| { |
| "case_id": "Case38", |
| "title": "Valley-resolved and Brillouin-zone-integrated topological high-harmonic emission", |
| "atoms": [ |
| { |
| "criterion_id": "F1", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Correctly instantiate the corrected visible primitive/neighbor vectors, Haldane Hamiltonian, shared parameters, two t2 cases, finite pulse, Gamma-M polarization and lower-band initial state.", |
| "award_conditions": [ |
| "The primitive vectors and nearest/next-nearest-neighbour vectors are mutually consistent with the given Hamiltonian, including its signs and hopping handedness.", |
| "Use $a=2.683$, $M=0.026$, $t_1=-0.1$, $t_2=-0.0013i$ and $t_2=-0.0087i$, and the stated five-cycle pulse with $A_0=0.1$ and $\\omega=0.0075$; identify the two cases and the driver direction.", |
| "Establish lower-band starting states in the appropriate crystal-momentum representation; judge material physical identity, not local equivalent notation." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Judged directly from the submitted formulation, report, method, data or claim, as applicable; no prerequisite award.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "A reciprocal-cell, basis-gauge or coordinate convention is accepted when lattice orientation, drive direction, hopping handedness, valley mapping, complex channels and conclusions are transformed consistently. Swapping valley labels alone is not a repair for an inconsistent corner/drive identity.", |
| "A different reciprocal basis or translated/swapped valley labels is acceptable only with a consistent global physical mapping. Mixing incompatible primitive and neighbour vectors is not equivalent." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer, Phys. Rev. A 102, 053112 (2020), p. 053112-7, Eqs. (68)-(71) and Fig. 2; p. 053112-11, Appendix B, Eqs. (B1)-(B8); pulse Eq. (67), p. 053112-6." |
| ], |
| "rc_relation": "Central-object role in the model-to-observable claim. RC0 is triggered only by an absent or materially invalid central physical identity, evaluated independently of the 0/0.5 award; a local presentation/convention weakness or valid physical equivalent does not itself trigger RC0." |
| }, |
| { |
| "criterion_id": "F2", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Establish Peierls-shift driven two-level propagation and construct physically consistent parallel/perpendicular velocity or an equivalent radiation observable from the propagated state.", |
| "award_conditions": [ |
| "Propagate $i\\dot C(\\mathbf k,t)=H[\\mathbf k+\\mathbf A(t)]C(\\mathbf k,t)$ from the lower band.", |
| "Construct $v_j(\\mathbf k,t)=C^\\dagger\\partial_{k_j}H[\\mathbf k+\\mathbf A(t)]C$ for the two physical response directions, or demonstrate an equivalent current/radiation construction.", |
| "The observable must belong to the specified model and drive; a computable but different model does not meet this item." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires the actual model, cases and pulse identity established in F1.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "A reciprocal-cell, basis-gauge or coordinate convention is accepted when lattice orientation, drive direction, hopping handedness, valley mapping, complex channels and conclusions are transformed consistently. Swapping valley labels alone is not a repair for an inconsistent corner/drive identity.", |
| "Any accurate propagator is accepted. Consistently transformed basis-gauge implementations and velocity/current/acceleration routes are accepted when the physical radiation and complex channel relation agree.", |
| "The analytical velocity formulation of Eq. (54), or the negligible-depletion reduction Eq. (57) within its justified validity domain, may replace direct state propagation; a second solver is not required." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), p. 053112-3, Eqs. (25)-(28); Eq. (54), p. 053112-4; Eq. (57), p. 053112-5." |
| ], |
| "rc_relation": "Central-object role in the model-to-observable claim. RC0 is triggered only by an absent or materially invalid central physical identity, evaluated independently of the 0/0.5 award; a local presentation/convention weakness or valid physical equivalent does not itself trigger RC0." |
| }, |
| { |
| "criterion_id": "F3", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Strictly distinguish the fixed K/K' single-point response from the coherent full-BZ velocity integral of a completely occupied lower band, with correct BZ weights, initial ensemble and case/channel binding.", |
| "award_conditions": [ |
| "Fixed $K$ and $K'$ initial-state responses remain single-$\\mathbf k$ objects, not BZ-integrated surrogates.", |
| "The filled-band response coherently integrates occupied lower-band velocities over the complete BZ with correct weights and ensemble identity before radiation yield is formed.", |
| "Keep the case, channel, initial-state and BZ-sampling mapping auditable." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires the same valid two-direction observable established in F2.", |
| "A full-BZ ensemble/weighting defect affects the integrated object and its truly dependent claims, not the independently valid fixed-$K$/$K'$ outputs, identifications or mechanisms.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "A reciprocal-cell, basis-gauge or coordinate convention is accepted when lattice orientation, drive direction, hopping handedness, valley mapping, complex channels and conclusions are transformed consistently. Swapping valley labels alone is not a repair for an inconsistent corner/drive identity.", |
| "Equivalent reciprocal-cell tilings, quadrature schemes and common current normalizations are accepted if they preserve complete lower-band occupation and coherent summation. No particular mesh density is prescribed." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Eq. (28), p. 053112-3; occupied-band coherence discussion, p. 053112-5; integrated discussion, p. 053112-8; Fig. 5(a,b), p. 053112-9." |
| ], |
| "rc_relation": "Central-object role in the model-to-observable claim. RC0 is triggered only by an absent or materially invalid central physical identity, evaluated independently of the 0/0.5 award; a local presentation/convention weakness or valid physical equivalent does not itself trigger RC0." |
| }, |
| { |
| "criterion_id": "F4", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Define reconstructible two-direction complex HHG amplitudes, yield, relative phase/helicity, common normalization and validity rules for weak/cancelled components.", |
| "award_conditions": [ |
| "Give a consistent complex-amplitude construction for both radiation channels and define yield and relative phase, for example $Y_j\\propto|\\mathcal A_j|^2$ and $\\Delta\\phi=\\arg\\mathcal A_\\parallel-\\arg\\mathcal A_\\perp$.", |
| "Document Fourier/derivative and common normalization conventions sufficiently to reconstruct the data-to-report mapping.", |
| "Interpret helicity only where both complex components are resolved; state an auditable weak/cancelled-component treatment without claiming certainty for an undefined phase." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires the valid two-direction radiation observable of F2.", |
| "An undefined phase at one weak harmonic does not invalidate other resolved harmonics or independent intensity data.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Separate or grouped plots, quantitative tables and physically equivalent displays are accepted when case, valley/ensemble, channel and complex-amplitude relations remain reconstructible. Consistent Fourier, derivative, window and common normalization conventions are accepted; no pixel, colour, panel-order, exact absolute intensity or prescribed harmonic-list target.", |
| "A consistently mapped phase sign, circular-polarization or Stokes representation is acceptable when its relation to both complex channels and helicity is explicit." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Eq. (72) and Fig. 3(a-d), p. 053112-8; Fig. 5(a,b), p. 053112-9. The restriction on unresolved phases follows from the complex-amplitude definition; the article specifies no mandatory weak-signal threshold or Fourier window.", |
| "Moos, Jürß and Bauer (2020), p. 053112-3, Eqs. (25)-(28); Eq. (54), p. 053112-4; Eq. (57), p. 053112-5." |
| ], |
| "rc_relation": "Central-object role in the model-to-observable claim. RC0 is triggered only by an absent or materially invalid central physical identity, evaluated independently of the 0/0.5 award; a local presentation/convention weakness or valid physical equivalent does not itself trigger RC0." |
| }, |
| { |
| "criterion_id": "O1", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Submit the two topological cases at fixed K, parallel/perpendicular complex channels, yields and reliable helicity evidence sufficient to judge the broad topology-sensitive response.", |
| "award_conditions": [ |
| "The physical output object is valid and reconstructible (object_valid).", |
| "The candidate's representation exposes the material structure with adequate range, resolution and dynamic range (presentation_adequate).", |
| "Claims from the output remain within its resolved support (claim_adequate). All three conditions are necessary for the half-point; record failures separately.", |
| "Show the source-consistent broad resolved helicity change between cases and claim-relevant spectral support; do not replace the fixed-$K$ object with the other valley or the filled-band response." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires the correct model/drive of F1, propagation/observable of F2 and complex-channel identity of F4.", |
| "Does not require the integrated ensemble of F3. A fixed-$K$ failure does not erase independent $K'$ or full-BZ evidence.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Separate or grouped plots, quantitative tables and physically equivalent displays are accepted when case, valley/ensemble, channel and complex-amplitude relations remain reconstructible. Consistent Fourier, derivative, window and common normalization conventions are accepted; no pixel, colour, panel-order, exact absolute intensity or prescribed harmonic-list target.", |
| "A reciprocal-cell, basis-gauge or coordinate convention is accepted when lattice orientation, drive direction, hopping handedness, valley mapping, complex channels and conclusions are transformed consistently. Swapping valley labels alone is not a repair for an inconsistent corner/drive identity.", |
| "Use a reliable harmonic subset and tolerate unresolved weak phases; broad physical structure, not exact every-harmonic phase matching, is the target." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Fig. 3(a,b), Fig. 4(a,b) and Eq. (72), p. 053112-8; construction and gap context, p. 053112-7." |
| ], |
| "rc_relation": "Indispensable-component role. RC1 is triggered only if the required output object is absent or materially invalid. Failure of presentation adequacy or claim adequacy alone does not trigger RC1 when the object exists and is valid; award failure is not an automatic closure downgrade." |
| }, |
| { |
| "criterion_id": "O2", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Submit the two topological cases at fixed K', parallel/perpendicular complex channels, yields and reliable helicity evidence sufficient to judge its alternating/harmonic-dependent response.", |
| "award_conditions": [ |
| "The physical output object is valid and reconstructible (object_valid).", |
| "The candidate's representation exposes the material structure with adequate range, resolution and dynamic range (presentation_adequate).", |
| "Claims from the output remain within its resolved support (claim_adequate). All three conditions are necessary for the half-point; record failures separately.", |
| "Expose the materially different response from $K$, rather than an odd-only or otherwise selectively presented universal sign-reversal template.", |
| "Use major spectral support/dip/rolloff/onset as tolerant structural support; neither a precise low-order sequence nor the detailed weak-channel envelope is compulsory." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires the correct model/drive of F1, propagation/observable of F2 and complex-channel identity of F4.", |
| "Does not require the integrated ensemble of F3. Failure of $K'$ does not erase independent fixed-$K$ or full-BZ evidence.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Separate or grouped plots, quantitative tables and physically equivalent displays are accepted when case, valley/ensemble, channel and complex-amplitude relations remain reconstructible. Consistent Fourier, derivative, window and common normalization conventions are accepted; no pixel, colour, panel-order, exact absolute intensity or prescribed harmonic-list target.", |
| "A reciprocal-cell, basis-gauge or coordinate convention is accepted when lattice orientation, drive direction, hopping handedness, valley mapping, complex channels and conclusions are transformed consistently. Swapping valley labels alone is not a repair for an inconsistent corner/drive identity.", |
| "A reliable subset establishing harmonic dependence is accepted without imposing a prescribed list; detailed $K'$ envelopes and near-cancelled phases are not pointwise reference targets." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Fig. 3(c,d), Fig. 4(c,d), Eq. (72) and valley-dependent discussion, p. 053112-8; Fig. 2 and gap context, p. 053112-7." |
| ], |
| "rc_relation": "Indispensable-component role. RC1 is triggered only if the required output object is absent or materially invalid. Failure of presentation adequacy or claim adequacy alone does not trigger RC1 when the object exists and is valid; award failure is not an automatic closure downgrade." |
| }, |
| { |
| "criterion_id": "O3", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Submit filled-band coherent full-BZ parallel/perpendicular complex channels and reconstructible yield/envelope for the two topological cases, correctly binding occupation, BZ sampling and common normalization.", |
| "award_conditions": [ |
| "The physical output object is valid and reconstructible (object_valid).", |
| "The candidate's representation exposes the material structure with adequate range, resolution and dynamic range (presentation_adequate).", |
| "Claims from the output remain within its resolved support (claim_adequate). All three conditions are necessary for the half-point; record failures separately.", |
| "Establish the complete occupied-band coherent observable, not a single valley or an incoherent sum of intensities.", |
| "The broad intensity structure and material secondary structures must be source-consistent after legitimate representation mapping; one matching conspicuous peak is insufficient." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires the correct model/drive of F1, propagation of F2, full-BZ ensemble/weight of F3 and complex definition of F4.", |
| "An intensity-envelope deficiency alone does not erase independently established integrated phase evidence in O4; full-BZ failure does not erase valid fixed-valley work.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Separate or grouped plots, quantitative tables and physically equivalent displays are accepted when case, valley/ensemble, channel and complex-amplitude relations remain reconstructible. Consistent Fourier, derivative, window and common normalization conventions are accepted; no pixel, colour, panel-order, exact absolute intensity or prescribed harmonic-list target.", |
| "Equivalent coherent time-domain integration or coherent complex-amplitude summation is accepted when linear operations and normalization are treated consistently and yield is formed only after coherent summation.", |
| "A converged candidate-chosen mesh and alternative display range are accepted; the reference density and tail display floor are not duties." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Eq. (28), p. 053112-3; occupied-band coherence discussion, p. 053112-5; integrated discussion, p. 053112-8; Fig. 5(a,b), p. 053112-9." |
| ], |
| "rc_relation": "Indispensable-component role. RC1 is triggered only if the required output object is absent or materially invalid. Failure of presentation adequacy or claim adequacy alone does not trigger RC1 when the object exists and is valid; award failure is not an automatic closure downgrade." |
| }, |
| { |
| "criterion_id": "O4", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Within the full-BZ family, submit reliable relative-phase/helicity evidence with both directions resolved, demonstrating the integrated polarization structure that remains adjudicable between the two cases.", |
| "award_conditions": [ |
| "The physical output object is valid and reconstructible (object_valid).", |
| "The candidate's representation exposes the material structure with adequate range, resolution and dynamic range (presentation_adequate).", |
| "Claims from the output remain within its resolved support (claim_adequate). All three conditions are necessary for the half-point; record failures separately.", |
| "Use a resolved total-response subset that supports a case-dependent integrated helicity relation.", |
| "Do not count phases where either channel is unresolved as definite evidence; weak/cancelled rows do not become strict reference targets." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires the valid full-BZ identity of F3 and complex-channel/phase identity of F4.", |
| "No automatic dependence on the separate O3 envelope award. Local phase failure preserves reliable phase subsets, spectral objects and fixed-valley branches.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Separate or grouped plots, quantitative tables and physically equivalent displays are accepted when case, valley/ensemble, channel and complex-amplitude relations remain reconstructible. Consistent Fourier, derivative, window and common normalization conventions are accepted; no pixel, colour, panel-order, exact absolute intensity or prescribed harmonic-list target.", |
| "Consistent phase, circular-polarization or Stokes evidence may establish the same integrated polarization relation. No mandatory harmonic list, exact trivial H9/H10 phase or every-harmonic reversal is required." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Eq. (28), p. 053112-3; occupied-band coherence discussion, p. 053112-5; integrated discussion, p. 053112-8; Fig. 5(a,b), p. 053112-9.", |
| "Moos, Jürß and Bauer (2020), Eq. (72) and Fig. 3(a-d), p. 053112-8; Fig. 5(a,b), p. 053112-9. The restriction on unresolved phases follows from the complex-amplitude definition; the article specifies no mandatory weak-signal threshold or Fourier window." |
| ], |
| "rc_relation": "Indispensable-component role. RC1 is triggered only if the required output object is absent or materially invalid. Failure of presentation adequacy or claim adequacy alone does not trigger RC1 when the object exists and is valid; award failure is not an automatic closure downgrade." |
| }, |
| { |
| "criterion_id": "I1", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify the robust topology-sensitive broad helicity response between the two cases from the candidate's own fixed K evidence, judging phase only at harmonics where both directions are resolved.", |
| "award_conditions": [ |
| "The candidate identifies the case-dependent broad resolved response, rather than merely possessing arrays or repeating general topological knowledge.", |
| "Phase judgments are confined to harmonics for which both complex directions are resolved." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires valid and adequately candidate-presented fixed-$K$ evidence in O1 relevant to this identification.", |
| "An unrelated unmet condition in O1 does not erase an independently supported identification; a failed $K$ identification does not erase $K'$ or integrated identification.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Separate or grouped plots, quantitative tables and physically equivalent displays are accepted when case, valley/ensemble, channel and complex-amplitude relations remain reconstructible. Consistent Fourier, derivative, window and common normalization conventions are accepted; no pixel, colour, panel-order, exact absolute intensity or prescribed harmonic-list target.", |
| "A quantitatively identified phase-stable subset, ellipticity/helicity measures or equivalent complex-channel comparison is accepted; a precise colour sequence is unnecessary." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Fig. 3(a,b), Fig. 4(a,b) and Eq. (72), p. 053112-8; construction and gap context, p. 053112-7." |
| ], |
| "rc_relation": "No direct closure-level gate. A failed award does not automatically lower RC; any closure consequence must satisfy an independently specified required-role trigger." |
| }, |
| { |
| "criterion_id": "I2", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify from the candidate's own fixed K' evidence its alternating/harmonic-dependent helicity response that differs from K, rather than applying a uniform sign-flip template.", |
| "award_conditions": [ |
| "The candidate distinguishes $K'$ from the broad $K$ response and identifies harmonic dependence and resolved exceptions.", |
| "A generic assertion that topology matters, or an unsupported universal sign-flip template, is insufficient." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires valid and adequately candidate-presented fixed-$K'$ evidence in O2 needed for this identification.", |
| "Failure in an unrelated output aspect does not automatically erase correct candidate identification; other valley and integrated identifications remain independent.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Separate or grouped plots, quantitative tables and physically equivalent displays are accepted when case, valley/ensemble, channel and complex-amplitude relations remain reconstructible. Consistent Fourier, derivative, window and common normalization conventions are accepted; no pixel, colour, panel-order, exact absolute intensity or prescribed harmonic-list target.", |
| "A resolved subset demonstrating the nonuniform pattern suffices; no compulsory exact low-order sequence or full weak-channel envelope is imposed." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Fig. 3(c,d), Fig. 4(c,d), Eq. (72) and valley-dependent discussion, p. 053112-8; Fig. 2 and gap context, p. 053112-7." |
| ], |
| "rc_relation": "No direct closure-level gate. A failed award does not automatically lower RC; any closure consequence must satisfy an independently specified required-role trigger." |
| }, |
| { |
| "criterion_id": "I3", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify from the candidate's own full-BZ complex evidence the reliably retained integrated phase/helicity branches between the two cases, excluding spuriously definite phases of weak or nearly cancelled channels.", |
| "award_conditions": [ |
| "The candidate identifies the case dependence of reliable total-response polarization.", |
| "Exclude pseudo-certain phase generated by an unresolved or nearly cancelled direction; arrays or an examiner-visible feature alone do not establish candidate identification." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires valid and adequately candidate-presented reliable integrated phase evidence in O4.", |
| "An integrated phase-identification failure does not erase the separate spectrum identity or fixed-valley identifications.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Separate or grouped plots, quantitative tables and physically equivalent displays are accepted when case, valley/ensemble, channel and complex-amplitude relations remain reconstructible. Consistent Fourier, derivative, window and common normalization conventions are accepted; no pixel, colour, panel-order, exact absolute intensity or prescribed harmonic-list target.", |
| "Any explicitly identified robust phase subset or equivalent complex-polarization evidence is accepted; the reference's preferred subset is not mandatory." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Eq. (28), p. 053112-3; occupied-band coherence discussion, p. 053112-5; integrated discussion, p. 053112-8; Fig. 5(a,b), p. 053112-9.", |
| "Moos, Jürß and Bauer (2020), Eq. (72) and Fig. 3(a-d), p. 053112-8; Fig. 5(a,b), p. 053112-9. The restriction on unresolved phases follows from the complex-amplitude definition; the article specifies no mandatory weak-signal threshold or Fourier window." |
| ], |
| "rc_relation": "No direct closure-level gate. A failed award does not automatically lower RC; any closure consequence must satisfy an independently specified required-role trigger." |
| }, |
| { |
| "criterion_id": "M1", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Use the candidate's own K complex-channel evidence to explain how topology change alters the broad helicity response through trajectory/orientation, band-gap or a functionally equivalent route.", |
| "award_conditions": [ |
| "Connect an identified resolved $K$ signal to a physical explanation through trajectory/orientation, band-gap comparison, velocity decomposition or an equally discriminating route.", |
| "At $K$, similar minimum gaps in the two cases and changed trajectory chirality/complex-channel phase support a topology-sensitive response; general knowledge without the signal-to-mechanism link is insufficient." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires the candidate's fixed-$K$ signal identification in I1; the explanation must use the valid physical branch.", |
| "Independent $K'$ and full-BZ mechanisms retain credit if $K$ fails.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Band-gap and complex-channel comparisons, velocity-plane trajectories, velocity decomposition or an equivalent physically discriminating analysis are accepted. A specific trajectory figure or alternate solver is not required." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Fig. 3(a,b), Fig. 4(a,b) and Eq. (72), p. 053112-8; construction and gap context, p. 053112-7.", |
| "Moos, Jürß and Bauer, Phys. Rev. A 102, 053112 (2020), p. 053112-7, Eqs. (68)-(71) and Fig. 2; p. 053112-11, Appendix B, Eqs. (B1)-(B8); pulse Eq. (67), p. 053112-6." |
| ], |
| "rc_relation": "Principal-mechanism role. With valid required material signals, an absent or wrong indispensable mechanism/commissioned conclusion triggers RC2. Evaluate the actual mechanism trigger independently of the atomic award; do not use the lost half-point as the RC rule." |
| }, |
| { |
| "criterion_id": "M2", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Use the candidate's own K' complex-channel evidence to explain how its different gap/envelope, weaker perpendicular channel or a functionally equivalent cause produces a harmonic-dependent/alternating response.", |
| "award_conditions": [ |
| "Connect the identified $K'$ signal to its different gap/envelope, smaller perpendicular velocity or a functionally equivalent mechanism.", |
| "Account for the nonuniform harmonic response rather than substituting a single universal valley sign rule; an intensity-only description is insufficient." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires the candidate's fixed-$K'$ signal identification in I2.", |
| "Failure in this valley does not erase independent fixed-$K$ or full-BZ mechanisms.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Band-gap, trajectory, velocity-decomposition, phase-stable-subset or equally discriminating evidence is accepted; exact dip depth, every weak-channel phase and a prescribed $K'$ envelope are unnecessary." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Fig. 3(c,d), Fig. 4(c,d), Eq. (72) and valley-dependent discussion, p. 053112-8; Fig. 2 and gap context, p. 053112-7." |
| ], |
| "rc_relation": "Principal-mechanism role. With valid required material signals, an absent or wrong indispensable mechanism/commissioned conclusion triggers RC2. Evaluate the actual mechanism trigger independently of the atomic award; do not use the lost half-point as the RC rule." |
| }, |
| { |
| "criterion_id": "M3", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Synthesize K and K' evidence to establish explicitly that topology-sensitive helicity has valley- and harmonic-dependent structure; one uniform flip rule cannot describe both valleys.", |
| "award_conditions": [ |
| "The candidate makes the cross-valley decision from both own identified branches.", |
| "State the broad $K$ behavior and material $K'$ difference/exception, without claiming a uniform flip for every harmonic in both valleys." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires both fixed-$K$ identification in I1 and fixed-$K'$ identification in I2.", |
| "A missing valley blocks the cross-valley synthesis but does not erase the other valley's established local mechanism or the independent integrated branch.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "A broad family-level comparison across resolved subsets is accepted without an exact source harmonic list or a prescribed layout." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Fig. 3(a,b), Fig. 4(a,b) and Eq. (72), p. 053112-8; construction and gap context, p. 053112-7.", |
| "Moos, Jürß and Bauer (2020), Fig. 3(c,d), Fig. 4(c,d), Eq. (72) and valley-dependent discussion, p. 053112-8; Fig. 2 and gap context, p. 053112-7." |
| ], |
| "rc_relation": "Principal-mechanism role. With valid required material signals, an absent or wrong indispensable mechanism/commissioned conclusion triggers RC2. Evaluate the actual mechanism trigger independently of the atomic award; do not use the lost half-point as the RC rule." |
| }, |
| { |
| "criterion_id": "M4", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Explain that the filled-band observable is the coherent time-domain/BZ integral of occupied lower-band k-resolved velocities and cannot be replaced by a fixed-valley spectrum or an incoherent intensity sum.", |
| "award_conditions": [ |
| "Connect the submitted total-response object to correct occupied-band weights and coherent addition.", |
| "Explain why a fixed-valley spectrum or an incoherent intensity sum cannot substitute for the filled-band response; explicitly distinguish amplitude coherence from intensity addition." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires correct ensemble identity and coherent weights from F3, together with the valid candidate-presented full-BZ object relevant to O3.", |
| "An unrelated O3 presentation/envelope deficiency does not automatically erase a coherently justified mechanism; fixed-valley mechanisms remain independent.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Equivalent quadrature, coherent time-domain summation, or coherent complex-amplitude integration is accepted when physically identical. The student need not use a particular BZ grid or separate integration code." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Eq. (28), p. 053112-3; occupied-band coherence discussion, p. 053112-5; integrated discussion, p. 053112-8; Fig. 5(a,b), p. 053112-9." |
| ], |
| "rc_relation": "Principal-mechanism role. With valid required material signals, an absent or wrong indispensable mechanism/commissioned conclusion triggers RC2. Evaluate the actual mechanism trigger independently of the atomic award; do not use the lost half-point as the RC rule." |
| }, |
| { |
| "criterion_id": "M5", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Use the candidate's own reliable full-BZ phase evidence to explain which topology-sensitive polarization/helicity structures survive coherent integration and how cancellation/weak channels limit that conclusion.", |
| "award_conditions": [ |
| "Connect the candidate's identified reliable integrated phases to a supported survival conclusion.", |
| "Explain why coherent cancellation and finite signal strength can make particular harmonics unreliable; unsupported weak-channel phase certainty cannot support the central claim." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires the candidate's integrated polarization identification in I3.", |
| "Failure of one weak row does not erase another resolved harmonic subset, the coherent-object explanation or fixed-valley mechanisms.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "A phase-stable subset, equivalent polarization estimator, or equally discriminating coherent-response analysis is accepted without imposing a preferred list or exact weak phases." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Eq. (28), p. 053112-3; occupied-band coherence discussion, p. 053112-5; integrated discussion, p. 053112-8; Fig. 5(a,b), p. 053112-9.", |
| "Moos, Jürß and Bauer (2020), Eq. (72) and Fig. 3(a-d), p. 053112-8; Fig. 5(a,b), p. 053112-9. The restriction on unresolved phases follows from the complex-amplitude definition; the article specifies no mandatory weak-signal threshold or Fourier window." |
| ], |
| "rc_relation": "Principal-mechanism role. With valid required material signals, an absent or wrong indispensable mechanism/commissioned conclusion triggers RC2. Evaluate the actual mechanism trigger independently of the atomic award; do not use the lost half-point as the RC rule." |
| }, |
| { |
| "criterion_id": "M6", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Close the fixed-valley and full-BZ results together: assess the topology sensitivity of observable polarization while stating explicitly that the integrated signal alone cannot uniquely locate a particular valley or microscopic k-origin.", |
| "award_conditions": [ |
| "Judge the observable polarization's topology sensitivity using the two-level evidence chain.", |
| "Explicitly explain that the integrated signal alone cannot uniquely identify one valley or microscopic crystal-momentum origin; the total signal is not simply a relabelled valley spectrum." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires the coherent-object mechanism of M4 and the integrated polarization-survival explanation of M5.", |
| "A failed integrated conclusion does not erase independently correct fixed-valley mechanisms; a generic final summary adds no substitute evidence.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Equivalent coherent representations and signal-to-conclusion reasoning are accepted when they preserve the attribution boundary; a decomposition uniquely assigning a microscopic source is not required." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Eq. (28), p. 053112-3; occupied-band coherence discussion, p. 053112-5; integrated discussion, p. 053112-8; Fig. 5(a,b), p. 053112-9.", |
| "Moos, Jürß and Bauer (2020), Fig. 3(a,b), Fig. 4(a,b) and Eq. (72), p. 053112-8; construction and gap context, p. 053112-7.", |
| "Moos, Jürß and Bauer (2020), Fig. 3(c,d), Fig. 4(c,d), Eq. (72) and valley-dependent discussion, p. 053112-8; Fig. 2 and gap context, p. 053112-7." |
| ], |
| "rc_relation": "Principal-mechanism role. With valid required material signals, an absent or wrong indispensable mechanism/commissioned conclusion triggers RC2. Evaluate the actual mechanism trigger independently of the atomic award; do not use the lost half-point as the RC rule." |
| }, |
| { |
| "criterion_id": "M7", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Use the candidate's own finite-pulse complex-channel evidence to reconcile theoretical phase organization with weak/resonant/window-sensitive regions, explaining why only harmonics with both directions resolved can support retained helicity conclusions.", |
| "award_conditions": [ |
| "Use actual phase-bearing output evidence to explain why retained helicity conclusions require both directions to be resolved.", |
| "Relate finite-pulse/weak-region behavior to the supported theoretical interpretation, rather than reciting a generic caveat or treating unstable phase as certain." |
| ], |
| "applicability_and_na": [ |
| "Applies to every scientifically assessable answer; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Requires at least one valid and adequately candidate-presented phase-bearing family: fixed-$K$ evidence of O1, fixed-$K'$ evidence of O2, or integrated phase evidence of O4. This is an alternative, not a requirement for all three families.", |
| "Failure of one family preserves a reconciliation established from another valid family; independent local mechanisms retain credit.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "A phase-stable subset, a functionally equivalent reduction, an uncertainty-aware polarization representation or an equally discriminating finite-pulse explanation may establish this obligation. No named window or threshold is mandatory." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), Eq. (72) and Fig. 3(a-d), p. 053112-8; Fig. 5(a,b), p. 053112-9. The restriction on unresolved phases follows from the complex-amplitude definition; the article specifies no mandatory weak-signal threshold or Fourier window." |
| ], |
| "rc_relation": "No direct closure-level gate. A failed award does not automatically lower RC; any closure consequence must satisfy an independently specified required-role trigger." |
| }, |
| { |
| "criterion_id": "V1", |
| "dimension": "V", |
| "points": 0.5, |
| "scientific_requirement": "Only when the candidate's own method/data/anomaly/claim exposes material risk, use discriminating evidence to address actual risks such as incorrect valley/case binding, fixed-k masquerading as full-BZ, an incoherent sum, BZ under-resolution, near-zero phase or window cancellation, or narrow the threatened conclusion.", |
| "award_conditions": [ |
| "When triggered, address an actual risk such as inconsistent valley/case binding, fixed-$\\mathbf k$ substitution for the BZ, incoherent intensity summation, BZ under-resolution, near-zero phase, window-sensitive cancellation, inconsistent basis/gauge or display scaling mistaken for physical yield.", |
| "The evidence must be able to expose the particular threatened error, or the candidate must restrict the threatened conclusion to its established domain; generic convergence or caveats alone are insufficient.", |
| "When no material risk is triggered in an otherwise scientifically assessable answer, award 0.5 as N/A without claiming the candidate supplied validation evidence." |
| ], |
| "applicability_and_na": [ |
| "Risk-triggered only: identify the candidate-origin material risk and the threatened retained claim before requiring a response.", |
| "If no such risk is triggered in an otherwise scientifically assessable answer, record N/A, award the fixed 0.5 point, and record no submitted validation evidence.", |
| "A sealed submission with no scientifically assessable required work receives terminal 0.0/RC0; N/A bookkeeping cannot generate credit in an empty answer.", |
| "An incomplete but scientifically assessable answer is scored from its submitted evidence; it is not treated as empty." |
| ], |
| "dependencies": [ |
| "Judged directly from the submitted formulation, report, method, data or claim, as applicable; no prerequisite award.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "Analytic identity checks, interventions, relevant convergence/sensitivity evidence, alternative estimators, cross-representation tests, held-out evidence or honest evidence-based scope restriction are accepted when they can discriminate the actual risk. No particular check is prescribed." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), assumptions, p. 053112-1; occupied-band and interference discussion, p. 053112-5; conclusions, p. 053112-9. Risk and scope requirements implement the stated research commission, not a prescribed source-specific validation test.", |
| "Moos, Jürß and Bauer (2020), Eq. (72) and Fig. 3(a-d), p. 053112-8; Fig. 5(a,b), p. 053112-9. The restriction on unresolved phases follows from the complex-amplitude definition; the article specifies no mandatory weak-signal threshold or Fourier window." |
| ], |
| "rc_relation": "Material-validation role. RC3 requires a triggered unresolved risk and all six burden-of-proof elements stated in the closure requirements, after the central signals and principal mechanisms are substantially correct. N/A does not block RC4 or trigger RC3. The atomic outcome itself is not an RC rule." |
| }, |
| { |
| "criterion_id": "V2", |
| "dimension": "V", |
| "points": 0.5, |
| "scientific_requirement": "Positively limit conclusions to the specified bulk, independent-electron, two-band Haldane model, given pulse/two cases, actual BZ sampling and support domain of resolved complex channels; do not extrapolate to edge, many-body, experimental efficiency or a universal marker.", |
| "award_conditions": [ |
| "State the given pulse/two cases, actual BZ sampling and resolved complex-channel support as the domain of the conclusion.", |
| "Do not extrapolate to edge-state physics, many-body correlations, experimental conversion efficiency or a universal topological marker." |
| ], |
| "applicability_and_na": [ |
| "Unconditional visible scope duty; N/A is forbidden.", |
| "An ordinary scope omission affects this award only: it does not automatically trigger RC3, invalidate independent work or create a new direct closure gate. A materially unsupported broader claim is assessed through its actual affected mechanism or triggered-risk role." |
| ], |
| "dependencies": [ |
| "Judged directly from the submitted formulation, report, method, data or claim, as applicable; no prerequisite award.", |
| "Propagate only the exact failed fact that is necessary for this obligation, not every unmet condition of an upstream criterion. Candidate-presented independent evidence retains credit; examiner reconstruction cannot supply candidate identification or inference." |
| ], |
| "equivalent_evidence": [ |
| "An explicit, scientifically honest scope restriction in any report location is accepted. It may remain independently correct after another branch fails; no prescribed wording is required." |
| ], |
| "source_support": [ |
| "Moos, Jürß and Bauer (2020), assumptions, p. 053112-1; occupied-band and interference discussion, p. 053112-5; conclusions, p. 053112-9. Risk and scope requirements implement the stated research commission, not a prescribed source-specific validation test." |
| ], |
| "rc_relation": "No direct closure-level gate. A failed award does not automatically lower RC; any closure consequence must satisfy an independently specified required-role trigger." |
| } |
| ], |
| "case_scientific_rules": [ |
| "Scoring uses exactly twenty binary awards of 0 or 0.5, totaling 10.0: F=2.0, O=2.0, I=1.5, M=3.5 and V=1.0. RC is descriptive and independently derived from required physical roles; it imposes no score ceiling, floor, multiplier or target distribution.", |
| "The geometry is fixed by $\\mathbf a_1=\\boldsymbol\\delta_1-\\boldsymbol\\delta_3=\\frac a2(3,\\sqrt3)$ and $\\mathbf a_2=\\boldsymbol\\delta_2-\\boldsymbol\\delta_3=\\frac a2(3,-\\sqrt3)$, hence $\\mathbf g_1=(0,\\sqrt3a)$, $\\mathbf g_2=-\\frac a2(3,\\sqrt3)$ and $\\mathbf g_3=\\frac a2(3,-\\sqrt3)$. A compatible reciprocal basis is $\\mathbf b_1=\\frac{2\\pi}{a}(\\frac13,\\frac1{\\sqrt3})$, $\\mathbf b_2=\\frac{2\\pi}{a}(\\frac13,-\\frac1{\\sqrt3})$. In this convention $K=(2\\mathbf b_1+\\mathbf b_2)/3=(0.78061688498,0.45068936868)$ and $K'=(\\mathbf b_1+2\\mathbf b_2)/3=(0.78061688498,-0.45068936868)$ for $a=2.683$. Other coordinates require a complete physical equivalence mapping, not arbitrary valley relabelling with the drive kept incompatible.", |
| "The model has $H=\\mathbf d\\cdot\\boldsymbol\\sigma$ and energies $E_\\pm=\\pm|\\mathbf d|$. The stated lattice, signs, two imaginary hoppings and finite pulse define one physical comparison; replacing their identity with a different model is material even if one spectral feature agrees.", |
| "The common calculation chain is $\\mathbf k(t)=\\mathbf k+\\mathbf A(t)$, $i\\dot C=H[\\mathbf k(t)]C$, $C(\\mathbf k,0)=C_-(\\mathbf k)$, and $v_j=C^\\dagger\\partial_{k_j}H[\\mathbf k(t)]C$. Fixed valleys use their single-point velocities. The filled band uses $v_j^{\\mathrm{BZ}}(t)=\\frac{V_{\\mathrm{cell}}}{(2\\pi)^2}\\int_{\\mathrm{BZ}}v_j(\\mathbf k,t)\\,d^2k$, with $V_{\\mathrm{cell}}=3\\sqrt3a^2/2$, before constructing radiation; an incoherent intensity sum is not equivalent.", |
| "An accepted acceleration convention is $\\mathcal A_j(\\Omega)=\\mathcal F[\\dot v_j](\\Omega)$, $Y_j(\\Omega)\\propto|\\mathcal A_j(\\Omega)|^2$ and $\\Delta\\phi=\\arg\\mathcal A_\\parallel-\\arg\\mathcal A_\\perp$. Equivalent velocity/current/Fourier routes must include the appropriate derivative-frequency/phase mapping and common normalization. Relative phase, together with magnitudes, determines polarization; helicity is interpretable only when both channels are resolved. A different overall phase-sign convention is accepted only with the helicity mapping transformed consistently.", |
| "At fixed $K$, the reference broad pattern is a change from about $-\\pi/2$ in the trivial case to about $+\\pi/2$ in the nontrivial case for most resolved harmonics, including the fundamental. Perpendicular even harmonics appear; the resolved trivial second harmonic has opposite helicity to the usual trivial family. These are robust family-level scientific anchors, not an every-harmonic sequence mandate.", |
| "At fixed $K'$, the trivial response is near $+\\pi/2$ and the nontrivial response has harmonic-dependent/alternating changes. The source's low-order example has no fundamental flip, a second-harmonic flip, no third-to-fifth flip and a sixth-harmonic flip. The nontrivial spectrum has a gap-related dip near H13, rolloff to its left and plateau onset to its right. These explain the valley distinction; exact sequence coverage, dip depth and the detailed weak $K'$ envelope are not mandatory or pointwise scoring targets.", |
| "The filled-band response preserves a reliable topology-sensitive helicity relation, but cannot alone uniquely identify a microscopic valley or crystal-momentum origin. Broad reference structure includes an approximately H5-H15 plateau and rolloff after H15; an independently checked structural tail can extend to about H25. A reference comparison has robust opposite-helicity branches at H3-H6, H8 and H11-H19; that subset is not a prescribed submission list. Trivial H9/H10, phases above H20 and any weak/cancelled phase are not strict targets; intensity support and phase reliability need not share a cutoff.", |
| "Similar minimum gaps at $K$ but changed trajectory chirality/complex-channel phase support the topology-sensitive broad reversal. Larger case-dependent gap differences and weaker perpendicular velocity at $K'$ support a different envelope and nonuniform phase response. Coherent occupied-band integration can preserve robust polarization while cancellation makes individual harmonics window-sensitive. Equivalent band-gap, trajectory, velocity-decomposition or equally discriminating mechanisms are accepted.", |
| "Numerical choices belong to the candidate: BZ grid, time step, solver, differentiation, Fourier window, weak-signal threshold and plot range. The $1500\\times1500$ reference grid is not a duty. Missing a routine convergence checklist is neither a separate deduction nor an automatic RC3 trigger. Reliability matters only through actual affected evidence, claims or a fairly triggered material risk.", |
| "First establish lattice/model, cases, driver, lower-band occupation, fixed-valley versus integrated ensemble, response directions, gauge/coordinates, Fourier convention and normalization. Compare broad support, symmetry, sign, ordering, component relations, major peaks/dips/plateaus/rolloffs and claim-relevant secondary structure. One matching conspicuous feature does not outweigh a materially inconsistent global family. No pixels, colours, line styles, panel count/order, crop, exact weak phases, exact absolute arbitrary-unit intensity, display floor or source-specific plotting range is scored. The reference's x1000 separation is a display factor, not a physical enhancement.", |
| "Output credit requires separately recorded object validity, presentation adequacy and claim adequacy. Distinguish submitted object existence, candidate presentation, candidate identification and physical inference. The examiner may verify objects using submitted data/reconstruction but may not manufacture candidate identification, reasoning or validation. A scientifically wrong yet internally consistent result cannot support a dependent scientific inference.", |
| "Dependency propagation is causal and local: identify the precise failed upstream fact, the downstream obligation that needs it and why submitted candidate evidence cannot establish that obligation independently. An unmet presentation or branch condition in a combined output criterion does not erase a correct inference about a different adequately presented valid subobject. Preserve independent valley, integrated, intensity/phase, risk and scope work. Charge the physical defect where it damages evidence or a claim, not again as generic incompleteness.", |
| "Reference comparisons are part of grading and are limited to the scientific issue that requires verification. Consult the relevant figure or panel from the source publication, or a verified reproduction within its stated scope, when resolution, fine-structure authenticity, branch completeness or physical equivalence materially decides an award/RC. Consult only the relevant passage if central formula, gauge/sign or method equivalence is disputed. A provisional score at least 9.0 or provisional RC4 requires one bounded central-output check and one principal-mechanism link check. Reference material cannot add a candidate duty or fill missing reasoning. Record scientific agreements, discrepancies, representation mapping, affected criteria and ambiguity. Resolve any remaining material scientific ambiguity through focused review before finalizing the affected grading decision; do not invent a numerical tolerance.", |
| "All conclusions are model-bounded: bulk, independent-electron, two-band, dipole-coupled Haldane dynamics under the stated pulse and cases. Edge states, many-body correlations, experimental efficiencies and universal topological markers are not established. Honest narrowing removes an unsupported broader claim but cannot repair a wrong signal, missing commissioned family or false mechanism.", |
| "A valid candidate-caused timeout/incomplete attempt is counted. If its sealed submission contains no scientifically assessable required work, score 0.0 and classify RC0 without summing atoms or awarding N/A validation credit. Otherwise score assessable incomplete work normally. Infrastructure validity and scientific completion are separate; logs or unsealed scratch do not become submitted scientific evidence.", |
| "Use an independent first grade followed by targeted principal review of validity, fairness, disputed awards, dependencies, descriptive closure and any material ambiguity. Inspect all submitted claim-bearing images and necessary data/code; use a further adjudicator only for residual material disagreement. No score is adjusted to fit a preferred closure interval." |
| ], |
| "closure_requirements": { |
| "RC0": [ |
| "Central model-to-observable role fails: the specified consistent Haldane lattice/cases/pulse/lower-band identity (F1), physical Peierls propagation and two-direction observable (F2), fixed-point versus coherently occupied-band ensemble identity (F3), or reconstructible complex-channel/yield/relative-phase identity (F4) is absent or materially invalid.", |
| "Evaluate these central-object triggers as physical pass/fail outcomes, not as awarded points. A local equivalent representation, ordinary documentation weakness or one unreliable harmonic is not itself central-object invalidity.", |
| "A sealed answer with no scientifically assessable required submission receives terminal 0.0/RC0 before any N/A awards. If valid independent work remains in an otherwise assessable answer, its earned score is preserved even when the central object is invalid." |
| ], |
| "RC1": [ |
| "After assessing central-object validity, an indispensable fixed-valley component is absent or materially invalid: fixed-$K$ outputs for both cases and both complex directions (O1), or fixed-$K'$ outputs for both cases and both directions (O2).", |
| "Alternatively an indispensable filled-band component is absent or materially invalid: coherent full-BZ channel spectra/yields with correct occupied-band identity (O3), or the required integrated complex polarization object (O4).", |
| "Judge object validity separately from presentation and claim adequacy. O=0 from inadequate presentation or an unsupported claim does not itself trigger RC1 when the underlying required object is valid and reconstructible.", |
| "Hidden panels, source mesh density, exact harmonic sequence/list, plotting range and weak-channel fine structure do not define an indispensable component. Correct independent branches retain their atomic credit." |
| ], |
| "RC2": [ |
| "With central objects and required material components valid, the fixed-valley principal-mechanism role fails if the own-evidence explanation of broad $K$ topology-sensitive helicity (M1), the own-evidence explanation of distinct harmonic-dependent $K'$ response (M2), or the cross-valley conclusion rejecting a single common flip rule (M3) is absent or wrong.", |
| "Alternatively the integrated principal-mechanism role fails if the explanation of coherent occupied-band summation rather than fixed-point/intensity substitution (M4), the supported survival/cancellation interpretation from reliable integrated polarization (M5), or the final relation and non-unique microscopic-attribution boundary (M6) is absent or wrong.", |
| "Candidate identification in I1/I2/I3 supports these actual mechanism claims; examiner-found signals cannot fill missing candidate reasoning. An atomic award failure does not replace the role-specific absence/wrongness trigger.", |
| "Finite-pulse reconciliation M7 and ordinary positive-scope V2 are separately scored and have no independent direct RC gate. A material error in a retained central claim is evaluated in its actual affected required role, not by inventing a new gate." |
| ], |
| "RC3": [ |
| "Central signals and indispensable principal mechanisms must first be substantially correct. A concrete material-validation risk originating in the candidate's method, data, anomaly or retained claim is unresolved and the threatened conclusion has not been adequately restricted; this is the triggered V1 role, not automatic checklist incompleteness.", |
| "Record (1) the exact unexcluded failure mode, (2) why it arises from this candidate's own method/data/claim rather than hidden reference knowledge, (3) the visible evidence or standard reasoning giving a fair basis to notice it, (4) the central conclusion it could overturn or materially weaken, (5) why submitted evidence cannot expose or exclude it, and (6) examples of functionally equivalent discriminating evidence or honest restriction that would resolve it.", |
| "Possible risks include valley/case/corner-drive misbinding, single-point substitution for the BZ, incoherent intensity addition, unresolved BZ structure, phase from a near-zero direction, Fourier-window cancellation, inconsistent basis/gauge or display scaling treated as physical yield. They are examples, not mandatory tests.", |
| "If any of the six elements is missing, do not apply RC3 by default. No particular mesh, step, norm check, residual, window or convergence protocol is prescribed.", |
| "A no-risk V1 N/A does not block closure and does not constitute validation evidence. Honest restriction to an established domain removes only the unsupported broader claim, not a wrong observable/mechanism or a missing commissioned branch. Substantive unresolved RC3 disagreement requires a further bounded independent adjudication rather than a downward tie-breaker." |
| ], |
| "RC4": [ |
| "All nonempty roles in all indispensable and co-primary scientific claims must close: consistent model/cases/pulse, propagation, occupied-band/fixed-point and complex-output identities (F1-F4 central-object roles); valid fixed-$K$ and fixed-$K'$ output components (O1-O2); valid coherent full-BZ spectrum and integrated-polarization components (O3-O4); own-evidence valley mechanisms and nonuniform cross-valley conclusion (M1-M3); coherent integration, supported polarization survival and non-unique microscopic-attribution conclusion (M4-M6); and all fairly triggered material risks handled or honestly restricted (V1).", |
| "Closure is a physical role-pass outcome, not a sum threshold or a requirement that all twenty awards pass. Identification must be attributable to the candidate wherever the mechanism needs it. Ordinary M7/V2 award failure alone supplies no separate RC gate.", |
| "No unresolved material risk may be dismissed merely because an output resembles the reference; equally, no untriggered preferred check may be added. V1 N/A does not block RC4.", |
| "Interpret the closed conclusions only within their supported bulk independent-electron two-band and resolved-data domain; a materially unsupported broader claim remains subject to its actual mechanism/risk role.", |
| "When multiple required-role failures coexist, select the lowest applicable closure level: central-object failure before component failure before mechanism failure before triggered material-validation failure. Supporting/ungated awards do not determine the overall level. Preserve the independently earned atomic score." |
| ] |
| }, |
| "references": [ |
| { |
| "citation": "Daniel Moos, Hannah Jürß and Dieter Bauer, Intense-laser-driven electron dynamics and high-order harmonic generation in solids including topological effects, Physical Review A 102, 053112 (2020).", |
| "url": "https://doi.org/10.1103/PhysRevA.102.053112", |
| "anchors": [ |
| "Eqs. (25)-(28), p. 053112-3", |
| "Eq. (54), p. 053112-4; Eq. (57), p. 053112-5", |
| "Eq. (67), p. 053112-6", |
| "Eqs. (68)-(71), Fig. 2 and model cases, p. 053112-7", |
| "Eq. (72), Fig. 3(a,b): fixed K; Fig. 3(c,d): fixed K-prime; Fig. 4(a-d): velocity-plane trajectories; discussion, p. 053112-8", |
| "Integrated-response discussion, p. 053112-8; Fig. 5(a,b) and conclusions, p. 053112-9", |
| "Appendix B, Eqs. (B1)-(B8), p. 053112-11; coupling continuation, p. 053112-12" |
| ], |
| "scientific_scope": "Two-band dynamics, radiation observables, valley-resolved response, coherent occupied-band integration, and polarization interpretation." |
| } |
| ] |
| } |
|
|
