cases/case28/grading_rubric.json

{
  "case_id": "Case28",
  "title": "Trajectory analysis of high-order-harmonic generation from periodic crystals",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Instantiate the visible one-dimensional periodic potential, two initially filled valence bands, finite-support pulse, velocity-gauge independent-electron TDSE and Brillouin-zone occupation consistently.",
      "award_conditions": [
        "The periodic potential, two filled valence bands, supplied finite-support pulse, velocity-gauge TDSE and BZ occupation identify one common model."
      ],
      "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.",
        "Preserve independent correct work in F2, F3 and all branches not using the failed premise.",
        "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.",
        "Independent foundation atom.",
        "Correct current/spectrum definitions and trajectory construction retain their own credit if this model instantiation has a localized defect; a different physical model still invalidates dependent outputs."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-2-3, Eqs. (1)-(5), Fig. 1, Fig. 2 and pulse paragraph: The periodic independent-electron crystal begins with two filled valence bands; finite-pulse support follows the stated task convention."
      ],
      "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": "Define a reconstructible physical total current from all occupied channels and a windowed Fourier HHG spectrum, declaring gauge, window, normalization and case binding.",
      "award_conditions": [
        "Occupied-state currents are summed coherently into a reconstructible windowed total-current spectrum with declared conventions."
      ],
      "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.",
        "Preserve independent correct work in F1, F3 and all branches not using the failed premise.",
        "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.",
        "Independent observable-definition atom.",
        "Correct model and trajectory foundations remain independently scoreable if the total-current construction is wrong."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article p. 043416-3, Eqs. (6)-(7) and following spectral paragraph: A coherent occupied-state/BZ total current, not incoherent band powers, defines the HHG spectrum."
      ],
      "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 a computable multiband electron-hole trajectory model using field-free bands, k(t) = k0 + A(t), transition/passage branches, recombination and instantaneous particle-hole gaps.",
      "award_conditions": [
        "The multiband trajectory route is computable from field-free bands, k0+A(t), branch passages and recombination gaps."
      ],
      "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.",
        "Preserve independent correct work in F1, F2 and all branches not using the failed premise.",
        "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.",
        "Independent mechanism-model foundation.",
        "Correct physical model and HHG observable definitions retain credit even if the trajectory construction is incomplete."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-4-6, Eq. (8), Eq. (10), Sec. IV steps (i)-(iii) and Figs. 4-6: Momentum displacement, repeated interband passage and particle-hole gaps define a computable multiband trajectory model."
      ],
      "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 reconstructible field-dependent HHG spectra over a domain resolving low-field simple response and higher-field high-energy branch families under consistent declared normalization.",
      "award_conditions": [
        "A common-scale field scan resolves low-field simple response and higher-field high-energy plateau/branch families.",
        "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": [
        "All of [F1: Instantiate the visible one-dimensional periodic potential, two initially filled valence bands, finite-support pulse, velocity-gauge independent-electron TDSE and Brillouin-zone occupation consistently.; F2: Define a reconstructible physical total current from all occupied channels and a windowed Fourier HHG spectrum, declaring gauge, window, normalization and case binding.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in F3 and all branches not using the failed premise.",
        "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.",
        "The submitted spectrum is valid only for the commissioned model and physical total-current observable.",
        "A valid independent trajectory construction retains credit even if the submitted HHG spectrum object is invalid.",
        "A claim about a particular plateau/opening needs the relevant spectrum and estimator-supported domain, not every unrelated field point. Threshold-sensitive onset coordinates do not override robust branch evidence."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-3-4, Fig. 3(a,b) and adjacent transition discussion: Low-field single-plateau response changes into several high-energy plateau families as field increases."
      ],
      "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": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide plateau/cutoff evidence whose estimator, resolution and uncertainty support material onset regions and limiting-energy structures without making threshold-sensitive point estimates a hidden gold standard.",
      "award_conditions": [
        "Plateau/cutoff estimators, resolution and uncertainty support material opening regions and energy limits without exact display-threshold targets.",
        "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": [
        "O1: Provide reconstructible field-dependent HHG spectra over a domain resolving low-field simple response and higher-field high-energy branch families under consistent declared normalization. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O3, F3 and all branches not using the failed premise.",
        "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.",
        "Plateau and cutoff claims require a valid reconstructible spectral family.",
        "Time-resolved evidence and trajectory construction remain independent of a weak cutoff estimator.",
        "A claim about a particular plateau/opening needs the relevant spectrum and estimator-supported domain, not every unrelated field point. Threshold-sensitive onset coordinates do not override robust branch evidence."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-3-6, Fig. 3(b), Eqs. (9), (12)-(14), and Fig. 7: Major branch openings track vector-potential excursion relative to Brillouin-zone scales; source onset coordinates and display cutoffs are not exact task thresholds."
      ],
      "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 reconstructible low/high-field time-resolved or physically equivalent diagnostics resolving material emission time-energy structures and their relation to multiband trajectory branches.",
      "award_conditions": [
        "Low/high-field time-energy diagnostics are reconstructible and distinguish material emission structures relevant to multiband branches.",
        "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": [
        "All of [F1: Instantiate the visible one-dimensional periodic potential, two initially filled valence bands, finite-support pulse, velocity-gauge independent-electron TDSE and Brillouin-zone occupation consistently.; F2: Define a reconstructible physical total current from all occupied channels and a windowed Fourier HHG spectrum, declaring gauge, window, normalization and case binding.; F3: Construct a computable multiband electron-hole trajectory model using field-free bands, k(t) = k0 + A(t), transition/passage branches, recombination and instantaneous particle-hole gaps.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O1, O2 and all branches not using the failed premise.",
        "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.",
        "The diagnostic must represent the commissioned signal and a computable trajectory comparison under the same case.",
        "Correct field-dependent spectra and cutoff evidence retain credit if only the time-frequency or equivalent diagnostic is damaged.",
        "Timing/trajectory correspondence needs candidate-presented low/high-field time-energy evidence or an equally discriminating representation. A spectrum alone does not create timing identification, but remains independently scoreable."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article p. 043416-5, Fig. 6(a-f), especially time-frequency panels (c,d) and trajectory panels (e,f): Low/high-field time-energy diagnostics test multiband emission timing; another physically discriminating time-resolved representation is allowed."
      ],
      "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 change from a simpler low-field plateau to multiple higher-field high-energy plateaus in candidate-presented spectra, bounded to the field domain covered.",
      "award_conditions": [
        "The candidate identifies the transition from a simpler low-field plateau to multiple high-field plateaus in their own spectra.",
        "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 reconstructible field-dependent HHG spectra over a domain resolving low-field simple response and higher-field high-energy branch families under consistent declared normalization. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in F3, O3, I3 and all branches not using the failed premise.",
        "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.",
        "Identification must come from valid candidate-presented field-dependent spectra; examiner discovery or source readback cannot be backfilled as I credit.",
        "Independent trajectory and time-resolved work retains credit if field-domain identification is incomplete.",
        "A claim about a particular plateau/opening needs the relevant spectrum and estimator-supported domain, not every unrelated field point. Threshold-sensitive onset coordinates do not override robust branch evidence."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-3-4, Fig. 3(a,b) and adjacent transition discussion: Low-field single-plateau response changes into several high-energy plateau families as field increases."
      ],
      "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 both material high-energy opening regions and associated new branch/plateau families at resolution commensurate with the candidate's spectral/cutoff estimator.",
      "award_conditions": [
        "The candidate identifies both material high-energy opening regions and new families with precision supported by their estimator.",
        "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": [
        "O2: Provide plateau/cutoff evidence whose estimator, resolution and uncertainty support material onset regions and limiting-energy structures without making threshold-sensitive point estimates a hidden gold standard. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I1, I3 and all branches not using the failed premise.",
        "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.",
        "The candidate must identify onset/branch structure from its own adequate plateau/cutoff evidence; examiner readback cannot create I credit.",
        "Global regime identification and time-resolved branch identification remain separately scoreable.",
        "A claim about a particular plateau/opening needs the relevant spectrum and estimator-supported domain, not every unrelated field point. Threshold-sensitive onset coordinates do not override robust branch evidence."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-3-6, Fig. 3(b), Eqs. (9), (12)-(14), and Fig. 7: Major branch openings track vector-potential excursion relative to Brillouin-zone scales; source onset coordinates and display cutoffs are not exact task thresholds."
      ],
      "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 emission structures and their low/high-field multiband trajectory branches in time and photon energy from the candidate-presented diagnostic.",
      "award_conditions": [
        "The candidate identifies time/energy emission structures and their low/high-field trajectory-branch counterparts.",
        "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": [
        "O3: Provide reconstructible low/high-field time-resolved or physically equivalent diagnostics resolving material emission time-energy structures and their relation to multiband trajectory branches. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I1, I2 and all branches not using the failed premise.",
        "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.",
        "Candidate identification requires its own valid diagnostic; the examiner may verify E0/E1 but must not backfill E2.",
        "Spectral regime and onset identification remain independent if the time-resolved diagnostic is absent.",
        "Timing/trajectory correspondence needs candidate-presented low/high-field time-energy evidence or an equally discriminating representation. A spectrum alone does not create timing identification, but remains independently scoreable."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article p. 043416-5, Fig. 6(a-f), especially time-frequency panels (c,d) and trajectory panels (e,f): Low/high-field time-energy diagnostics test multiband emission timing; another physically discriminating time-resolved representation is allowed."
      ],
      "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": "Explain the low-field response through intraband displacement in the first conduction band and its particle-hole gap limit before reaching the Brillouin-zone edge.",
      "award_conditions": [
        "Low-field response is explained through first-conduction-band displacement and its particle-hole gap limit before the zone edge is reached.",
        "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 [F3: Construct a computable multiband electron-hole trajectory model using field-free bands, k(t) = k0 + A(t), transition/passage branches, recombination and instantaneous particle-hole gaps.; I1: Identify the change from a simpler low-field plateau to multiple higher-field high-energy plateaus in candidate-presented spectra, bounded to the field domain covered.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M2, M3 and all branches not using the failed premise.",
        "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.",
        "The low-field mechanism requires a valid trajectory construction and candidate-identified low-field signal.",
        "Correct higher-field onset mechanisms retain independent credit if the low-field branch explanation is incomplete.",
        "A claim about a particular plateau/opening needs the relevant spectrum and estimator-supported domain, not every unrelated field point. Threshold-sensitive onset coordinates do not override robust branch evidence."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-4-5, Eqs. (8)-(12), Figs. 4(c,d), 5(c,d): Before reaching the zone edge the first-conduction-band particle-hole gap limits the branch; recombination energies track instantaneous gaps to the initial hole."
      ],
      "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 first material spectral opening to vector-potential excursion reaching the first Brillouin-zone boundary and enabling additional interband passage and displacement.",
      "award_conditions": [
        "The first opening is tied to vector-potential excursion reaching the zone boundary and enabling an additional interband passage.",
        "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 [F3: Construct a computable multiband electron-hole trajectory model using field-free bands, k(t) = k0 + A(t), transition/passage branches, recombination and instantaneous particle-hole gaps.; I1: Identify the change from a simpler low-field plateau to multiple higher-field high-energy plateaus in candidate-presented spectra, bounded to the field domain covered.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M1, M3 and all branches not using the failed premise.",
        "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.",
        "The causal opening claim needs the candidate's trajectory construction and identified regime change.",
        "Other low- and high-field mechanism atoms retain credit if this onset is mislocated.",
        "A claim about a particular plateau/opening needs the relevant spectrum and estimator-supported domain, not every unrelated field point. Threshold-sensitive onset coordinates do not override robust branch evidence."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-3-6, Fig. 3(b), Eqs. (9), (12)-(14), and Fig. 7: Major branch openings track vector-potential excursion relative to Brillouin-zone scales; source onset coordinates and display cutoffs are not exact task thresholds."
      ],
      "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 second high-energy opening to larger excursion accessing an additional multiband branch, without fixing an approximate source onset as a hidden threshold.",
      "award_conditions": [
        "The second opening is tied to larger excursion and an additional multiband branch, not an exact hidden source onset.",
        "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 [F3: Construct a computable multiband electron-hole trajectory model using field-free bands, k(t) = k0 + A(t), transition/passage branches, recombination and instantaneous particle-hole gaps.; I2: Identify both material high-energy opening regions and associated new branch/plateau families at resolution commensurate with the candidate's spectral/cutoff estimator.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M1, M2 and all branches not using the failed premise.",
        "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.",
        "The second-opening mechanism requires a valid trajectory model and candidate identification of the material additional branch.",
        "The first-opening and low-field mechanisms remain independently scoreable.",
        "A claim about a particular plateau/opening needs the relevant spectrum and estimator-supported domain, not every unrelated field point. Threshold-sensitive onset coordinates do not override robust branch evidence."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-3-6, Fig. 3(b), Eqs. (9), (12)-(14), and Fig. 7: Major branch openings track vector-potential excursion relative to Brillouin-zone scales; source onset coordinates and display cutoffs are not exact task thresholds."
      ],
      "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 higher-field multiple plateaus through repeated interband excitation and intraband displacement, a multiband band-climbing chain rather than one two-band narrative.",
      "award_conditions": [
        "Repeated excitation and intraband displacement explain band climbing and multiple plateaus beyond a single two-band narrative.",
        "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 [F3: Construct a computable multiband electron-hole trajectory model using field-free bands, k(t) = k0 + A(t), transition/passage branches, recombination and instantaneous particle-hole gaps.; I2: Identify both material high-energy opening regions and associated new branch/plateau families at resolution commensurate with the candidate's spectral/cutoff estimator.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M5, M6 and all branches not using the failed premise.",
        "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.",
        "The candidate must connect its identified high-energy branches to its own multiband trajectory construction; examiner interpretation cannot be backfilled as M credit.",
        "Correct recombination-energy or timing relations retain independent credit if band-climbing prose is incomplete.",
        "A claim about a particular plateau/opening needs the relevant spectrum and estimator-supported domain, not every unrelated field point. Threshold-sensitive onset coordinates do not override robust branch evidence."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-4-6, Sec. IV, Fig. 5 and Eq. (14): Repeated interband excitation and intraband displacement allow band climbing; one two-band cutoff cannot explain all high-field plateaus."
      ],
      "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": "Relate recombination with the initial valence-band hole to instantaneous particle-hole gaps, explaining limiting-energy/cutoff branches.",
      "award_conditions": [
        "Recombination with the original hole and instantaneous gaps explain limiting-energy/cutoff branches.",
        "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 [F3: Construct a computable multiband electron-hole trajectory model using field-free bands, k(t) = k0 + A(t), transition/passage branches, recombination and instantaneous particle-hole gaps.; I2: Identify both material high-energy opening regions and associated new branch/plateau families at resolution commensurate with the candidate's spectral/cutoff estimator.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M4, M6 and all branches not using the failed premise.",
        "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.",
        "The cutoff explanation requires a candidate-identified branch and a valid trajectory gap construction.",
        "Band-climbing and timing mechanisms retain independent credit if one gap-to-cutoff assignment is incomplete.",
        "A claim about a particular plateau/opening needs the relevant spectrum and estimator-supported domain, not every unrelated field point. Threshold-sensitive onset coordinates do not override robust branch evidence."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-4-5, Eqs. (8)-(12), Figs. 4(c,d), 5(c,d): Before reaching the zone edge the first-conduction-band particle-hole gap limits the branch; recombination energies track instantaneous gaps to the initial hole."
      ],
      "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": "Use candidate-presented time-resolved or equivalent evidence to test trajectory-model timing and branch ordering, honestly treating material residual mismatch.",
      "award_conditions": [
        "Candidate time-resolved or equivalent evidence actually tests timing/branch ordering and honestly addresses material residual mismatch.",
        "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 [F3: Construct a computable multiband electron-hole trajectory model using field-free bands, k(t) = k0 + A(t), transition/passage branches, recombination and instantaneous particle-hole gaps.; I3: Identify emission structures and their low/high-field multiband trajectory branches in time and photon energy from the candidate-presented diagnostic.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M4, M5 and all branches not using the failed premise.",
        "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.",
        "Timing inference must be made by the candidate from its own identified time-energy evidence and trajectory model; examiner overlays cannot backfill M credit.",
        "Correct band-climbing and recombination-energy explanations retain credit if timing resolution is weak.",
        "Timing/trajectory correspondence needs candidate-presented low/high-field time-energy evidence or an equally discriminating representation. A spectrum alone does not create timing identification, but remains independently scoreable."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article p. 043416-5, Fig. 6(a-f), especially time-frequency panels (c,d) and trajectory panels (e,f): Low/high-field time-energy diagnostics test multiband emission timing; another physically discriminating time-resolved representation is allowed."
      ],
      "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": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Reach a field-domain-bounded conclusion on changing spectral regimes and limiting energies, with uncertainty commensurate with estimator and sampled domain.",
      "award_conditions": [
        "The spectral-regime conclusion stays within sampled field coverage with uncertainty matching its estimator.",
        "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 change from a simpler low-field plateau to multiple higher-field high-energy plateaus in candidate-presented spectra, bounded to the field domain covered.; I2: Identify both material high-energy opening regions and associated new branch/plateau families at resolution commensurate with the candidate's spectral/cutoff estimator.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M8 and all branches not using the failed premise.",
        "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.",
        "The conclusion must follow from the candidate's own identified regime and onset evidence; source anchors cannot substitute for candidate inference.",
        "The trajectory-model assessment remains separately scoreable if field-domain uncertainty reporting is weak."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-6-7, timing/approximation discussion, Fig. 7 and Conclusion: Field-domain and finite-pulse trajectory conclusions remain independent-electron, single-cell and one-dimensional; pulse-duration behavior is context, not a mandatory extra scan."
      ],
      "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": "M8",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Answer whether momentum-space trajectories account for observed regimes, limiting energies and emission timing, distinguishing established relations from residual approximation/model dependence.",
      "award_conditions": [
        "The candidate answers what the trajectory model explains about regimes, limiting energies and emission timing and what remains approximation dependent.",
        "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 [M6: Use candidate-presented time-resolved or equivalent evidence to test trajectory-model timing and branch ordering, honestly treating material residual mismatch.; M7: Reach a field-domain-bounded conclusion on changing spectral regimes and limiting energies, with uncertainty commensurate with estimator and sampled domain.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in V3 and all branches not using the failed premise.",
        "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.",
        "The overall model-accounting decision requires both candidate-supported timing/branch testing and the field-domain conclusion.",
        "A correct independent scope limitation retains credit even if the positive accounting conclusion is incomplete."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-6-7, timing/approximation discussion, Fig. 7 and Conclusion: Field-domain and finite-pulse trajectory conclusions remain independent-electron, single-cell and one-dimensional; pulse-duration behavior is context, not a mandatory extra scan."
      ],
      "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": "If basis/band truncation, sampling, window, finite record, display threshold or morphology raises a concrete material risk to a claimed branch/onset, discriminate it or restrict the claim; otherwise record N/A without validation evidence.",
      "award_conditions": [
        "An actual truncation, sampling, window, record-length or threshold threat to branch/onset identity is discriminated or restricted; otherwise 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.",
        "Preserve independent correct work in F1, F2, F3, O1, O2, O3, I1, I2, I3, M1, M2, M3, M4, M5, M6, M7, M8, V2, V3 and all branches not using the failed premise.",
        "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.",
        "Triggered validation is evaluated independently of atomic award and only for a concrete risk arising from the candidate's work.",
        "No unrelated correct atom is deducted merely because this risk is absent, not applicable, or localized; a material defect is charged first where it damages the evidence."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-3-6, spectral construction, Fig. 6 and discussion of trajectory timing and pulse-duration effects: Truncation, display thresholds, windowing and a concrete simpler-model alternative can threaten specific branch claims. Source grids and Gabor windows are examples, not required validation procedures."
      ],
      "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."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "If candidate data/claims raise a material intraband-only/two-band alternative, pulse-duration dependence or trajectory-approximation mismatch, use equivalent discriminating evidence or restrict scope; otherwise record N/A.",
      "award_conditions": [
        "An actual simpler-model alternative, pulse-duration claim or timing-model mismatch is discriminated or restricted; otherwise 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.",
        "Preserve independent correct work in F1, F2, F3, O1, O2, O3, I1, I2, I3, M1, M2, M3, M4, M5, M6, M7, M8, V1, V3 and all branches not using the failed premise.",
        "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.",
        "The atom activates only for a concrete alternative raised by the candidate's own method, data, or conclusion.",
        "Absence of a triggered risk is N/A and cannot create a deduction; when triggered, only the threatened claim is affected and equivalent discriminators are accepted."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-3-6, spectral construction, Fig. 6 and discussion of trajectory timing and pulse-duration effects: Truncation, display thresholds, windowing and a concrete simpler-model alternative can threaten specific branch claims. Source grids and Gabor windows are examples, not required validation procedures."
      ],
      "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."
    },
    {
      "criterion_id": "V3",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Keep scope within the one-dimensional independent-electron finite-pulse single-cell model; do not turn simplified trajectories into unsupported many-body, dephasing, disorder, macroscopic-propagation or universal-material conclusions.",
      "award_conditions": [
        "The conclusion remains one-dimensional, independent-electron, single-cell and finite-pulse rather than claiming uncomputed many-body or macroscopic physics."
      ],
      "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.",
        "Preserve independent correct work in F1, F2, F3, O1, O2, O3, I1, I2, I3, M1, M2, M3, M4, M5, M6, M7, M8, V1, V2 and all branches not using the failed premise.",
        "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.",
        "Honest scope is independently judgeable and must not be disabled by upstream output or mechanism failure.",
        "Award this atom for a correct evidence-based limitation even when another branch is wrong; it cannot repair a wrong signal or mechanism."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent gauges, bases, Fourier signs, total-current/acceleration representations with correct frequency factors, Brillouin-zone folding and common normalization preserving branch relations.",
        "A diagnostic other than Gabor is accepted if it retains emission time-energy structure and comparable mechanism discrimination. Self-chosen cutoff estimators and controls are accepted with uncertainty and scope appropriate to their evidence.",
        "No source mesh, propagator, time step, momentum count, window, fixed field points or exact panel is required. Alternative representations must not erase the plateau/branch structure being judged."
      ],
      "source_support": [
        "Ikemachi et al. (2017), article pp. 043416-6-7, timing/approximation discussion, Fig. 7 and Conclusion: Field-domain and finite-pulse trajectory conclusions remain independent-electron, single-cell and one-dimensional; pulse-duration behavior is context, not a mandatory extra scan."
      ],
      "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."
    }
  ],
  "case_scientific_rules": [
    "For each initial k and both initially filled valence bands propagate i partial_t u_nk = {[-i partial_x + k + A(t)]^2/2 + V(x)} u_nk. Form each channel current from <p+A>, sum occupied channels and integrate over the Brillouin zone before constructing the windowed total-current spectrum.",
    "The prescribed total nonzero pulse support is Tp = 99.66 fs. Do not multiply it by pi again based on an ambiguous source pulse symbol. Occupy two valence bands regardless of a questionable printed/extracted summation index.",
    "Low fields show a simpler lower-cutoff plateau; increased field opens high-energy branches and multiple plateaus. Broad source onset neighborhoods around 1.4 and 2.8 V/nm correspond to peak-to-valley vector-potential excursions reaching pi/a and 2 pi/a, respectively. These are structural anchors, not exact hidden thresholds or required scan points.",
    "Source representative 0.87,1.65,2.11 V/nm spectra and approximate added plateau energies are context, not mandatory cases. The actual scan must cover material regimes needed by the claim; one discrete field cannot establish their field-dependent change.",
    "Let Delta epsilon_nm(k) = epsilon_nk - epsilon_mk and k(t) = k0 + A(t). Before the zone edge, the low-field limit follows Delta epsilon_21(A_peak). Higher branches include E31 = Delta epsilon_31(A_peak) and E41 = Delta epsilon_41(pi/a - A_peak), plus higher limits depending on the second-largest peak-to-valley excursion A_peak_prime.",
    "Repeated interband passage at accessible gaps and intraband displacement permit climbing to higher bands. Recombination with the initial valence hole emits the instantaneous particle-hole gap. A single two-band cutoff account cannot explain all higher-field structures.",
    "A time-frequency transform or equivalent discriminating representation must test low/high-field timing and branch order. Residual mismatch can arise because transitions occur near, not exactly at, a minimum gap; simplified trajectories are not a unique exact microscopic generator.",
    "A source-style sin^4 window, 1.78 fs Gabor window, exact cutoff threshold, fixed field range or original three-spectrum layout is not prescribed. Cutoff uncertainty must reflect estimator/resolution; threshold-sensitive numerical cutoff arrays are not pointwise references.",
    "Pulse-duration variation is one possible discriminating control but not mandatory without a concrete risk. Relevant triggered risks include inconsistent pulse support, BZ/gauge/occupation errors, window/display-induced branches, omitted bands or a viable intraband/two-band alternative. Time-resolved fine-structure ambiguity requires bounded source readback, not an assumed exact reproduction.",
    "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.",
    "$V(x)=-V_0[1+\\cos(2\\pi x/a)]$ and $H_k(t)=\\tfrac12[-i\\partial_x+k+A(t)]^2+V(x)$ act on cell-periodic states with both valence bands initially filled (Eqs. (3)-(5)). $j(t)\\propto\\sum_{n\\in\\mathrm{VB}}\\int_{\\rm BZ}dk\\langle u_{nk}|-i\\partial_x+k+A|u_{nk}\\rangle$ and $S(\\omega)\\propto|\\int w(t)j(t)e^{i\\omega t}dt|^2$ (Eqs. (6)-(7)); use one consistent normalization.",
    "The acceleration theorem gives $k(t)=k_0+A(t)$; for excitation at the zone center, $k(t)=A(t)-A(t_0)$ (Eq. (10)). Emitted energy is $\\Delta\\varepsilon_{n,n_0}[k(t)]=\\varepsilon_n[k(t)]-\\varepsilon_{n_0}[k(t)]$ (Eq. (8), Sec. IV). The source peak-to-valley excursion $A_{\\rm peak}$ reaching $\\pi/a$ and then $2\\pi/a$ organizes new branches, but its finite-pulse band-climbing/cutoff relations are approximate and not hidden exact onset coordinates."
  ],
  "closure_requirements": {
    "RC0": [
      "Required claim CL1, central object: All of [F1: Instantiate the visible one-dimensional periodic potential, two initially filled valence bands, finite-support pulse, velocity-gauge independent-electron TDSE and Brillouin-zone occupation consistently.; F2: Define a reconstructible physical total current from all occupied channels and a windowed Fourier HHG spectrum, declaring gauge, window, normalization and case binding.; O1: Provide reconstructible field-dependent HHG spectra over a domain resolving low-field simple response and higher-field high-energy branch families under consistent declared normalization.]. 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: O2: Provide plateau/cutoff evidence whose estimator, resolution and uncertainty support material onset regions and limiting-energy structures without making threshold-sensitive point estimates a hidden gold standard.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL2, indispensable component: O3: Provide reconstructible low/high-field time-resolved or physically equivalent diagnostics resolving material emission time-energy structures and their relation to multiband trajectory branches.. 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 CL1, principal mechanism: All of [M1: Explain the low-field response through intraband displacement in the first conduction band and its particle-hole gap limit before reaching the Brillouin-zone edge.; M2: Connect the first material spectral opening to vector-potential excursion reaching the first Brillouin-zone boundary and enabling additional interband passage and displacement.; M3: Connect the second high-energy opening to larger excursion accessing an additional multiband branch, without fixing an approximate source onset as a hidden threshold.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL2, principal mechanism: All of [M4: Explain higher-field multiple plateaus through repeated interband excitation and intraband displacement, a multiband band-climbing chain rather than one two-band narrative.; M5: Relate recombination with the initial valence-band hole to instantaneous particle-hole gaps, explaining limiting-energy/cutoff branches.; M6: Use candidate-presented time-resolved or equivalent evidence to test trajectory-model timing and branch ordering, honestly treating material residual mismatch.]. 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 CL3, material validation: All of [V1: If basis/band truncation, sampling, window, finite record, display threshold or morphology raises a concrete material risk to a claimed branch/onset, discriminate it or restrict the claim; otherwise record N/A without validation evidence.; V2: If candidate data/claims raise a material intraband-only/two-band alternative, pulse-duration dependence or trajectory-approximation mismatch, use equivalent discriminating evidence or restrict scope; otherwise record N/A.]. 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": "Takuya Ikemachi, Yasushi Shinohara, Takeshi Sato, Junji Yumoto, Makoto Kuwata-Gonokami, and Kenichi L. Ishikawa. 2017. Trajectory analysis of high-order-harmonic generation from periodic crystals. Physical Review A, 95, 043416.",
      "url": "https://doi.org/10.1103/PhysRevA.95.043416",
      "scientific_scope": "Field-dependent solid HHG plateaus/cutoffs, Brillouin-zone-edge multiband climbing and time-energy trajectory tests. Approximate onsets and estimator-dependent cutoffs are robust structural anchors, not fixed numerical thresholds.",
      "anchors": [
        "article pp. 043416-2-3, Eqs. (1)-(5), Fig. 1, Fig. 2 and pulse paragraph",
        "article p. 043416-3, Eqs. (6)-(7) and following spectral paragraph",
        "article pp. 043416-4-6, Eq. (8), Eq. (10), Sec. IV steps (i)-(iii) and Figs. 4-6",
        "article pp. 043416-3-4, Fig. 3(a,b) and adjacent transition discussion",
        "article pp. 043416-3-6, Fig. 3(b), Eqs. (9), (12)-(14), and Fig. 7",
        "article p. 043416-5, Fig. 6(a-f), especially time-frequency panels (c,d) and trajectory panels (e,f)",
        "article pp. 043416-4-5, Eqs. (8)-(12), Figs. 4(c,d), 5(c,d)",
        "article pp. 043416-4-6, Sec. IV, Fig. 5 and Eq. (14)",
        "article pp. 043416-6-7, timing/approximation discussion, Fig. 7 and Conclusion",
        "article pp. 043416-3-6, spectral construction, Fig. 6 and discussion of trajectory timing and pulse-duration effects"
      ]
    }
  ]
}