{
  "case_id": "Case42",
  "title": "Collective-mode classification in a driven structured superconductor",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Establish the second-order inertial complex TDGL and uniform zero-velocity initial state as the global central initial-value problem.",
      "award_conditions": [
        "Establish the second-order inertial complex TDGL and uniform zero-velocity initial state as the global central initial-value problem."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Kang et al. (2025), article pp. 2–3, Eqs. (1)–(3), initial-state and boundary paragraphs. Inertial complex-field initial-value problem and propagation. Peak normalization and far-field ground-state boundary identity are explicitly task-defined, not guessed from the source Dirichlet label."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Establish stable auditable central complex-field propagation and global object validity; only a materially invalid global propagation or central complex object can invalidate all output gates.",
      "award_conditions": [
        "Establish stable auditable central complex-field propagation and global object validity; only a materially invalid global propagation or central complex object can invalidate all output gates."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.",
        "Local driver, transform, coordinate or normalization problems are localized to the actually affected branch rather than global failure."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Kang et al. (2025), article pp. 2–3, Eqs. (1)–(3), initial-state and boundary paragraphs. Inertial complex-field initial-value problem and propagation. Peak normalization and far-field ground-state boundary identity are explicitly task-defined, not guessed from the source Dirichlet label."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Construct the correct S driver and present valid reconstructible spatial complex/topological evidence with correct physical identity, global morphology, coordinates and normalization.",
      "award_conditions": [
        "Construct the correct S driver and present valid reconstructible spatial complex/topological evidence with correct physical identity, global morphology, coordinates and normalization.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F1 AND F2). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for O2, O3, O4, I2, I3, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 5, Fig. 3(a), caption, supercurrent/vorticity paragraph; Eqs. (4)–(6), p. 3. Single Gaussian S branch, co-located depletion and phase/topological organization. Winding, covariant current or equivalent complex-field evidence is accepted without a mandatory triad or fixed count."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "For the same correct S driver, present reconstructible collective-response evidence with valid physical identity, major response morphology, transform and normalization.",
      "award_conditions": [
        "For the same correct S driver, present reconstructible collective-response evidence with valid physical identity, major response morphology, transform and normalization.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F1 AND F2). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for O1, O3, O4, I1, I2, I3, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 5, Fig. 3(b,c) and Higgs/NG paragraph; transform definition on p. 3. Complementary collective response for the same S field, not another real-space amplitude image."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Construct the correct P driver and present valid reconstructible real-space complex/topological response with correct global morphology, coordinates and normalization.",
      "award_conditions": [
        "Construct the correct P driver and present valid reconstructible real-space complex/topological response with correct global morphology, coordinates and normalization.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F1 AND F2). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for O1, O2, O4, I1, I3, M3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 4, Fig. 2(a), caption and opening Results paragraphs; Eq. (6), p. 3. Strong two-beam P complex/topological real-space response, not the weak two-beam Fig. 5 case."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present complementary reconstructible P collective-response evidence, distinct from its real-space order-parameter image, with material discriminating power for the claimed classification.",
      "award_conditions": [
        "The correct P driver has a reconstructible complementary collective-response object distinct from its real-space order-parameter image.",
        "That object has material discriminating power for the actual classification; orthogonal-direction cuts are sufficient but not the only eligible evidence.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all must hold for the applicable full or explicitly bounded local award."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F1 AND F2). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for O1, O2, O3, I1, I2, M3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 4, Fig. 2(b,c), opening Results; pp. 6–7, Fig. 5(b,c) and contrast paragraph. Complementary P evidence must carry material classification information. Orthogonal momentum cuts discriminate the canonical example but are not an exclusive required display."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify the actually established S depletion, winding/singularity or equivalent complex/topological organization from the candidate's own valid spatial evidence, without a mandatory topology triad.",
      "award_conditions": [
        "Identify the actually established S depletion, winding/singularity or equivalent complex/topological organization from the candidate's own valid spatial evidence, without a mandatory topology triad."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O1. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for I2, I3, I4, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 5, Fig. 3(a), caption, supercurrent/vorticity paragraph; Eqs. (4)–(6), p. 3. Single Gaussian S branch, co-located depletion and phase/topological organization. Winding, covariant current or equivalent complex-field evidence is accepted without a mandatory triad or fixed count."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify the actually established complex/topological organization from the candidate's own valid P real-space evidence.",
      "award_conditions": [
        "Identify the actually established complex/topological organization from the candidate's own valid P real-space evidence."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O3. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for I1, I3, I4, M3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 4, Fig. 2(a), caption and opening Results paragraphs; Eq. (6), p. 3. Strong two-beam P complex/topological real-space response, not the weak two-beam Fig. 5 case."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify a classification-material feature in the candidate's own valid complementary P evidence; orthogonal-direction contrast is sufficient but not unique and cannot be supplied by examiner array reconstruction.",
      "award_conditions": [
        "Identify a classification-material feature in the candidate's own valid complementary P evidence; orthogonal-direction contrast is sufficient but not unique and cannot be supplied by examiner array reconstruction."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O4. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for I1, I2, I4, M3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 4, Fig. 2(b,c), opening Results; pp. 6–7, Fig. 5(b,c) and contrast paragraph. Complementary P evidence must carry material classification information. Orthogonal momentum cuts discriminate the canonical example but are not an exclusive required display."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "I4",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify near-drive/phase and near-Higgs/amplitude frequency families from valid S or P collective evidence or an equivalent time-domain/response-family representation; source attribution is not this identification act.",
      "award_conditions": [
        "Identify near-drive/phase and near-Higgs/amplitude frequency families from valid S or P collective evidence or an equivalent time-domain/response-family representation; source attribution is not this identification act."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (O2 OR O4). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for O1, O3, I1, I2, I3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article pp. 4–5, Figs. 2(b,c), 3(b,c), frequency-family discussion. Candidate identification of near-drive/phase and near-Higgs/amplitude families; identification is distinct from a causal mechanism or source attribution."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain amplitude/Higgs-scale response through the A² contribution to the covariant source.",
      "award_conditions": [
        "Explain amplitude/Higgs-scale response through the A² contribution to the covariant source."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: I4. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M2, M3, M4, M7; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 3, Eq. (3); p. 5, Eq. (7) and surrounding coupling paragraphs. Physical expansion of the covariant kinetic term distinguishes quadratic-A amplitude driving from linear-A/current/phase-gradient coupling."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain phase/current response through linear-A and phase-gradient/current coupling.",
      "award_conditions": [
        "Explain phase/current response through linear-A and phase-gradient/current coupling."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: I4. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M1, M3, M4, M7; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 3, Eq. (3); p. 5, Eq. (7) and surrounding coupling paragraphs. Physical expansion of the covariant kinetic term distinguishes quadratic-A amplitude driving from linear-A/current/phase-gradient coupling."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Establish the candidate's causal connection between S complex/topological organization and collective response, beyond juxtaposed displays.",
      "award_conditions": [
        "Establish the candidate's causal connection between S complex/topological organization and collective response, beyond juxtaposed displays."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (O1 AND O2 AND I1 AND I4). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for O3, O4, I2, I3, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 5, Fig. 3(a–c), Eq. (7) and single-beam vortex/Higgs discussion. Positive causal link between S phase/amplitude organization and collective response, beyond coexistence."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Establish the candidate's causal connection between P winding/complex organization and the chosen complementary collective signal; orthogonal-direction response is sufficient but not exclusive.",
      "award_conditions": [
        "Establish the candidate's causal connection between P winding/complex organization and the chosen complementary collective signal; orthogonal-direction response is sufficient but not exclusive."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (I2 AND I3). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for O1, O2, I1, I4, M3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article pp. 4–5, Fig. 2(a–c), Eq. (7), vortex-mediated linear-coupling discussion. Positive P topology/phase-gradient mechanism and its collective signature. A missing preferred control cannot substitute for judging this mechanism."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Positively explain why phase/topology-mediated coupling can produce the claimed collective-response relation.",
      "award_conditions": [
        "A relevant established S or P signal-to-mechanism branch grounds the positive explanation of phase/topology-mediated collective coupling.",
        "Alternative exclusion alone does not establish this positive mechanism; failure of one branch does not erase a mechanism established by the other."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (M3 OR M4). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M1, M2, M6, M7, V2; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.",
        "This positive mechanism criterion does not score alternative-control sufficiency and is not automatically satisfied by the same object used for V2."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article pp. 4–5, Fig. 2(a–c), Eq. (7), vortex-mediated linear-coupling discussion. Positive P topology/phase-gradient mechanism and its collective signature. A missing preferred control cannot substitute for judging this mechanism."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use the candidate's signals and relevant positive mechanisms to reach a bounded vortex-mediated or equivalent physical classification; a correct evidence-supported negative conclusion is also acceptable.",
      "award_conditions": [
        "At least one relevant candidate-established signal-to-mechanism branch supports the bounded physical classification.",
        "A correct evidence-supported negative or restricted result is eligible; the source-preferred label/control is not compulsory, and failed classification does not erase independently correct branch work."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (M3 OR M4). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M1, M2, M5, M7, V1, V2, V3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article pp. 4–7, Figs. 2(a–c), 3(a–c), 5(a–c), associated directional comparison. Task-defined evidence-bounded physical classification, including a correct supported negative or restricted judgment; a source-preferred label is not compulsory."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Recognize that S/P simultaneously change beam number, amplitude, waist and damping, and avoid treating them as a single-variable causal experiment.",
      "award_conditions": [
        "Recognize that S/P simultaneously change beam number, amplitude, waist and damping, and avoid treating them as a single-variable causal experiment."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 4, Fig. 2 caption and Results parameters; p. 5, Fig. 3 caption. S/P change beam count, amplitude, waist and damping together; physical entailment forbids treating them as a one-variable causal control."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "V1",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "For a concrete claim-relevant numerical, method or representation failure mode triggered by the actual method/data/anomaly/claim, provide discriminating evidence or an evidence-based restriction; otherwise record N/A.",
      "award_conditions": [
        "For a concrete claim-relevant numerical, method or representation failure mode triggered by the actual method/data/anomaly/claim, provide discriminating evidence or an evidence-based restriction; otherwise record N/A.",
        "When triggered, award only if claim-relevant discriminating evidence resolves the threat or an evidence-based restriction makes it immaterial; merely acknowledging an unresolved material threat is not positive validation credit. With no trigger, record N/A and retain the fixed 0.5 without claiming performed validation."
      ],
      "applicability_and_na": [
        "Applies only when the submitted method, data, anomaly or conclusion creates the concrete material risk described here. If untriggered, record not_applicable and retain the fixed 0.5 contribution; this is not evidence that validation was performed, and does not block RC4."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.",
        "This criterion owns triggered numerical/method/representation threats; the same numerical failure is not charged again as the physical alternative under V2."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article p. 3, Eq. (3), initial/boundary and transform definitions; Figs. 2(b,c), 3(b,c), pp. 4–5. Task-defined conditional risk against boundary, switch-on, transform and coordinate artefacts. No mandatory grid, late-time window or absolute source momentum peak."
      ],
      "rc_relation": "Material-validation role: RC3 only for a triggered, unresolved threat to a central conclusion, with all six burden-of-proof elements established. N/A does not block RC4."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "For a concrete physical or causal alternative that remains capable of changing classification, provide discriminating exclusion or honestly leave it open; ordinary two-source interference is one possible alternative, not a fixed hidden duty.",
      "award_conditions": [
        "For a concrete physical or causal alternative that remains capable of changing classification, provide discriminating exclusion or honestly leave it open; ordinary two-source interference is one possible alternative, not a fixed hidden duty.",
        "When triggered, award only if claim-relevant discriminating evidence resolves the threat or an evidence-based restriction makes it immaterial; merely acknowledging an unresolved material threat is not positive validation credit. With no trigger, record N/A and retain the fixed 0.5 without claiming performed validation."
      ],
      "applicability_and_na": [
        "Applies only when the submitted method, data, anomaly or conclusion creates the concrete material risk described here. If untriggered, record not_applicable and retain the fixed 0.5 contribution; this is not evidence that validation was performed, and does not block RC4."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.",
        "This criterion owns triggered physical/causal alternatives, not the positive mechanism M5 or numerical-risk V1. The same evidence may have two distinct functions, but the same threat is not double charged."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article pp. 5–7, weak-two-beam discussion and Fig. 5(a–c). Ordinary interference is a possible alternative; the weak source case is optional. Same-object control, localization or equivalent evidence may discriminate it; honest unresolved classification remains possible."
      ],
      "rc_relation": "Material-validation role: RC3 only for a triggered, unresolved threat to a central conclusion, with all six burden-of-proof elements established. N/A does not block RC4."
    },
    {
      "criterion_id": "V3",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Restrict conclusions to the stated two-dimensional phenomenological fixed-A TDGL and computed S/P branches, with coordinate/normalization declared; avoid real-material or fixed-vortex-count claims and restrict fine structure only where genuinely unresolved and claim-relevant.",
      "award_conditions": [
        "Restrict conclusions to the stated two-dimensional phenomenological fixed-A TDGL and computed S/P branches, with coordinate/normalization declared; avoid real-material or fixed-vortex-count claims and restrict fine structure only where genuinely unresolved and claim-relevant."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept reconstructible complex-field, winding, covariant-current/vorticity, defect, correlation or response diagnostics preserving the same decisive physical invariants. Amplitude minima alone do not establish topology; no fixed diagnostic triad is mandatory.",
        "Two orthogonal momentum-frequency cuts are sufficient complementary P evidence but not uniquely required. Equivalent time/frequency/response-family representations, controls, counterfactuals, localization and cross-representation tests are acceptable if genuinely discriminating. A weak-two-beam case is optional, not hidden compulsory work.",
        "No fixed vortex count, winding label, source frame, absolute momentum peak, stripe intensity, crop, colour, solver, box, mesh or late-time window. Consistently declared angular/cyclic wave-number conventions are accepted."
      ],
      "source_support": [
        "Article pp. 2–3, phenomenological model; pp. 5–7, mode-observability and interpretation caveats. Fixed-A two-dimensional model and computed-case scope. Absolute printed momentum coordinates and exact vortex totals are not quantitative gold."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    }
  ],
  "case_scientific_rules": [
    "Use tau partial_t² psi+gamma partial_t psi=psi−|psi|²psi+(grad−iA)²psi with tau=1/2, uniform psi=1 and zero initial velocity. First-order overdamped TDGL is a different model. Far-field treatment must not launch spurious normal-rim waves into the driven region.",
    "For these p=l=0 linearly polarized continuous resonant beams, A=xhat cos(t) sum_j A_j exp(−[(x−x_j)²+y²]/w0²); A_j is each beam's peak amplitude, not an unannounced integrated-normalization coefficient. Preserve the stated S/P positions, amplitudes, waists and damping.",
    "Construct Js=Im[psi*(grad−iA)psi] and its curl, phase winding, |psi|, phase, background-separated psi−1 and/or equally discriminating same-field observables. A claimed defect needs phase/current or invariant support, not just a depletion picture.",
    "The canonical S structure has paired co-located depletion/phase singularities and localized opposite-signed covariant vorticity, plus near-drive phase/linear and near-Higgs amplitude response families. Exact positions, number and a prescribed three-plot layout are not targets.",
    "The P source supports complex real-space/vortex texture and complementary directional interference, including a discriminating response transverse to beam separation. This is sufficient evidence for vortex-mediated diffraction, not a required source label or unique evidence path. Correctly evidence-supported bounded or negative classification is acceptable.",
    "The covariant source contains A²-driven amplitude response and linear-A phase/current coupling. With psi=|psi|exp(i theta), the source coupling includes iA exp(i theta)grad|psi|−A psi grad theta; nonremovable winding enables a phase-gradient/amplitude coupling channel.",
    "The printed q'=q xi/(2pi) label conflicts with angular-wave-number-like ticks; compare consistently transformed symmetry, directions and branches, not absolute source-coordinate peaks. Full-record switch-on transients cannot serve as fine momentum/low-frequency gold; bounded references support only robust structure.",
    "S/P change beam number, amplitude, waist and damping together and are not a one-variable causal intervention. Physical classification must be grounded in the candidate's own positive signal-to-mechanism chain and independently considered triggered alternatives. One genuinely dual-purpose object may support different evidential functions without requiring duplicate controls.",
    "Score exactly twenty fixed 0/0.5 material-core criteria. Do not import numerical score ranges or RC score caps. A valid run with no assessable scientific work receives score 0 and RC0 before criterion summation; assessable partial work and timeouts are graded on available evidence.",
    "Object existence, candidate presentation, candidate identification, physical inference and validation are different acts. Inspect every candidate-authored claim-bearing figure. A reference, rerender or examiner reconstruction can verify an object but cannot create missing candidate reasoning.",
    "When a material decision depends on feature resolution, fine structure, component relations, formula identity, representation equivalence or suspicious morphology, perform a focused applicable source/reference check. Establish model/observable/case/component, units, basis/gauge, normalization and transformations first; do not turn source-only display choices into new duties. A provisional score at least 9.0 or provisional RC4 requires a focused check of one central output and one principal-mechanism link. Reference verification is examiner-side, not a new candidate deliverable.",
    "In the stated dimensionless model, $\\tau\\partial_t^2\\psi+\\gamma\\partial_t\\psi=\\psi-|\\psi|^2\\psi+(\\nabla-i\\mathbf A)^2\\psi$, $\\tau=1/2$, $\\psi(0)=1$, $\\partial_t\\psi(0)=0$ (Eq. (3), task initial-velocity identity). The Gaussian member uses $\\mathbf A=\\hat{\\mathbf x}\\cos t\\sum_jA_j\\exp[-((x-x_j)^2+y^2)/w_0^2]$ with task-declared per-beam peak amplitudes, not an additional hidden LG normalization.",
    "The covariant source expands as $(\\nabla-i\\mathbf A)^2\\psi=\\nabla^2\\psi-2i\\mathbf A\\cdot\\nabla\\psi-i(\\nabla\\cdot\\mathbf A)\\psi-A^2\\psi$. For $\\psi=\\rho e^{i\\theta}$, $i\\mathbf A\\cdot\\nabla\\psi=i\\mathbf A e^{i\\theta}\\cdot\\nabla\\rho-\\rho e^{i\\theta}\\mathbf A\\cdot\\nabla\\theta$ (Eq. (7)). These are positive amplitude/phase-coupling mechanisms; neither coexistence alone nor alternative exclusion alone establishes them.",
    "$\\mathbf J_s=\\operatorname{Im}[\\psi^*(\\nabla-i\\mathbf A)\\psi]=\\rho^2(\\nabla\\theta-\\mathbf A)$ and $\\omega_s=\\nabla\\times\\mathbf J_s$ are source-defined diagnostics. A phase winding $w=(2\\pi)^{-1}\\oint\\nabla\\theta\\cdot d\\boldsymbol\\ell$ around a contour avoiding zeros is a derived equivalent topological test. Amplitude minima alone do not establish winding; no prescribed topology triad is required.",
    "With one declared convention $\\widetilde{\\delta\\psi}(\\mathbf k,\\Omega)=\\int d^2r\\,dt\\,[\\psi(\\mathbf r,t)-1]e^{-i\\mathbf k\\cdot\\mathbf r+i\\Omega t}$; equivalent background/normalization choices are accepted if they preserve the claim-bearing family. Angular wavevector $k$ and cyclic wavevector $q=k/(2\\pi)$ must not be silently interchanged. The source printed coordinate ambiguity prevents exact absolute-peak grading.",
    "M1–M5 test positive physical mechanisms and candidate signal-to-mechanism links. V2 tests a genuinely capable competing account; neither can be collapsed into the other. One diagnostic may support both roles if it really has both functions, without requiring two independent controls. Equivalent classifying evidence and evidence-supported negative conclusions retain credit; they do not excuse a materially invalid complex-field object."
  ],
  "closure_requirements": {
    "RC0": [
      "The central physical object is absent or materially invalid. Establish this scientific fact independently of atomic credit; a local notation or presentation weakness is not itself RC0.",
      "(F1 AND F2): Establish the second-order inertial complex TDGL and uniform zero-velocity initial state as the global central initial-value problem. Establish stable auditable central complex-field propagation and global object validity; only a materially invalid global propagation or central complex object can invalidate all output gates."
    ],
    "RC1": [
      "The central object exists, but a required indispensable component is absent or materially invalid. A failed presentation or overextended claim alone does not establish object absence or invalidity.",
      "(O1 AND O2): Construct the correct S driver and present valid reconstructible spatial complex/topological evidence with correct physical identity, global morphology, coordinates and normalization. For the same correct S driver, present reconstructible collective-response evidence with valid physical identity, major response morphology, transform and normalization.",
      "O3: Construct the correct P driver and present valid reconstructible real-space complex/topological response with correct global morphology, coordinates and normalization.",
      "O4: Present complementary reconstructible P collective-response evidence, distinct from its real-space order-parameter image, with material discriminating power for the claimed classification."
    ],
    "RC2": [
      "Required objects are scientifically valid, but a required principal mechanism or state-dependence inference is absent or incorrect. Reference evidence cannot provide omitted candidate reasoning.",
      "(M1 AND M2 AND M3 AND M4 AND M5 AND M6 AND M7): Explain amplitude/Higgs-scale response through the A² contribution to the covariant source. Explain phase/current response through linear-A and phase-gradient/current coupling. Establish the candidate's causal connection between S complex/topological organization and collective response, beyond juxtaposed displays. Establish the candidate's causal connection between P winding/complex organization and the chosen complementary collective signal; orthogonal-direction response is sufficient but not exclusive. Positively explain why phase/topology-mediated coupling can produce the claimed collective-response relation. Use the candidate's signals and relevant positive mechanisms to reach a bounded vortex-mediated or equivalent physical classification; a correct evidence-supported negative conclusion is also acceptable. Recognize that S/P simultaneously change beam number, amplitude, waist and damping, and avoid treating them as a single-variable causal experiment."
    ],
    "RC3": [
      "Required objects and principal mechanisms are established, but a concrete material validation or scope threat to a central conclusion remains unresolved.",
      "(V1 AND V2): For a concrete claim-relevant numerical, method or representation failure mode triggered by the actual method/data/anomaly/claim, provide discriminating evidence or an evidence-based restriction; otherwise record N/A. For a concrete physical or causal alternative that remains capable of changing classification, provide discriminating exclusion or honestly leave it open; ordinary two-source interference is one possible alternative, not a fixed hidden duty.",
      "Before assigning RC3, establish all six elements: the concrete failure mode; its origin in the submitted method/data/conclusion; a fair recognizable scientific risk; the affected central conclusion; why the submitted evidence cannot discriminate or exclude it; and functionally equivalent remedies. Evidence-based restriction may remove unsupported breadth, but cannot repair an incorrect signal, absent component or missing mechanism."
    ],
    "RC4": [
      "Every indispensable and co-primary claim has all its nonempty required role slots closed; supporting claims do not independently determine overall RC. Preserve AND/OR branch logic shown above and use scientific gate outcomes, not atomic scores.",
      "No triggered material risk remains unresolved. Untriggered risk criteria recorded N/A do not block RC4 and do not establish validation evidence.",
      "Classify descriptively by the most severe applicable failed required role (lowest RC), without score ceilings or target distributions. A score/RC tension prompts scientific review, not forced adjustment."
    ]
  },
  "references": [
    {
      "citation": "Daemo Kang, Tien-Tien Yeh, Takahiro Morimoto, and Alexander V. Balatsky. 2025. *Kapitza-Dirac interference of Higgs waves in superconductors*. *arXiv*, 2511.10954.  Version 1.",
      "url": "https://arxiv.org/abs/2511.10954v1",
      "scientific_scope": "Inertial complex TDGL S/P responses and evidence-bounded classification. Single-beam is Fig. 3; strong two-beam is Fig. 2; weak Fig. 5 is optional discrimination, not a compulsory third branch. No absolute source wavevector or fixed-vortex-count target is imposed.",
      "anchors": [
        "Kang et al. (2025), article pp. 2–3, Eqs. (1)–(3), initial-state and boundary paragraphs.",
        "Article p. 5, Fig. 3(a), caption, supercurrent/vorticity paragraph; Eqs. (4)–(6), p. 3.",
        "Article p. 5, Fig. 3(b,c) and Higgs/NG paragraph; transform definition on p. 3.",
        "Article p. 4, Fig. 2(a), caption and opening Results paragraphs; Eq. (6), p. 3.",
        "Article p. 4, Fig. 2(b,c), opening Results; pp. 6–7, Fig. 5(b,c) and contrast paragraph.",
        "Article pp. 4–5, Figs. 2(b,c), 3(b,c), frequency-family discussion.",
        "Article p. 3, Eq. (3); p. 5, Eq. (7) and surrounding coupling paragraphs.",
        "Article p. 5, Fig. 3(a–c), Eq. (7) and single-beam vortex/Higgs discussion.",
        "Article pp. 4–5, Fig. 2(a–c), Eq. (7), vortex-mediated linear-coupling discussion.",
        "Article pp. 4–7, Figs. 2(a–c), 3(a–c), 5(a–c), associated directional comparison.",
        "Article p. 4, Fig. 2 caption and Results parameters; p. 5, Fig. 3 caption.",
        "Article p. 3, Eq. (3), initial/boundary and transform definitions; Figs. 2(b,c), 3(b,c), pp. 4–5.",
        "Article pp. 5–7, weak-two-beam discussion and Fig. 5(a–c).",
        "Article pp. 2–3, phenomenological model; pp. 5–7, mode-observability and interpretation caveats."
      ]
    }
  ]
}