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"case_id": "Case13",
"title": "Case13 — Nonadiabatic redshifts in high-order harmonic generation from solids",
"atoms": [
{
"criterion_id": "F1",
"dimension": "F",
"points": 0.5,
"scientific_requirement": "Establish the specified periodic potential and field-free k=0 valence-band-top central matter-system identity; local numbering or conversion defects matter only when they change that identity.",
"award_conditions": [
"The specified periodic potential and physical k=0 valence-top matter state are preserved; local numbering defects matter only if they change that state."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
"Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23656,23658, Secs.2-3, Eqs.(1),(2): periodic SAE potential, accelerated k(t), finite-pulse driver and emitted TDSE response; numerical construction refers to Guan et al. (2016), Sec.II, Eqs.(1)-(12)."
],
"rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "M1",
"dimension": "M",
"points": 0.5,
"scientific_requirement": "Use submitted band dispersion, populations/dynamics or equivalent evidence to connect plateau/cutoff ordering to successively higher conduction-band participation.",
"award_conditions": [
"Band dispersion/population or equivalent driven evidence explains successive higher-band plateau/cutoff ordering."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: all of: O1 (Correctly construct the Case-A driver and present a physically valid, reconstructible emitted spectrum exposing multi-region/plateau support, cutoff ordering and claim-sufficient global structure.); I1 (Explicitly identify principal Case-A plateaus/regions and cutoff ordering from submitted valid evidence; examiner reconstruction cannot supply identification.)",
"Preserve independently valid work in O2, I2, M2, M3, O3, O4, I3, I4, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23657-23659, Figs.1-3, Eq.(3): conduction-band gap differences and plateau cutoffs near 32,66,112 in flat-envelope Case A. Those scales are recognition anchors, not exact pixel/cutoff tolerances."
],
"rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "M2",
"dimension": "M",
"points": 0.5,
"scientific_requirement": "Explain the identified even/odd emitted response using candidate-presented time/k-space population symmetry or equivalent dynamical evidence.",
"award_conditions": [
"Candidate-presented population-symmetry or equivalent dynamical evidence explains identified even/odd response."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: all of: O2 (For the same correct Case-A driver, present an independently valid, sufficiently resolved and reconstructible parity aspect of the emitted response sufficient to assess material even/odd structure.); I2 (Explicitly identify the material parity family/even-order signal from submitted valid Case-A evidence without pre-awarding its physical mechanism.)",
"Preserve independently valid work in O1, I1, M1, O3, O4, I3, I4, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23659-23660, Fig.3 insets, Fig.4 and Sec.3.1: even/odd emitted structure and loss of half-cycle population symmetry during indirect multiband excitation; optional two-band control removes even-order contribution."
],
"rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "M3",
"dimension": "M",
"points": 0.5,
"scientific_requirement": "Explain why inversion symmetry of the coordinate potential alone does not guarantee an odd-only finite nonstationary response, connecting the judgment to submitted evidence.",
"award_conditions": [
"The candidate explains why coordinate inversion symmetry does not ensure odd-only finite nonstationary emission, with evidence-linked dynamical reasoning."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: all of: O2 (For the same correct Case-A driver, present an independently valid, sufficiently resolved and reconstructible parity aspect of the emitted response sufficient to assess material even/odd structure.); I2 (Explicitly identify the material parity family/even-order signal from submitted valid Case-A evidence without pre-awarding its physical mechanism.)",
"Preserve independently valid work in M2, O1, I1, M1, O3, O4, I3, I4, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23659-23660, Fig.3 insets, Fig.4 and Sec.3.1: even/odd emitted structure and loss of half-cycle population symmetry during indirect multiband excitation; optional two-band control removes even-order contribution."
],
"rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "M6",
"dimension": "M",
"points": 0.5,
"scientific_requirement": "Connect identified finite-pulse displacement to the effect of delayed higher-band emission on observable peaks rather than generic short-pulse description.",
"award_conditions": [
"The candidate links observed finite-pulse peak displacement to delayed higher-band emission rather than generic short-pulse language."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: all of: I3 (Explicitly identify peak-displacement direction and 10/15-cycle relative ordering from valid B/C evidence; spectral-region extension is independently assessed.); at least one of: M4 (Establish from presented dynamics the temporal/participation relation between stepwise higher-band population and high-order emission under finite pulses; data existence or examiner discovery cannot supply it.); M5 (Establish from presented timing/asymmetry or equivalent evidence that high-order emission favors the falling pulse; data existence or examiner discovery cannot supply it.)",
"Preserve independently valid work in I4, O1, O2, I1, I2, M1, M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23660-23661, Sec.3.2 and Figs.5-6: 10-cycle versus 15-cycle finite cosine-squared pulse spectra, stronger/earlier high-order redshift at shorter duration and later higher-region shift at longer duration."
],
"rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "M7",
"dimension": "M",
"points": 0.5,
"scientific_requirement": "Explain how the weaker instantaneous falling-pulse field causes delayed higher-band emission to redshift.",
"award_conditions": [
"The weaker falling-pulse field at delayed emission explains redshift through an actual model-to-signal chain."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: M6 (Connect identified finite-pulse displacement to the effect of delayed higher-band emission on observable peaks rather than generic short-pulse description.)",
"Preserve independently valid work in I4, M4, M5, O1, O2, I1, I2, M1, M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23658,23660,23662, stepwise-excitation discussion, Fig.4, Eqs.(4),(5) and Fig.7: delayed higher-band population/emission favors the falling pulse, whose weaker instantaneous field yields redshift. Asymmetry coefficient is a canonical diagnostic, not mandatory."
],
"rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "M8",
"dimension": "M",
"points": 0.5,
"scientific_requirement": "Use the established delayed-emission/redshift mechanism to explain 10/15-cycle and main spectral-region ordering; incomplete closure of either relation does not erase independent identification of the other.",
"award_conditions": [
"The established delay/redshift mechanism explains 10/15-cycle ordering and spectral-region dependence, preserving independently supported parts."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: all of: I3 (Explicitly identify peak-displacement direction and 10/15-cycle relative ordering from valid B/C evidence; spectral-region extension is independently assessed.); I4 (Explicitly identify the main spectral-region dependence of displacement from valid B/C evidence, independently of displacement direction and duration ordering.); M6 (Connect identified finite-pulse displacement to the effect of delayed higher-band emission on observable peaks rather than generic short-pulse description.); M7 (Explain how the weaker instantaneous falling-pulse field causes delayed higher-band emission to redshift.)",
"Preserve independently valid work in M4, M5, O1, O2, I1, I2, M1, M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23660-23661, Sec.3.2 and Figs.5-6: 10-cycle versus 15-cycle finite cosine-squared pulse spectra, stronger/earlier high-order redshift at shorter duration and later higher-region shift at longer duration."
],
"rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "F2",
"dimension": "F",
"points": 0.5,
"scientific_requirement": "Construct a standard emitted HHG observable from the propagated state in a declared equivalent TDSE representation, treating Fourier/sign/frequency-weighting identity wherever it changes the claim.",
"award_conditions": [
"A declared equivalent TDSE representation yields the emitted HHG observable with transform/sign/frequency identity correct wherever it affects claims."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
"Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23656,23658, Secs.2-3, Eqs.(1),(2): periodic SAE potential, accelerated k(t), finite-pulse driver and emitted TDSE response; numerical construction refers to Guan et al. (2016), Sec.II, Eqs.(1)-(12)."
],
"rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "O1",
"dimension": "O",
"points": 0.5,
"scientific_requirement": "Correctly construct the Case-A driver and present a physically valid, reconstructible emitted spectrum exposing multi-region/plateau support, cutoff ordering and claim-sufficient global structure.",
"award_conditions": [
"The correct flat-envelope Case-A driver yields a reconstructible spectrum resolving material multi-region/plateau support and cutoff ordering.",
"Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: all of: F1 (Establish the specified periodic potential and field-free k=0 valence-band-top central matter-system identity; local numbering or conversion defects matter only when they change that identity.); F2 (Construct a standard emitted HHG observable from the propagated state in a declared equivalent TDSE representation, treating Fourier/sign/frequency-weighting identity wherever it changes the claim.)",
"Preserve independently valid work in O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23657-23659, Figs.1-3, Eq.(3): conduction-band gap differences and plateau cutoffs near 32,66,112 in flat-envelope Case A. Those scales are recognition anchors, not exact pixel/cutoff tolerances."
],
"rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
},
{
"criterion_id": "O2",
"dimension": "O",
"points": 0.5,
"scientific_requirement": "For the same correct Case-A driver, present an independently valid, sufficiently resolved and reconstructible parity aspect of the emitted response sufficient to assess material even/odd structure.",
"award_conditions": [
"The correct Case-A driver separately yields valid, sufficiently resolved parity evidence for material even/odd emission; plateau presentation alone does not supply it.",
"Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: all of: F1 (Establish the specified periodic potential and field-free k=0 valence-band-top central matter-system identity; local numbering or conversion defects matter only when they change that identity.); F2 (Construct a standard emitted HHG observable from the propagated state in a declared equivalent TDSE representation, treating Fourier/sign/frequency-weighting identity wherever it changes the claim.)",
"Preserve independently valid work in O1, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23659-23660, Fig.3 insets, Fig.4 and Sec.3.1: even/odd emitted structure and loss of half-cycle population symmetry during indirect multiband excitation; optional two-band control removes even-order contribution."
],
"rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
},
{
"criterion_id": "O3",
"dimension": "O",
"points": 0.5,
"scientific_requirement": "Correctly construct the Case-B driver and present a physically valid, reconstructible and adequate emitted spectrum of its high-order structure.",
"award_conditions": [
"The correct 10-cycle Case-B finite driver yields a valid reconstructible high-order emission spectrum.",
"Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: all of: F1 (Establish the specified periodic potential and field-free k=0 valence-band-top central matter-system identity; local numbering or conversion defects matter only when they change that identity.); F2 (Construct a standard emitted HHG observable from the propagated state in a declared equivalent TDSE representation, treating Fourier/sign/frequency-weighting identity wherever it changes the claim.)",
"Preserve independently valid work in O1, O2, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23660-23661, Sec.3.2 and Figs.5-6: 10-cycle versus 15-cycle finite cosine-squared pulse spectra, stronger/earlier high-order redshift at shorter duration and later higher-region shift at longer duration."
],
"rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
},
{
"criterion_id": "O4",
"dimension": "O",
"points": 0.5,
"scientific_requirement": "Correctly construct the Case-C driver and present a physically valid, reconstructible and adequate emitted spectrum of its high-order structure.",
"award_conditions": [
"The correct 15-cycle Case-C finite driver yields a valid reconstructible high-order emission spectrum.",
"Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: all of: F1 (Establish the specified periodic potential and field-free k=0 valence-band-top central matter-system identity; local numbering or conversion defects matter only when they change that identity.); F2 (Construct a standard emitted HHG observable from the propagated state in a declared equivalent TDSE representation, treating Fourier/sign/frequency-weighting identity wherever it changes the claim.)",
"Preserve independently valid work in O1, O2, O3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23660-23661, Sec.3.2 and Figs.5-6: 10-cycle versus 15-cycle finite cosine-squared pulse spectra, stronger/earlier high-order redshift at shorter duration and later higher-region shift at longer duration."
],
"rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
},
{
"criterion_id": "I1",
"dimension": "I",
"points": 0.5,
"scientific_requirement": "Explicitly identify principal Case-A plateaus/regions and cutoff ordering from submitted valid evidence; examiner reconstruction cannot supply identification.",
"award_conditions": [
"The candidate identifies Case-A principal plateaus/regions and cutoff ordering from their presented evidence."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: O1 (Correctly construct the Case-A driver and present a physically valid, reconstructible emitted spectrum exposing multi-region/plateau support, cutoff ordering and claim-sufficient global structure.)",
"Preserve independently valid work in I2, I3, I4, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23657-23659, Figs.1-3, Eq.(3): conduction-band gap differences and plateau cutoffs near 32,66,112 in flat-envelope Case A. Those scales are recognition anchors, not exact pixel/cutoff tolerances."
],
"rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "I2",
"dimension": "I",
"points": 0.5,
"scientific_requirement": "Explicitly identify the material parity family/even-order signal from submitted valid Case-A evidence without pre-awarding its physical mechanism.",
"award_conditions": [
"The candidate identifies material Case-A even/odd content without being awarded its mechanism merely for observing peaks."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: O2 (For the same correct Case-A driver, present an independently valid, sufficiently resolved and reconstructible parity aspect of the emitted response sufficient to assess material even/odd structure.)",
"Preserve independently valid work in I1, I3, I4, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23659-23660, Fig.3 insets, Fig.4 and Sec.3.1: even/odd emitted structure and loss of half-cycle population symmetry during indirect multiband excitation; optional two-band control removes even-order contribution."
],
"rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "I3",
"dimension": "I",
"points": 0.5,
"scientific_requirement": "Explicitly identify peak-displacement direction and 10/15-cycle relative ordering from valid B/C evidence; spectral-region extension is independently assessed.",
"award_conditions": [
"The candidate identifies B/C redshift direction and duration ordering from actual valid evidence, independently of spectral-region extension."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: all of: O3 (Correctly construct the Case-B driver and present a physically valid, reconstructible and adequate emitted spectrum of its high-order structure.); O4 (Correctly construct the Case-C driver and present a physically valid, reconstructible and adequate emitted spectrum of its high-order structure.)",
"Preserve independently valid work in O1, O2, I1, I2, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23660-23661, Sec.3.2 and Figs.5-6: 10-cycle versus 15-cycle finite cosine-squared pulse spectra, stronger/earlier high-order redshift at shorter duration and later higher-region shift at longer duration."
],
"rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "I4",
"dimension": "I",
"points": 0.5,
"scientific_requirement": "Explicitly identify the main spectral-region dependence of displacement from valid B/C evidence, independently of displacement direction and duration ordering.",
"award_conditions": [
"The candidate separately identifies spectral-region dependence of B/C displacement from valid presented evidence."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: all of: O3 (Correctly construct the Case-B driver and present a physically valid, reconstructible and adequate emitted spectrum of its high-order structure.); O4 (Correctly construct the Case-C driver and present a physically valid, reconstructible and adequate emitted spectrum of its high-order structure.)",
"Preserve independently valid work in O1, O2, I1, I2, I3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23660-23661, Sec.3.2 and Figs.5-6: 10-cycle versus 15-cycle finite cosine-squared pulse spectra, stronger/earlier high-order redshift at shorter duration and later higher-region shift at longer duration."
],
"rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "M4",
"dimension": "M",
"points": 0.5,
"scientific_requirement": "Establish from presented dynamics the temporal/participation relation between stepwise higher-band population and high-order emission under finite pulses; data existence or examiner discovery cannot supply it.",
"award_conditions": [
"Presented dynamics establish stepwise higher-band participation and its temporal relation to high-order emission, not merely the existence of arrays."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
"Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23658,23660,23662, stepwise-excitation discussion, Fig.4, Eqs.(4),(5) and Fig.7: delayed higher-band population/emission favors the falling pulse, whose weaker instantaneous field yields redshift. Asymmetry coefficient is a canonical diagnostic, not mandatory."
],
"rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "M5",
"dimension": "M",
"points": 0.5,
"scientific_requirement": "Establish from presented timing/asymmetry or equivalent evidence that high-order emission favors the falling pulse; data existence or examiner discovery cannot supply it.",
"award_conditions": [
"Presented timing/asymmetry or equivalent evidence establishes that relevant high-order emission favors the falling pulse."
],
"applicability_and_na": [
"This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
],
"dependencies": [
"Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
"Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23658,23660,23662, stepwise-excitation discussion, Fig.4, Eqs.(4),(5) and Fig.7: delayed higher-band population/emission favors the falling pulse, whose weaker instantaneous field yields redshift. Asymmetry coefficient is a canonical diagnostic, not mandatory."
],
"rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "V1",
"dimension": "V",
"points": 0.5,
"scientific_requirement": "Address a concrete material threat to the actual central conclusion, whether numerical/display failure or physical alternative, with discriminating evidence or an honest restriction; no fixed source control/check is required.",
"award_conditions": [
"A concrete triggered numerical/display/physical alternative is excluded with capable evidence or a justified claim restriction; no fixed control is mandatory."
],
"applicability_and_na": [
"Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
"If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
],
"dependencies": [
"Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
"Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23656,23658,23660,23662, SAE model, finite-pulse interpretation and conclusion. Actual alternative discrimination and model/range restrictions are task obligations; coordinate inversion alone is not evidence of dynamical half-cycle symmetry."
],
"rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
},
{
"criterion_id": "V2",
"dimension": "V",
"points": 0.5,
"scientific_requirement": "Restrict conclusions to the specified one-dimensional SAE periodic model, established pulse subset and covered spectral domain, without absolute-yield or universal-material claims; honest restriction is not another penalty for a missing branch.",
"award_conditions": [
"The conclusion stays within the specified 1D SAE periodic model, established pulse subset and covered emission domain without universal/absolute-yield claims."
],
"applicability_and_na": [
"This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
],
"dependencies": [
"Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
"Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
],
"equivalent_evidence": [
"Coordinate-space, Bloch, gauge, split-operator and other TDSE routes are accepted if they preserve the same potential, k=0 valence-top state and emitted observable.",
"Current, dipole-velocity and acceleration spectra are accepted after handling transform relations and frequency weighting wherever they affect plateau, parity, shift or relative structure. Common normalization/log displays are accepted; peak-frequency similarity alone does not establish equivalence.",
"Band populations, resolved currents, time-frequency maps, rising/falling measures, band-removal interventions and comparable diagnostics are accepted by their ability to distinguish the claimed mechanism; no named wavelet/asymmetry coefficient is required."
],
"source_support": [
"Jia et al. (2017), article pp.23656,23658,23660,23662, SAE model, finite-pulse interpretation and conclusion. Actual alternative discrimination and model/range restrictions are task obligations; coordinate inversion alone is not evidence of dynamical half-cycle symmetry."
],
"rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
}
],
"case_scientific_rules": [
"Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
"Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
"For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
"Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
"Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
"Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
"Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
"Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
"Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
"Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
"A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
"The canonical potential is V(x)=-0.37[1+cos(2pi x/8)] with H=p^2/2+V+xE. Band 2 is only a source-cited finite-box label for the physical k=0 valence-top state.",
"The flat-envelope baseline has multiple plateaus with principal semiclassical cutoff scales near orders 32,66,112; exact arrows, crops and pointwise cutoff tolerances are not targets.",
"Both parities can occur despite coordinate inversion symmetry because indirect multiband excitation breaks half-cycle time/k-space population symmetry. A two-band control is canonical but not mandatory; observing even peaks alone does not establish their origin.",
"Finite cosine-squared pulses have weaker even-order content, broadened higher peaks and nonadiabatic redshifts. At 10 cycles shifts emerge earlier/stronger, around orders above 60 in the source, while at 15 cycles the second-region shift is weaker and clear effects occur later in the third region.",
"Delayed stepwise population/emission of higher bands favors the falling pulse, where the instantaneous driver is weaker than in the preceding cycle. This explains duration and region dependence; a generic short-pulse statement does not close the chain.",
"Case-A plateau and parity evidence, I3 direction/duration ordering and I4 spectral-region extension are separately owned; a defect in one must not erase the independent other aspect.",
"Finite-pulse total-current references establish shift direction/ordering, not weak even-order amplitudes, complete populations or the source asymmetry coefficient. A material decision on those structures requires appropriate source evidence and submitted data, not an out-of-scope reproduction.",
"No source solver, window, peak estimator, exact intensity, cross-panel absolute scale or numerical precision establishes physical certainty.",
"In the canonical length-gauge route,",
"$$\nH(t)=\\frac{p^2}{2}+V(x)+xE(t),\n\\qquad\nV(x)=-0.37\\left[1+\\cos\\left(\\frac{2\\pi x}{8}\\right)\\right].\n$$",
"The initial state is the field-free $k=0$ state at the top of the valence band (band 2 in the source-cited finite-box ordering). The canonical source method expands the state in a B-spline basis, propagates with Crank-Nicolson, evaluates $j(t)=-\\langle p\\rangle$, and Fourier analyzes the current after a Hanning window. These implementation choices are not mandatory. A velocity-gauge, split-operator, Bloch-basis or other route may earn full credit if it preserves the same model, initial state and emitted observable.",
"A current-, dipole-velocity- or dipole-acceleration-form spectrum is accepted when its transform relation and any frequency weighting are handled wherever they could change a plateau, parity, peak-shift or relative-structure claim. Common normalization and log display changes are equivalent. A spectrum of the driving field, norm loss or a band population alone is not the central emitted observable.",
"Band populations, band-resolved currents, time-frequency emission maps, rising/falling-half measures, band-removal interventions and comparable diagnostics are accepted by function. No one diagnostic or control is required by name. The evidence must be capable of distinguishing the mechanism actually claimed.",
"The flat-envelope Case A has several plateau regions. The source's semiclassical band-gap estimates place the principal cutoffs near harmonic orders 32, 66 and 112 for the first three conduction bands. The exact source arrows and a pointwise cutoff tolerance are not grading targets; the large-scale multi-region structure and its consistency with the calculated band dispersion are.",
"The resolved Case-A spectrum contains even as well as odd harmonic orders. The source associates this with loss of half-cycle symmetry in higher-band populations and electron motion after indirect multiband excitation. Its two-band calculation removes the even-order contribution. A functionally equivalent causal distinction receives full credit; merely observing even peaks does not establish their origin.",
"In finite cosine-squared pulses, even-order content is substantially weaker than in the abrupt flat-envelope case. Higher-order peaks broaden, and the pulse-duration comparison contains a nonadiabatic displacement of spectral peaks toward lower harmonic order. For 10 cycles the source reports gradual displacement above approximately order 60 and a larger effect at higher plateaus. For 15 cycles the second-plateau displacement is much weaker and the clear effect begins later, in the third-plateau region.",
"The source mechanism is delayed stepwise population and emission from higher conduction bands. Emission weighted toward the falling part of the pulse experiences a weaker driver than the preceding cycle. The source's rising/falling asymmetry coefficient tracks the spectral displacement. The coefficient and its wavelet implementation are canonical evidence, not a required student diagnostic.",
"The conclusion is model-level. It does not establish a material-specific experimental yield, a universal solid-state mechanism, or an absolute spectrum normalization.",
"For M1/M4-M8, article pp.23656-23658, Eq.(1),(3), the semiclassical interpretation uses $k(t)=k_0+A(t)$ and $N_b\\omega\\simeq\\varepsilon_{C_b}(k_{\\max})-\\varepsilon_v(k_{\\max})$, not the gas-phase $I_p+3.17U_p$ rule. The optional falling/rising diagnostic (article pp.23660,23662, Eqs.(4),(5)) is\n$$A(N)=\\frac{S_f-S_r}{S_f+S_r},\\quad\nS_f=\\int_{\\tau/2}^{\\tau}g(N\\omega,t)dt,\\quad S_r=\\int_0^{\\tau/2}g(N\\omega,t)dt.$$\nHere $g$ is a declared time-local harmonic signal. This coefficient is meaningful only with nonzero resolved denominator and correctly bound pulse centre; equivalent timing, intervention or pulse-segment evidence may replace it. The spectral parity and displacement aspects remain independently scored; a total-current redshift reference cannot establish uncomputed population symmetry or weak even-order amplitude."
],
"closure_requirements": {
"RC0": [
"The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
"Required indispensable claim CL1, central physical object: all of: F1 (Establish the specified periodic potential and field-free k=0 valence-band-top central matter-system identity; local numbering or conversion defects matter only when they change that identity.); F2 (Construct a standard emitted HHG observable from the propagated state in a declared equivalent TDSE representation, treating Fourier/sign/frequency-weighting identity wherever it changes the claim.). Judge the role-specific failure facts, not the corresponding atom scores."
],
"RC1": [
"With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
"Required co primary claim CL2, indispensable material component: all of: O1 (Correctly construct the Case-A driver and present a physically valid, reconstructible emitted spectrum exposing multi-region/plateau support, cutoff ordering and claim-sufficient global structure.); O2 (For the same correct Case-A driver, present an independently valid, sufficiently resolved and reconstructible parity aspect of the emitted response sufficient to assess material even/odd structure.). Judge the role-specific failure facts, not the corresponding atom scores.",
"Required co primary claim CL3, indispensable material component: O3 (Correctly construct the Case-B driver and present a physically valid, reconstructible and adequate emitted spectrum of its high-order structure.). Judge the role-specific failure facts, not the corresponding atom scores.",
"Required co primary claim CL4, indispensable material component: O4 (Correctly construct the Case-C driver and present a physically valid, reconstructible and adequate emitted spectrum of its high-order structure.). Judge the role-specific failure facts, not the corresponding atom scores."
],
"RC2": [
"With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
"Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M1 (Use submitted band dispersion, populations/dynamics or equivalent evidence to connect plateau/cutoff ordering to successively higher conduction-band participation.); M2 (Explain the identified even/odd emitted response using candidate-presented time/k-space population symmetry or equivalent dynamical evidence.); M3 (Explain why inversion symmetry of the coordinate potential alone does not guarantee an odd-only finite nonstationary response, connecting the judgment to submitted evidence.). Judge the role-specific failure facts, not the corresponding atom scores.",
"Required co primary claim CL5, principal mechanism or commissioned conclusion: all of: M4 (Establish from presented dynamics the temporal/participation relation between stepwise higher-band population and high-order emission under finite pulses; data existence or examiner discovery cannot supply it.); M5 (Establish from presented timing/asymmetry or equivalent evidence that high-order emission favors the falling pulse; data existence or examiner discovery cannot supply it.); M6 (Connect identified finite-pulse displacement to the effect of delayed higher-band emission on observable peaks rather than generic short-pulse description.); M7 (Explain how the weaker instantaneous falling-pulse field causes delayed higher-band emission to redshift.); M8 (Use the established delayed-emission/redshift mechanism to explain 10/15-cycle and main spectral-region ordering; incomplete closure of either relation does not erase independent identification of the other.). Judge the role-specific failure facts, not the corresponding atom scores."
],
"RC3": [
"With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
"Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
"Required co primary claim CL6, material validation/scope: V1 (Address a concrete material threat to the actual central conclusion, whether numerical/display failure or physical alternative, with discriminating evidence or an honest restriction; no fixed source control/check is required.). Judge the role-specific failure facts, not the corresponding atom scores."
],
"RC4": [
"All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
"Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
"Close CL1 central physical object: all of: F1 (Establish the specified periodic potential and field-free k=0 valence-band-top central matter-system identity; local numbering or conversion defects matter only when they change that identity.); F2 (Construct a standard emitted HHG observable from the propagated state in a declared equivalent TDSE representation, treating Fourier/sign/frequency-weighting identity wherever it changes the claim.).",
"Close CL2 indispensable material component: all of: O1 (Correctly construct the Case-A driver and present a physically valid, reconstructible emitted spectrum exposing multi-region/plateau support, cutoff ordering and claim-sufficient global structure.); O2 (For the same correct Case-A driver, present an independently valid, sufficiently resolved and reconstructible parity aspect of the emitted response sufficient to assess material even/odd structure.).",
"Close CL2 principal mechanism or commissioned conclusion: all of: M1 (Use submitted band dispersion, populations/dynamics or equivalent evidence to connect plateau/cutoff ordering to successively higher conduction-band participation.); M2 (Explain the identified even/odd emitted response using candidate-presented time/k-space population symmetry or equivalent dynamical evidence.); M3 (Explain why inversion symmetry of the coordinate potential alone does not guarantee an odd-only finite nonstationary response, connecting the judgment to submitted evidence.).",
"Close CL3 indispensable material component: O3 (Correctly construct the Case-B driver and present a physically valid, reconstructible and adequate emitted spectrum of its high-order structure.).",
"Close CL4 indispensable material component: O4 (Correctly construct the Case-C driver and present a physically valid, reconstructible and adequate emitted spectrum of its high-order structure.).",
"Close CL5 principal mechanism or commissioned conclusion: all of: M4 (Establish from presented dynamics the temporal/participation relation between stepwise higher-band population and high-order emission under finite pulses; data existence or examiner discovery cannot supply it.); M5 (Establish from presented timing/asymmetry or equivalent evidence that high-order emission favors the falling pulse; data existence or examiner discovery cannot supply it.); M6 (Connect identified finite-pulse displacement to the effect of delayed higher-band emission on observable peaks rather than generic short-pulse description.); M7 (Explain how the weaker instantaneous falling-pulse field causes delayed higher-band emission to redshift.); M8 (Use the established delayed-emission/redshift mechanism to explain 10/15-cycle and main spectral-region ordering; incomplete closure of either relation does not erase independent identification of the other.).",
"Close CL6 material validation/scope: V1 (Address a concrete material threat to the actual central conclusion, whether numerical/display failure or physical alternative, with discriminating evidence or an honest restriction; no fixed source control/check is required.).",
"Supporting claim CL7 is separately scored but does not determine overall closure: Restrict conclusions to the specified one-dimensional SAE periodic model, established pulse subset and covered spectral domain, without absolute-yield or universal-material claims; honest restriction is not another penalty for a missing branch."
]
},
"references": [
{
"citation": "Guang-Rui Jia, Xiao-Huan Huang, and Xue-Bin Bian. 2017. *Nonadiabatic redshifts in high-order harmonic generation from solids*. *Optics Express*, 25, 23654-23662.",
"url": "https://doi.org/10.1364/OE.25.023654",
"scientific_scope": "Nonadiabatic redshifts in high-order harmonic generation from solids",
"anchors": [
"Jia et al. (2017), article pp.23656,23658, Secs.2-3, Eqs.(1),(2): periodic SAE potential, accelerated k(t), finite-pulse driver and emitted TDSE response; numerical construction refers to Guan et al. (2016), Sec.II, Eqs.(1)-(12).",
"Jia et al. (2017), article pp.23657-23659, Figs.1-3, Eq.(3): conduction-band gap differences and plateau cutoffs near 32,66,112 in flat-envelope Case A. Those scales are recognition anchors, not exact pixel/cutoff tolerances.",
"Jia et al. (2017), article pp.23659-23660, Fig.3 insets, Fig.4 and Sec.3.1: even/odd emitted structure and loss of half-cycle population symmetry during indirect multiband excitation; optional two-band control removes even-order contribution.",
"Jia et al. (2017), article pp.23660-23661, Sec.3.2 and Figs.5-6: 10-cycle versus 15-cycle finite cosine-squared pulse spectra, stronger/earlier high-order redshift at shorter duration and later higher-region shift at longer duration.",
"Jia et al. (2017), article pp.23658,23660,23662, stepwise-excitation discussion, Fig.4, Eqs.(4),(5) and Fig.7: delayed higher-band population/emission favors the falling pulse, whose weaker instantaneous field yields redshift. Asymmetry coefficient is a canonical diagnostic, not mandatory.",
"Jia et al. (2017), article pp.23656,23658,23660,23662, SAE model, finite-pulse interpretation and conclusion. Actual alternative discrimination and model/range restrictions are task obligations; coordinate inversion alone is not evidence of dynamical half-cycle symmetry."
]
},
{
"citation": "Zhong Guan, Xiao-Xin Zhou, and Xue-Bin Bian. 2016. *High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses*. *Physical Review A*, 93, 033852.",
"url": "https://doi.org/10.1103/PhysRevA.93.033852",
"scientific_scope": "Source-cited periodic-potential TDSE method, physical k=0 band-2 initial-state identity and current-derived HHG observable.",
"anchors": [
"Sections II-III, Eqs. (1)-(8); p. 2: k=0 band-2 initial state and Eqs. (7)-(8)."
]
}
]
}
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