussion, Figs. 2-7; stated task comparison and scope: Model-specific robust trends must be separated from representation-sensitive peak/component details. Reliability and triggered-risk treatment do not impose source grids or an exact ninth-order optimum."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "V1",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Supply reconstructible branch/common-scale evidence and limitations commensurate with the actual claims.",
      "award_conditions": [
        "Branch/common-scale data and actual evidence limitations make the stated claims reconstructible."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article pp. 063412-4-6, model/case discussion, Figs. 2-7; stated task comparison and scope: Model-specific robust trends must be separated from representation-sensitive peak/component details. Reliability and triggered-risk treatment do not impose source grids or an exact ninth-order optimum."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "If a concrete coherent-channel, polarization-projection, gauge, resolution, normalization or alternative-mechanism risk emerges from candidate work, discriminate it minimally or restrict scope; otherwise record N/A with fixed credit.",
      "award_conditions": [
        "A triggered channel, projection, gauge, singular-point, resolution or normalization risk is discriminated or restricted; otherwise apply N/A."
      ],
      "applicability_and_na": [
        "Activate only for a concrete material risk arising from the candidate method, data, anomaly or claim; no fixed test is required in the absence of a trigger.",
        "Without a triggered risk record N/A and award 0.5 without positive validation evidence; this neither blocks RC4 nor triggers RC3.",
        "When triggered, accept functionally equivalent discriminating evidence or a justified restriction of the threatened claim."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept equivalent complete reciprocal primitive cells, gauge-consistent matrix elements, Fourier conventions, integration bands, units and common multiplicative scales preserving the observable.",
        "Current decompositions, momentum-local controls, gauge-consistent optical-coupling analysis or other physically discriminating evidence may replace the source mechanism layout; no fixed decomposition or truncation radius is compulsory.",
        "Accept stable lower-resolution evidence with honest limitations when claim-bearing structure is established. Exact ninth-harmonic optimum, absolute scale, pointwise component heights and source display matching are not targets."
      ],
      "source_support": [
        "Liu et al. (2018), article pp. 063412-4-6, model/case discussion, Figs. 2-7; stated task comparison and scope: Model-specific robust trends must be separated from representation-sensitive peak/component details. Reliability and triggered-risk treatment do not impose source grids or an exact ninth-order optimum."
      ],
      "rc_relation": "RC3: an unresolved applicable material risk, only after signals and principal mechanisms are substantially supported and all six risk-proof requirements are met. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    }
  ],
  "case_scientific_rules": [
    "The nearest-neighbor bands are Ev,c = -/+ gamma |f|. Use the same eigenstates for transition dipole, band velocity and off-diagonal momentum matrix. Houston momentum is k + A(t); only off-diagonal density-matrix elements decay with T2. Dephasing populations or varying field normalization with ellipticity changes the physical case.",
    "The total current is J_intra(t) + J_inter(t) before Fourier transformation and squaring. Spectrum is proportional to |omega J_tilde(omega)|^2 and harmonic yield integrates each peak. Separately squared channel powers do not reconstruct a coherent total.",
    "Fifth order is maximal at linear driving and suppressed toward circular. Seventh order has a robust finite-ellipticity maximum, near 0.32 for the source case, and circular suppression. Ninth order has strong finite-ellipticity enhancement and circular suppression, but its exact total optimum is excluded from scoring.",
    "For the seventh-harmonic split on a common scale, interband emission exceeds intraband across the scan and has the robust finite-ellipticity maximum; intraband is largest at linear driving and may have a weaker shoulder. Compare ordering/structure, not pointwise component heights.",
    "The source associates the nontrivial response with optical transition-dipole magnitude/direction near band-touching points. A current decomposition, momentum-local intervention, gauge-consistent matrix-element analysis or another discriminating route is acceptable. A static dipole picture alone must still perform the claimed discriminating function.",
    "Source and independent implementations differ on the precise ninth-order total optimum and component heights. A stable earlier broad ninth-order maximum from the coherent vector total is not wrong on that basis. Source-density grids are not hidden accuracy tolerances.",
    "The dynamic momentum-local truncation is an optional source-supported mechanism anchor, not a mandatory output or a high-weight numerical standard. No hidden local radius, curve or exact panel is prescribed.",
    "Each baseline harmonic may be normalized to its own linear-driving value, but component comparisons retain one common scale. Reciprocal cells, gauges, units, peak bands and display choices may differ only if they preserve the same physical object.",
    "Concrete risks include unresolved channel interference, polarization projection ambiguity, unresolved dipole structure, gauge/singular-point handling, ratio-erasing normalization and a mechanism alternative actually raised by candidate evidence. No named refinement, window comparison or local-truncation run is required by default.",
    "The score is the sum of twenty material-core criteria, each worth either 0 or 0.5, for a maximum of 10.0. Research Closure is descriptive and never caps, floors, rescales or repairs the score.",
    "Judge physical object identity and correctness before display similarity. For each output record object_valid, presentation_adequate and claim_adequate separately; all three must hold for its atomic award. A presentation or claim defect alone is not evidence that an existing physical object is absent or invalid.",
    "Candidate-created data, candidate presentation, candidate identification, physical inference and validation are distinct evidential acts. Examiner inspection or reconstruction may verify an object but cannot create missing candidate identification, reasoning or risk resolution.",
    "A dependency propagates only the failed necessary physical fact, not the whole upstream atomic verdict or unrelated missing detail. Name the failed premise, the downstream obligation needing it, and why independent candidate-presented evidence does not establish it. Preserve unaffected branches, independent work and honest scope.",
    "Numerical reliability has no separate generic penalty. Charge a defect where it materially damages a physical object or evidence, and a dependent conclusion only when that same defect makes the conclusion false or unsupported. Missing a preferred convergence study, control, solver or named self-check is not itself a failure.",
    "Risk-triggered validation applies only to a concrete material risk arising from the candidate method, data, anomaly or claim. With no such risk record N/A and award the fixed atomic credit without treating it as positive validation evidence; N/A does not block RC4. Unconditional scope obligations cannot be N/A.",
    "Before assigning RC3 establish all six: the concrete failure mode; its origin in candidate work; the fair task or standard-knowledge basis; the threatened central conclusion; why submitted evidence cannot expose or exclude it; and examples of functionally equivalent discriminating evidence or an honest scope restriction that would resolve it. A generic possibility of further testing is insufficient.",
    "Use bounded examiner-side source/reference readback only to resolve a material scientific uncertainty, not to demand pixels, an undeclared tolerance or additional candidate deliverables. A provisional score of at least 9.0 or provisional RC4 triggers one bounded central-output-anchor check and one principal-mechanism-link check. Reference conflict or insufficiency remains an explicit unresolved decision, not an invented target.",
    "Evaluate closure-role trigger facts independently of atomic awards and select the most severe failed required role across all indispensable and co-primary claims. Supporting claims do not independently set overall closure. A point loss alone is not a closure-gate fact.",
    "A valid candidate-caused incomplete or timeout attempt with no scientifically assessable required submission has score 0.0 and RC0 before N/A bookkeeping. Assessable incomplete work is graded from the submitted evidence; unsubmitted scratch or logs do not become scientific answers.",
    "$H_0(\\mathbf k)=-\\gamma\\begin{pmatrix}0&f(\\mathbf k)\\\\f^*(\\mathbf k)&0\\end{pmatrix}$ gives $E_{c,v}=\\pm\\gamma|f|$. With common eigenstates, $\\mathbf d_{mn}=i\\langle u_m|\\nabla_k u_n\\rangle$ and $\\mathbf p_{cv}=i(E_c-E_v)\\mathbf d_{cv}$ (Eqs. (1)-(6), (11)); gauge/reciprocal-cell changes must preserve these physical matrices.",
    "At $\\mathbf k+\\mathbf A(t)$ the Houston density evolves as $\\dot\\rho=-i[E,\\rho]-i\\mathbf F\\cdot[\\mathbf d,\\rho]-(1-\\delta_{mn})\\rho_{mn}/T_2$ (Eq. (4)). The drive components scale as $F_0/\\sqrt{1+\\epsilon^2}$ and $\\epsilon F_0/\\sqrt{1+\\epsilon^2}$ (Eqs. (12)-(13)), not two independently fixed amplitudes.",
    "Use $\\mathbf J=\\mathbf J_{\\rm intra}+\\mathbf J_{\\rm inter}$ (Eqs. (7)-(9)) and $I(\\omega)\\propto\\omega^2|\\widetilde{\\mathbf J}_{\\rm intra}+\\widetilde{\\mathbf J}_{\\rm inter}|^2$. The cross term $2\\operatorname{Re}(\\widetilde{\\mathbf J}_{\\rm intra}\\cdot\\widetilde{\\mathbf J}_{\\rm inter}^*)$ cannot be discarded. $Y_n=\\int_{B_n}I(\\omega)d\\omega$ may use declared equivalent peak bands; independent channel rescaling cannot support a channel-strength comparison."
  ],
  "closure_requirements": {
    "RC0": [
      "Required claim CL1, central object: All of [F1: Derive the two bands and gauge-consistent transition-dipole/current matrices from the supplied nearest-neighbor Hamiltonian, including complete reciprocal-cell identity.; F2: Instantiate the Houston density-matrix dynamics, initial state, fixed field normalization across ellipticity and off-diagonal dephasing for the supplied physical case.; F3: Construct the coherent vector total current as the time-domain sum of intra- and interband amplitudes; an incoherent sum of channel powers is not equivalent.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Apply for a missing or materially invalid required central object; a presentation-only or claim-only defect does not establish object invalidity.",
      "No scientifically assessable required submission gives the terminal 0.0/RC0 disposition."
    ],
    "RC1": [
      "Required claim CL1, indispensable component: All of [O1: Provide the fifth-harmonic ellipticity response with its linear-driving maximum and suppression toward circular driving.; O2: Provide the seventh-harmonic ellipticity response with a robust finite-ellipticity maximum and suppression toward circular driving.; O3: Provide strong finite-ellipticity ninth-harmonic enhancement and circular suppression; its exact total-current optimum is expressly not a required target.; O4: Provide discriminating channel or momentum-space optical-coupling evidence for the mechanism, preserving the physical case and common component scale.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "The central object is established but a required physical component is absent or materially invalid. Preserve independent valid branches; do not invent a hidden canonical plot, sampling grid or implementation duty."
    ],
    "RC2": [
      "Required claim CL2, principal mechanism: All of [M1: Synthesize the order-dependent physical conclusion about how ellipticity changes the modeled HHG response.; M2: Connect the nontrivial ellipticity response to interband versus intraband emission using the candidate's discriminating evidence.; M3: Connect the response to the momentum-space optical transition-dipole structure near band-touching points.; M4: Explain why the selected evidence discriminates plausible microscopic alternatives rather than merely naming a mechanism.; M5: Preserve and explain the distinction between coherent total-current emission and an incoherent channel-power sum.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required signal objects/components exist, but an indispensable principal mechanism or co-primary scientific conclusion is missing, wrong or unsupported by candidate-presented and identified evidence. Correct data do not let an examiner supply missing reasoning."
    ],
    "RC3": [
      "Required claim CL2, material validation: V2: If a concrete coherent-channel, polarization-projection, gauge, resolution, normalization or alternative-mechanism risk emerges from candidate work, discriminate it minimally or restrict scope; otherwise record N/A with fixed credit.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "All indispensable signal and principal-mechanism roles are substantially supported, but a concrete triggered material risk remains unresolved and inadequately restricted.",
      "Establish the failure mode, candidate origin, fair task/knowledge basis, threatened central conclusion, insufficiency of submitted evidence, and equivalent resolution or scope restriction. Missing an examiner-preferred check alone never suffices."
    ],
    "RC4": [
      "Every nonempty required role in every indispensable and co-primary claim above is scientifically established from candidate evidence, with the correct case/model/observable identities and evidence-bounded conclusion.",
      "All applicable material risks are discriminated or honestly restricted; no unresolved material ambiguity remains. Risk N/A does not block closure or supply positive validation evidence. Honest limitations cannot repair a false signal or mechanism.",
      "Select the most severe failed required role if any; otherwise RC4. No score threshold, score ceiling or required display/solver checklist determines this classification."
    ]
  },
  "references": [
    {
      "citation": "Candong Liu, Yinghui Zheng, Zhinan Zeng, and Ruxin Li. 2018. Driving-laser ellipticity dependence of high-order harmonic generation in graphene. Physical Review A, 97, 063412.",
      "url": "https://doi.org/10.1103/PhysRevA.97.063412",
      "scientific_scope": "Coherent vector-current ellipticity dependence and model-local channel/optical-coupling mechanism. Robust fifth/seventh/ninth response structures are assessable; exact ninth-order optimum and pointwise component heights are not settled numerical targets.",
      "anchors": [
        "article pp. 063412-2-3, Eqs. (1)-(3), (5)-(6), (10)-(11), Fig. 1(a,b)",
        "article pp. 063412-2-4, Eq. (4), Eqs. (12)-(13) and supplied-case paragraph",
        "article p. 063412-3, Eqs. (7)-(11) and following spectrum definition; p. 063412-4, yield definition",
        "article p. 063412-4, Fig. 2(a), HH5 branch, and adjacent text",
        "article p. 063412-4, Fig. 2(a), HH7/HH9 branches",
        "article p. 063412-4, Fig. 3 and interband/intraband discussion",
        "article p. 063412-5, Fig. 4, Eq. (6), and Figs. 5-6 intervention discussion",
        "article pp. 063412-4-6, model/case discussion, Figs. 2-7; stated task comparison and scope"
      ]
    }
  ]
}