cases/case36/grading_rubric.json

{
  "case_id": "Case36",
  "title": "Temporal control of solid-state HHG cutoffs by shaped drivers",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Instantiate the stated periodic potential, reference and shaped drivers, consistent field/vector-potential convention, wavelength/intensity/duration/phase and delay binding, preserving matched comparison.",
      "award_conditions": [
        "Instantiate the stated periodic potential, reference and shaped drivers, consistent field/vector-potential convention, wavelength/intensity/duration/phase and delay binding, preserving matched comparison."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "R, Holkundkar and Bandyopadhyay (2023), article p. 063503-2, Eqs. (1)–(3), Fig. 2(a,b), p. 063503-3. Periodic model, reference/shaped fields and vector potentials; matched case and delay binding."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Construct field-free bands, the occupied initial valence manifold and driven band equations or a gauge-equivalent computable route.",
      "award_conditions": [
        "Construct field-free bands, the occupied initial valence manifold and driven band equations or a gauge-equivalent computable route."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article pp. 063503-2–3, Fig. 1, Eqs. (4)–(11). Bloch bands, driven coefficients and coherent occupied-valence full-BZ current. The initial-VB1 population diagnostic in Fig. 4 does not replace the main VB0+VB1 current sum."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Construct the coherent filled-valence full-BZ total current with correct occupied-band sum, BZ weights and current identity; the main case includes VB0+VB1 rather than only a diagnostic VB1 channel.",
      "award_conditions": [
        "The physical current sums all initially occupied valence channels with correct BZ weights before the coherent radiation transform.",
        "The main model uses VB0+VB1; a separate initial-VB1 population diagnostic does not substitute for it."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article pp. 063503-2–3, Fig. 1, Eqs. (4)–(11). Bloch bands, driven coefficients and coherent occupied-valence full-BZ current. The initial-VB1 population diagnostic in Fig. 4 does not replace the main VB0+VB1 current sum."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "F4",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Define reconstructible HHG, cutoff, yield and emission-time observables, normalization and case-to-data mapping adequate for each conclusion.",
      "award_conditions": [
        "Define reconstructible HHG, cutoff, yield and emission-time observables, normalization and case-to-data mapping adequate for each conclusion."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article p. 063503-3, text following Eq. (11); Figs. 7(a–d), p. 063503-6, and 9(a–c), p. 063503-7. Current-derived spectrum, yield integral and claim-relevant timing/cutoff definitions. Reconstructibility and common-scale reporting are task-defined; no source threshold/window is compulsory."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present matched conventional/shaped spectra with sufficient domain to resolve the genuine cutoff-support and multiband/interband structure relation.",
      "award_conditions": [
        "Present matched conventional/shaped spectra with sufficient domain to resolve the genuine cutoff-support and multiband/interband structure relation.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article p. 063503-4, Fig. 3(a–d) and Sec. III A. Matched spectral support, gap-organized plateaus and timing structure distinguish temporal-driver change from scalar rescaling."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present a reconstructible delay-dependent cutoff-energy family over a domain sufficient to assess the stated control claim.",
      "award_conditions": [
        "Present a reconstructible delay-dependent cutoff-energy family over a domain sufficient to assess the stated control claim.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article p. 063503-7, Fig. 9(a,b) and Sec. III D. Delay-dependent cutoff-energy family and finite-domain optimum; no unique sample mesh or optimum coordinate."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present yield versus delay with declared integration band/window and normalization, resolving its dependence/turnover within the claimed domain without requiring a fixed source window or exponent.",
      "award_conditions": [
        "Present yield versus delay with declared integration band/window and normalization, resolving its dependence/turnover within the claimed domain without requiring a fixed source window or exponent.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article p. 063503-7, Fig. 9(a,c) and Sec. III D. Band-integrated yield versus delay; plotted high-energy yield is rescaled for visibility, not a required absolute ratio."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Tie cutoff branches to physically correct field-free gaps, populations, trajectories, current components or equivalent discriminating band-access evidence.",
      "award_conditions": [
        "Tie cutoff branches to physically correct field-free gaps, populations, trajectories, current components or equivalent discriminating band-access evidence.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article pp. 063503-4–6, Fig. 3(a,b), Fig. 4(a–c), Fig. 6(a,c–e); Eqs. (12)–(14), p. 063503-4. Successive band access and interband gap identity. Gauge-correct populations, trajectories, gaps or equivalent discriminating evidence are accepted; no fixed band-population plot is required."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify genuine shaped-driver cutoff change beyond overall intensity rescaling from the candidate's matched comparison.",
      "award_conditions": [
        "Identify genuine shaped-driver cutoff change beyond overall intensity rescaling from the candidate's matched comparison."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O1. This identifies facts, not prerequisite half-point awards.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article p. 063503-4, Fig. 3(a–d) and Sec. III A. Matched spectral support, gap-organized plateaus and timing structure distinguish temporal-driver change from scalar rescaling."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify cutoff-emission-time dependence and stable timing-feature identity versus delay from reconstructible timing evidence, independently of cutoff-energy or yield credit.",
      "award_conditions": [
        "The candidate identifies the same resolved highest-energy emission feature across the delay cases.",
        "Timing evidence is reconstructible and adequate for the stated dependence; missing energy/yield work does not automatically erase a correct independent timing result."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.",
        "Timing is judged directly; missing energy or yield work does not automatically erase valid timing evidence."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article p. 063503-6, Fig. 7(a–d), caption and timing paragraphs. Cutoff-emission-time feature identity and delay dependence, independently of energy/yield credit. The printed exponent is a finite-model example, not a universal fitting target."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify the material band-access or transition branch responsible for the candidate's cutoff.",
      "award_conditions": [
        "Identify the material band-access or transition branch responsible for the candidate's cutoff."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O4. This identifies facts, not prerequisite half-point awards.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article pp. 063503-4–6, Fig. 3(a,b), Fig. 4(a–c), Fig. 6(a,c–e); Eqs. (12)–(14), p. 063503-4. Successive band access and interband gap identity. Gauge-correct populations, trajectories, gaps or equivalent discriminating evidence are accepted; no fixed band-population plot is required."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use the matched signal and band identification to conclude whether genuine temporal control, rather than only overall scaling, has been established.",
      "award_conditions": [
        "Use the matched signal and band identification to conclude whether genuine temporal control, rather than only overall scaling, has been established."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (I1 AND I3). This identifies facts, not prerequisite half-point awards.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article p. 063503-4, Fig. 3(a–d) and Sec. III A. Matched spectral support, gap-organized plateaus and timing structure distinguish temporal-driver change from scalar rescaling."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect vector potential to crystal-momentum motion in the identified delay/transition response.",
      "award_conditions": [
        "Connect vector potential to crystal-momentum motion in the identified delay/transition response."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (O2 AND I2 AND I3). This identifies facts, not prerequisite half-point awards.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article pp. 063503-1, 063503-4–6, crystal-momentum paragraph, Fig. 2(b), Fig. 6(b,c). Physical entailment of $k(t)=k_0+A(t)$ linking vector potential to band traversal."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect successive Zener access and interband recombination to the observed cutoff branches.",
      "award_conditions": [
        "Connect successive Zener access and interband recombination to the observed cutoff branches."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (O2 AND I2 AND I3). This identifies facts, not prerequisite half-point awards.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article pp. 063503-4–6, Fig. 3(a,b), Fig. 4(a–c), Fig. 6(a,c–e); Eqs. (12)–(14), p. 063503-4. Successive band access and interband gap identity. Gauge-correct populations, trajectories, gaps or equivalent discriminating evidence are accepted; no fixed band-population plot is required."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain the competition between enhanced band access and overdrive/trajectory dispersion using independently established timing and yield evidence.",
      "award_conditions": [
        "Explain the competition between enhanced band access and overdrive/trajectory dispersion using independently established timing and yield evidence."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (I2 AND O3). This identifies facts, not prerequisite half-point awards.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.",
        "The competing-access/dispersion explanation uses independently established timing and yield, not a mandatory award for the separately owned cutoff-energy output."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article p. 063503-7, Fig. 9(b,c), competition paragraph referring to Fig. 6(b–e). Enhanced access competes with overdrive, longer trajectories and dispersion; stronger vector potential alone need not increase cutoff or yield."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Quantify the functional cutoff-energy, timing and yield dependence and its supported delay domain, without turning a finite-domain exponent into a universal law.",
      "award_conditions": [
        "Quantify the functional cutoff-energy, timing and yield dependence and its supported delay domain, without turning a finite-domain exponent into a universal law."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (O2 AND I2 AND O3). This identifies facts, not prerequisite half-point awards.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article pp. 063503-6–8, Fig. 7(d), Fig. 9(b,c), Appendix Fig. 11(d). Distinct energy, timing and yield dependences; changed lattice gives a different timing exponent. Alternate lattice/driver calculations are context, not compulsory transfer outputs."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use discriminating band/observable evidence to distinguish a physical cutoff from a transform, ridge or representation artefact.",
      "award_conditions": [
        "Use discriminating band/observable evidence to distinguish a physical cutoff from a transform, ridge or representation artefact."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O4. This identifies facts, not prerequisite half-point awards.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article p. 063503-4, Fig. 3(a–d); pp. 063503-5–6, Fig. 6(a–e), Fig. 7(a–d); Eq. (11), p. 063503-3. Band/timing cross-representation checks can expose wrong ridges, incomplete currents or spectral artefacts. Conditional validation does not prescribe a particular FFT or Gabor procedure."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Limit conclusions to the coherent one-dimensional single-electron filled-valence thin-crystal model; do not infer macroscopic propagation, phase matching, many-body dephasing, experimental yield or universal band-structure scaling.",
      "award_conditions": [
        "Limit conclusions to the coherent one-dimensional single-electron filled-valence thin-crystal model; do not infer macroscopic propagation, phase matching, many-body dephasing, experimental yield or universal band-structure scaling."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article pp. 063503-2–3, Sec. II; p. 063503-5, Sec. III B; p. 063503-8, Sec. V. Coherent thin-crystal single-electron model scope. Dephasing-on, subcycle-driver and alternate-lattice examples are not required main outputs."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "V1",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Provide reconstructible matched cases, observable definitions and method/data scope commensurate with each claim.",
      "award_conditions": [
        "Provide reconstructible matched cases, observable definitions and method/data scope commensurate with each claim."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article p. 063503-3, text following Eq. (11); Figs. 7(a–d), p. 063503-6, and 9(a–c), p. 063503-7. Current-derived spectrum, yield integral and claim-relevant timing/cutoff definitions. Reconstructibility and common-scale reporting are task-defined; no source threshold/window is compulsory."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "If field/driver/delay binding, incomplete occupation/BZ integration, FFT leakage/normalization, wrong timing ridge, narrow-domain fitting, band identity or damping contamination creates a material threat, resolve it with discriminating evidence or an evidence-based restriction; otherwise record N/A.",
      "award_conditions": [
        "If field/driver/delay binding, incomplete occupation/BZ integration, FFT leakage/normalization, wrong timing ridge, narrow-domain fitting, band identity or damping contamination creates a material threat, resolve it with discriminating evidence or an evidence-based restriction; otherwise record N/A.",
        "When triggered, award only if claim-relevant discriminating evidence resolves the threat or an evidence-based restriction makes it immaterial; merely acknowledging an unresolved material threat is not positive validation credit. With no trigger, record N/A and retain the fixed 0.5 without claiming performed validation."
      ],
      "applicability_and_na": [
        "Applies only when the submitted method, data, anomaly or conclusion creates the concrete material risk described here. If untriggered, record not_applicable and retain the fixed 0.5 contribution; this is not evidence that validation was performed, and does not block RC4."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept consistent gauge, basis, propagator, current/dipole/acceleration radiation estimator, Fourier convention, cutoff/yield estimator and time-frequency or other timing representation preserving physical case, observable relation and claim-relevant ordering.",
        "Accept gaps, populations, trajectories, current decomposition or equally discriminating band evidence. Mesh, truncation, timestep, taper, Gabor width, threshold, interpolation, plot range and normalization are candidate choices; no source panel, exact delay list, yield window, weak floor or absolute spectral height is mandatory."
      ],
      "source_support": [
        "Article p. 063503-4, Fig. 3(a–d); pp. 063503-5–6, Fig. 6(a–e), Fig. 7(a–d); Eq. (11), p. 063503-3. Band/timing cross-representation checks can expose wrong ridges, incomplete currents or spectral artefacts. Conditional validation does not prescribe a particular FFT or Gabor procedure."
      ],
      "rc_relation": "Material-validation role: RC3 only for a triggered, unresolved threat to a central conclusion, with all six burden-of-proof elements established. N/A does not block RC4."
    }
  ],
  "case_scientific_rules": [
    "The main object is coherent U-off filled-valence HHG, not a decoherence-on calculation. For this model the main occupied sum is VB0+VB1; a diagnostic initialized only in VB1 is not the main spectrum.",
    "H0=p²/2+V(x); expand driven states in field-free Bloch bands with Hint=A(t)p in the velocity-gauge representation. With A(0)=0, A(t)=-integral_0^t E(t')dt'. Other constant/gauge choices are acceptable only with consistent momentum origin, initial occupation and observable.",
    "For an initial occupied band s, j_ks=-Re<psi_ks|p+A(t)|psi_ks>; j(t)=sum_(s in VB) integral_BZ j_ks dk. Sum coherent currents before forming S(omega)=|integral j(t) exp(i omega t)dt|². A source yield convention is Y_[omega1,omega2]=T^(-1)integral S d omega; equivalent declared definitions are accepted.",
    "The shaped vector potential is approximately unipolar over the main interaction interval, promotes successive BZ-boundary/Zener access to higher conduction bands, and supports greater high-energy emission than the matched reference. Source regions near 14,26,47,79 eV correspond to successive band differences, with the last weak region not a fixed completeness target.",
    "Delay controls cutoff energy, cutoff-emission time and declared yield; a source timing relation is t_peak proportional to t_d^(5/2), within its studied domain. The source's three example delays and exact optimum are not compulsory. A fitted law must have sufficient domain and stable identification of the same highest-energy cutoff feature, not the overall time maximum.",
    "Cutoff/yield can turn over at intermediate delay: increased vector potential promotes higher-band access but also boundary crossing, longer trajectories and dispersion. The source focus around 50 eV involves CB3−VB1; labels must be bound to the candidate's actual signal.",
    "Raw weak tails depend on endpoint/window policy; no hidden taper, 80–88 eV floor, exact weak peaks or absolute height. U-on damping construction, alternate-lattice transfer and author numerical settings are outside the required main task.",
    "Score exactly twenty fixed 0/0.5 material-core criteria. Do not import numerical score ranges or RC score caps. A valid run with no assessable scientific work receives score 0 and RC0 before criterion summation; assessable partial work and timeouts are graded on available evidence.",
    "Object existence, candidate presentation, candidate identification, physical inference and validation are different acts. Inspect every candidate-authored claim-bearing figure. A reference, rerender or examiner reconstruction can verify an object but cannot create missing candidate reasoning.",
    "When a material decision depends on feature resolution, fine structure, component relations, formula identity, representation equivalence or suspicious morphology, perform a focused applicable source/reference check. Establish model/observable/case/component, units, basis/gauge, normalization and transformations first; do not turn source-only display choices into new duties. A provisional score at least 9.0 or provisional RC4 requires a focused check of one central output and one principal-mechanism link. Reference verification is examiner-side, not a new candidate deliverable.",
    "In atomic units $H_0=p^2/2+V(x)$, $V(x)=-V_0[1+\\cos(2\\pi x/d)]$; $H_0\\phi_k^n=E_k^n\\phi_k^n$ and $i\\dot\\alpha_k^s=E_k^s\\alpha_k^s+A(t)\\sum_u p_k^{su}\\alpha_k^u$ (Eqs. (1), (4), (8)). $n,s,u$ label bands, $k$ is crystal momentum and $p_k^{su}$ the momentum matrix element.",
    "$E=-\\dot A$, with a consistently declared integration constant; $j_{ks}=-\\operatorname{Re}\\langle\\psi_{ks}|p+A|\\psi_{ks}\\rangle$ and $j(t)=\\sum_{s\\in\\mathrm{VB}}\\int_{\\mathrm{BZ}}j_{ks}(t)dk$ (Eqs. (10)–(11)). The coherent main object includes VB0+VB1; Fourier-transforming separate channel intensities and then summing is not equivalent to transforming the total current.",
    "$S(\\Omega)=|\\int j(t)e^{i\\Omega t}dt|^2$, $Y_{[\\Omega_1,\\Omega_2]}=T^{-1}\\int_{\\Omega_1}^{\\Omega_2}S(\\Omega)d\\Omega$; $T$ is the analyzed pulse duration and the integration band and window must be declared. Cutoff emission time belongs to the same resolved high-energy feature, not the overall time maximum. Equivalent radiation/timing estimators are accepted with consistent mappings.",
    "The semiclassical relation $k(t)=k_0+A(t)$ and emitted interband energy $\\Omega_{mn}(t)=E_m[k(t)]-E_n[k(t)]$ (with $\\hbar=1$) explain the band-access/cutoff mapping; a trajectory diagnostic is not a substitute for the filled-valence quantum current. Timing exponents and optimum delays are domain- and band-structure-dependent."
  ],
  "closure_requirements": {
    "RC0": [
      "The central physical object is absent or materially invalid. Establish this scientific fact independently of atomic credit; a local notation or presentation weakness is not itself RC0.",
      "(F1 AND F2 AND F3): Instantiate the stated periodic potential, reference and shaped drivers, consistent field/vector-potential convention, wavelength/intensity/duration/phase and delay binding, preserving matched comparison. Construct field-free bands, the occupied initial valence manifold and driven band equations or a gauge-equivalent computable route. Construct the coherent filled-valence full-BZ total current with correct occupied-band sum, BZ weights and current identity; the main case includes VB0+VB1 rather than only a diagnostic VB1 channel."
    ],
    "RC1": [
      "The central object exists, but a required indispensable component is absent or materially invalid. A failed presentation or overextended claim alone does not establish object absence or invalidity.",
      "(O1 AND O2 AND O3): Present matched conventional/shaped spectra with sufficient domain to resolve the genuine cutoff-support and multiband/interband structure relation. Present a reconstructible delay-dependent cutoff-energy family over a domain sufficient to assess the stated control claim. Present yield versus delay with declared integration band/window and normalization, resolving its dependence/turnover within the claimed domain without requiring a fixed source window or exponent."
    ],
    "RC2": [
      "Required objects are scientifically valid, but a required principal mechanism or state-dependence inference is absent or incorrect. Reference evidence cannot provide omitted candidate reasoning.",
      "(M1 AND M2 AND M3 AND M4 AND M5): Use the matched signal and band identification to conclude whether genuine temporal control, rather than only overall scaling, has been established. Connect vector potential to crystal-momentum motion in the identified delay/transition response. Connect successive Zener access and interband recombination to the observed cutoff branches. Explain the competition between enhanced band access and overdrive/trajectory dispersion using independently established timing and yield evidence. Quantify the functional cutoff-energy, timing and yield dependence and its supported delay domain, without turning a finite-domain exponent into a universal law."
    ],
    "RC3": [
      "Required objects and principal mechanisms are established, but a concrete material validation or scope threat to a central conclusion remains unresolved.",
      "V2: If field/driver/delay binding, incomplete occupation/BZ integration, FFT leakage/normalization, wrong timing ridge, narrow-domain fitting, band identity or damping contamination creates a material threat, resolve it with discriminating evidence or an evidence-based restriction; otherwise record N/A.",
      "Before assigning RC3, establish all six elements: the concrete failure mode; its origin in the submitted method/data/conclusion; a fair recognizable scientific risk; the affected central conclusion; why the submitted evidence cannot discriminate or exclude it; and functionally equivalent remedies. Evidence-based restriction may remove unsupported breadth, but cannot repair an incorrect signal, absent component or missing mechanism."
    ],
    "RC4": [
      "Every indispensable and co-primary claim has all its nonempty required role slots closed; supporting claims do not independently determine overall RC. Preserve AND/OR branch logic shown above and use scientific gate outcomes, not atomic scores.",
      "No triggered material risk remains unresolved. Untriggered risk criteria recorded N/A do not block RC4 and do not establish validation evidence.",
      "Classify descriptively by the most severe applicable failed required role (lowest RC), without score ceilings or target distributions. A score/RC tension prompts scientific review, not forced adjustment."
    ]
  },
  "references": [
    {
      "citation": "Nivash R, Amol R. Holkundkar, and Jayendra N. Bandyopadhyay. 2023. *Temporal control of high-order harmonic cutoffs in periodic crystals*. *Physical Review A*, 108, 063503.",
      "url": "https://doi.org/10.1103/PhysRevA.108.063503",
      "scientific_scope": "Coherent filled-valence full-BZ total-current HHG: matched driver support, delay-controlled cutoff energy/time and yield, and band-access mechanisms. Dephasing-on, subcycle transfer and alternate-lattice studies are contextual only.",
      "anchors": [
        "R, Holkundkar and Bandyopadhyay (2023), article p. 063503-2, Eqs. (1)–(3), Fig. 2(a,b), p. 063503-3.",
        "Article pp. 063503-2–3, Fig. 1, Eqs. (4)–(11).",
        "Article p. 063503-3, text following Eq. (11); Figs. 7(a–d), p. 063503-6, and 9(a–c), p. 063503-7.",
        "Article p. 063503-4, Fig. 3(a–d) and Sec. III A.",
        "Article p. 063503-7, Fig. 9(a,b) and Sec. III D.",
        "Article p. 063503-7, Fig. 9(a,c) and Sec. III D.",
        "Article pp. 063503-4–6, Fig. 3(a,b), Fig. 4(a–c), Fig. 6(a,c–e); Eqs. (12)–(14), p. 063503-4.",
        "Article p. 063503-6, Fig. 7(a–d), caption and timing paragraphs.",
        "Article pp. 063503-1, 063503-4–6, crystal-momentum paragraph, Fig. 2(b), Fig. 6(b,c).",
        "Article p. 063503-7, Fig. 9(b,c), competition paragraph referring to Fig. 6(b–e).",
        "Article pp. 063503-6–8, Fig. 7(d), Fig. 9(b,c), Appendix Fig. 11(d).",
        "Article p. 063503-4, Fig. 3(a–d); pp. 063503-5–6, Fig. 6(a–e), Fig. 7(a–d); Eq. (11), p. 063503-3.",
        "Article pp. 063503-2–3, Sec. II; p. 063503-5, Sec. III B; p. 063503-8, Sec. V."
      ]
    }
  ]
}