{
  "case_id": "Case23",
  "title": "Strong field physics in open quantum systems",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Bind the implementation to the visible one-dimensional driven two-band Hamiltonian, band/dipole functions, pulse, accelerated momentum, initial electronic state and equilibrium longitudinal bosonic bath with consistent units and signs.",
      "award_conditions": [
        "The implemented band/dipole, accelerated momentum, pulse and initial state belong to the specified longitudinal equilibrium-boson model with consistent units."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge the physical-case identity directly before downstream evidence.",
        "A localized failure here does not erase independently correct work that does not rely on the changed physical case."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint p. 2, Eqs. (1)-(2), Theory; p. 3, Results pulse/model paragraph: Longitudinal spin-boson coupling modifies the driven two-band system through a thermal bosonic bath, not a fitted transverse transition rate."
      ],
      "rc_relation": "RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Implement the visible positive-frequency spectral-density normalization, odd all-frequency extension and dimensionless coupling consistently, or provide an exact conversion preserving the same bath influence.",
      "award_conditions": [
        "The positive-frequency spectral density, odd extension and dimensionless coupling preserve the stated bath influence under an explicit normalization conversion."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "This convention identity is judged directly.",
        "An error is localized to work whose bath influence changes; unaffected independent work remains creditable."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint p. 3, Eq. (5); Supplement Sec. IV spectral-density convention; stated task spectral-density annex: Positive-frequency normalization and the odd extension must preserve the bath influence. The visible normalization annex fixes the numerical convention; there is no interchangeable unconverted coupling strength."
      ],
      "rc_relation": "RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Derive or correctly instantiate the bath-traced second-order momentum-resolved population with dressed action, thermal correlation, causal time ordering and Brillouin-zone integration for the visible final observable.",
      "award_conditions": [
        "The bath-traced population retains causal second-order ordering, Stark-dressed action, complex thermal correlation and Brillouin-zone integration."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [F1: Bind the implementation to the visible one-dimensional driven two-band Hamiltonian, band/dipole functions, pulse, accelerated momentum, initial electronic state and equilibrium longitudinal bosonic bath with consistent units and signs.; F2: Implement the visible positive-frequency spectral-density normalization, odd all-frequency extension and dimensionless coupling consistently, or provide an exact conversion preserving the same bath influence.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The population formula must use the same visible model and spectral convention.",
        "Correct formula work may retain credit when a localized upstream convention defect is repairable under the explicit physical-equivalence boundary."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint p. 3, Eqs. (3)-(5): Causally ordered second-order population contains the Stark-dressed action and complex thermal correlation before Brillouin-zone integration."
      ],
      "rc_relation": "RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Define the stated long-time integrated-population ratio, no-bath normalization and representation metadata, and submit a valid reconstructible bath/no-bath comparison covering all eight visible mandatory cases.",
      "award_conditions": [
        "The no-bath ratio and all eight mandatory long-time populations are valid and reconstructible under one declared case/normalization convention.",
        "The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "F3: Derive or correctly instantiate the bath-traced second-order momentum-resolved population with dressed action, thermal correlation, causal time ordering and Brillouin-zone integration for the visible final observable. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O2, I2, M3, M4, M5, M6 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The submitted matrix must be the bath-traced population object.",
        "A ratio, denominator, metadata or missing-case defect is charged at O1 and propagated only to conclusions it actually invalidates; independently valid mechanism-control evidence and mechanism distinctions remain creditable."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 3-5, Eqs. (4)-(6), Fig. 3(a)(i-iii) and Fig. 4(a); stated task eight-case matrix: The source establishes temperature/coupling/cutoff-dependent enhancement and suppression. The exact mandatory endpoints belong to the task; the source panels use illustrative cutoffs and are not the eight-case numerical answer."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Submit a physically well-defined same-object intervention or functionally equivalent discriminating output for at least one mandatory case capable of isolating the claimed phase/memory or decohering contribution.",
      "award_conditions": [
        "At least one mandatory case has a same-object intervention or equally discriminating output isolating the claimed phase/memory or decohering contribution.",
        "The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "F3: Derive or correctly instantiate the bath-traced second-order momentum-resolved population with dressed action, thermal correlation, causal time ordering and Brillouin-zone integration for the visible final observable. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O1, O3, I1, I3, M1, M2, M3, M4, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The control must preserve the same bath-resolved population object.",
        "Mandatory-matrix, surrogate-boundary and correlation-part/decohering-retention work remain independently judgeable when the control is absent.",
        "The intervention must preserve the same population object, case and other physical inputs while isolating the claimed bath contribution. A valid mandatory population does not establish this mechanism; a failed intervention does not erase independent mandatory-case output."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint p. 4, Fig. 3(b,c), especially caption identifying removal of Im C; Eq. (5): A same-object change of the phase-bearing correlation isolates a causal contribution; the plotted source example is not a compulsory additional parameter case or unique control."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present like-for-like mandatory-matrix comparisons exposing temperature, coupling and cutoff dependence while retaining case and normalization metadata.",
      "award_conditions": [
        "The mandatory matrix is compared like for like across temperature, coupling and cutoff without losing case metadata or relative scale.",
        "The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "O1: Define the stated long-time integrated-population ratio, no-bath normalization and representation metadata, and submit a valid reconstructible bath/no-bath comparison covering all eight visible mandatory cases. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O2, I2, M3, M4, M5, M6 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Parameter dependence requires valid like-for-like mandatory-case objects.",
        "Mechanism-control evidence remains independent of completeness of the three-axis comparison."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 3-5, Eqs. (4)-(6), Fig. 3(a)(i-iii) and Fig. 4(a); stated task eight-case matrix: The source establishes temperature/coupling/cutoff-dependent enhancement and suppression. The exact mandatory endpoints belong to the task; the source panels use illustrative cutoffs and are not the eight-case numerical answer."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from the submitted mandatory-case evidence the enhancement/suppression sign, ordering and order-of-magnitude class material to the comparison.",
      "award_conditions": [
        "The candidate identifies mandatory-case enhancement/suppression signs, orderings and meaningful magnitude classes from their own results.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "O1: Define the stated long-time integrated-population ratio, no-bath normalization and representation metadata, and submit a valid reconstructible bath/no-bath comparison covering all eight visible mandatory cases. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I2, M3, M4, M5, M6 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The identified signs and ordering must come from a valid candidate-presented matrix.",
        "Mechanism-control identification remains separately judgeable."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 3-5, Eqs. (4)-(6), Fig. 3(a)(i-iii) and Fig. 4(a); stated task eight-case matrix: The source establishes temperature/coupling/cutoff-dependent enhancement and suppression. The exact mandatory endpoints belong to the task; the source panels use illustrative cutoffs and are not the eight-case numerical answer."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from candidate-presented discriminating output the material effect of the isolated phase/memory or decohering contribution; examiner readback cannot create the observation.",
      "award_conditions": [
        "The candidate explicitly identifies the contribution-isolating intervention effect in their submitted output.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "O2: Submit a physically well-defined same-object intervention or functionally equivalent discriminating output for at least one mandatory case capable of isolating the claimed phase/memory or decohering contribution. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I1, I3, M1, M2, M3, M4, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The signal identification requires a valid discriminating output.",
        "Mandatory-case regime, parameter-dependence and correlation-part/decohering-retention reasoning retain independent credit when control-signal identification is absent.",
        "The intervention must preserve the same population object, case and other physical inputs while isolating the claimed bath contribution. A valid mandatory population does not establish this mechanism; a failed intervention does not erase independent mandatory-case output."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint p. 4, Fig. 3(b,c), especially caption identifying removal of Im C; Eq. (5): A same-object change of the phase-bearing correlation isolates a causal contribution; the plotted source example is not a compulsory additional parameter case or unique control."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify temperature-, coupling- and cutoff-dependent structures used in the claim from like-for-like mandatory comparisons.",
      "award_conditions": [
        "The candidate identifies the temperature/coupling/cutoff structures actually used in their scientific claim.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "O3: Present like-for-like mandatory-matrix comparisons exposing temperature, coupling and cutoff dependence while retaining case and normalization metadata. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I2, M3, M4, M5, M6 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The parameter-dependent signal must be identified from valid like-for-like comparisons.",
        "Control-based mechanism identification remains independent."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 3-5, Eqs. (4)-(6), Fig. 3(a)(i-iii) and Fig. 4(a); stated task eight-case matrix: The source establishes temperature/coupling/cutoff-dependent enhancement and suppression. The exact mandatory endpoints belong to the task; the source panels use illustrative cutoffs and are not the eight-case numerical answer."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use specific identified mandatory-case structures to determine the visible regimes where the bath enhances or suppresses post-pulse population.",
      "award_conditions": [
        "Specific mandatory-case observations establish the regimes of enhancement and suppression rather than a generic statement that baths change ionization.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [I1: Identify from the submitted mandatory-case evidence the enhancement/suppression sign, ordering and order-of-magnitude class material to the comparison.; I3: Identify temperature-, coupling- and cutoff-dependent structures used in the claim from like-for-like mandatory comparisons.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M3, M4, M5, M6, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The regime conclusion must be grounded in candidate-identified central and parameter-dependent signals.",
        "Correct mechanism or surrogate analysis not relying on a missing regime comparison remains creditable."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 3-5, Eqs. (4)-(6), Fig. 3(a)(i-iii) and Fig. 4(a); stated task eight-case matrix: The source establishes temperature/coupling/cutoff-dependent enhancement and suppression. The exact mandatory endpoints belong to the task; the source panels use illustrative cutoffs and are not the eight-case numerical answer."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use submitted evidence to distinguish robust bath-parameter regime structure from isolated numerical, normalization or presentation effects.",
      "award_conditions": [
        "The regime interpretation distinguishes parameter-dependent physics from isolated numerical, ratio-normalization or display effects.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [I1: Identify from the submitted mandatory-case evidence the enhancement/suppression sign, ordering and order-of-magnitude class material to the comparison.; I3: Identify temperature-, coupling- and cutoff-dependent structures used in the claim from like-for-like mandatory comparisons.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M3, M4, M5, M6, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Robustness interpretation requires the candidate-identified signal and its parameter structure.",
        "Correct causal mechanism work retains independent credit when robustness is not established."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 3-5, Eqs. (4)-(6), Fig. 3(a)(i-iii) and Fig. 4(a); stated task eight-case matrix: The source establishes temperature/coupling/cutoff-dependent enhancement and suppression. The exact mandatory endpoints belong to the task; the source panels use illustrative cutoffs and are not the eight-case numerical answer."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Correctly distinguish the real decohering bath-correlation contribution from the phase-bearing finite-memory contribution within the stated spectral convention.",
      "award_conditions": [
        "The argument correctly separates real decohering correlation from imaginary phase-bearing finite memory under the actual J convention.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "F3: Derive or correctly instantiate the bath-traced second-order momentum-resolved population with dressed action, thermal correlation, causal time ordering and Brillouin-zone integration for the visible final observable. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M1, M2, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The mechanism distinction requires the correct bath-correlation object but is independently judgeable when intervention linkage is incomplete.",
        "Correct regime and surrogate-boundary conclusions remain separately judgeable; absent control evidence is charged to O2/I2 and the evidence-link atoms M5/M6, not backfilled into this correlation-part distinction.",
        "The intervention must preserve the same population object, case and other physical inputs while isolating the claimed bath contribution. A valid mandatory population does not establish this mechanism; a failed intervention does not erase independent mandatory-case output."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 3-5, Eq. (5), Fig. 3(b,c) and following physical-interpretation paragraphs: The real correlation dephases while the imaginary finite-memory part modifies phase/action. A correct causal explanation must remain tied to the submitted intervention."
      ],
      "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain how thermal/decohering response can allow transient field-driven population to be retained in the post-pulse observable.",
      "award_conditions": [
        "The explanation connects thermal/decohering influence to retention of transient field-driven population after the pulse.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [M3: Correctly distinguish the real decohering bath-correlation contribution from the phase-bearing finite-memory contribution within the stated spectral convention.; I1: Identify from the submitted mandatory-case evidence the enhancement/suppression sign, ordering and order-of-magnitude class material to the comparison.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M5, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "This causal link needs the correct bath-part distinction and an identified population signal.",
        "The phase-memory and surrogate branches remain independently creditable.",
        "The intervention must preserve the same population object, case and other physical inputs while isolating the claimed bath contribution. A valid mandatory population does not establish this mechanism; a failed intervention does not erase independent mandatory-case output."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 3-5, Eq. (5), Fig. 3(b,c) and following physical-interpretation paragraphs: The real correlation dephases while the imaginary finite-memory part modifies phase/action. A correct causal explanation must remain tied to the submitted intervention."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain how the phase-bearing finite-memory contribution modifies effective action or gap consistently with the candidate's same-object evidence.",
      "award_conditions": [
        "The phase-bearing finite-memory contribution is linked to an effective action/gap change consistent with the same-object diagnostic.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [M3: Correctly distinguish the real decohering bath-correlation contribution from the phase-bearing finite-memory contribution within the stated spectral convention.; I2: Identify from candidate-presented discriminating output the material effect of the isolated phase/memory or decohering contribution; examiner readback cannot create the observation.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M4, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "This link needs the correct bath-part distinction and the discriminating signal.",
        "The decohering-retention and surrogate branches remain independently creditable.",
        "The intervention must preserve the same population object, case and other physical inputs while isolating the claimed bath contribution. A valid mandatory population does not establish this mechanism; a failed intervention does not erase independent mandatory-case output."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 3-5, Eq. (5), Fig. 3(b,c) and following physical-interpretation paragraphs: The real correlation dephases while the imaginary finite-memory part modifies phase/action. A correct causal explanation must remain tied to the submitted intervention."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect the claimed bath mechanism to the candidate's discriminating output; generic dephasing narratives and fitted relaxation times are not equivalent evidence.",
      "award_conditions": [
        "The claimed bath mechanism is causally tied to candidate-presented contribution-isolating evidence; a fitted T2 or generic dephasing narrative is insufficient.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [I2: Identify from candidate-presented discriminating output the material effect of the isolated phase/memory or decohering contribution; examiner readback cannot create the observation.; M3: Correctly distinguish the real decohering bath-correlation contribution from the phase-bearing finite-memory contribution within the stated spectral convention.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M1, M2, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The causal attribution needs both a candidate-identified control signal and the correct mechanism distinction.",
        "Regime and relaxation-boundary conclusions remain independently judgeable.",
        "The intervention must preserve the same population object, case and other physical inputs while isolating the claimed bath contribution. A valid mandatory population does not establish this mechanism; a failed intervention does not erase independent mandatory-case output."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint p. 4, Fig. 3(b,c), especially caption identifying removal of Im C; Eq. (5): A same-object change of the phase-bearing correlation isolates a causal contribution; the plotted source example is not a compulsory additional parameter case or unique control."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "State the physically defensible boundary for adequacy of a single relaxation-time surrogate; the high-temperature Debye limit is not globally equivalent.",
      "award_conditions": [
        "The candidate states an evidence-supported relaxation-time adequacy boundary and does not turn the high-temperature Debye limit into global bath equivalence.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "F3: Derive or correctly instantiate the bath-traced second-order momentum-resolved population with dressed action, thermal correlation, causal time ordering and Brillouin-zone integration for the visible final observable. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M1, M2, M3, M4, M5, M6 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Surrogate adequacy must be assessed against the bath-resolved formulation.",
        "Correct bath-regime and mechanism work retains credit if the surrogate boundary is incomplete.",
        "Surrogate adequacy is an unconditional commissioned scientific question, not the risk-triggered V2 atom. An evidenced boundary need not include every source alternative-bath curve."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 3-4, paragraph following Eq. (5), Fig. 2(b,c) and Debye-limit discussion: The high-temperature Debye limit gives a relaxation-time form, not global equivalence for arbitrary bath spectra or low temperature."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M8",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Integrate mandatory-case signals, bath mechanism, parameter dependence and surrogate boundary into the strongest conclusion supported by reconstructible evidence.",
      "award_conditions": [
        "The final answer integrates mandatory-case regimes, causal bath mechanism, parameter dependence and surrogate boundary within the demonstrated scope.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [M1: Use specific identified mandatory-case structures to determine the visible regimes where the bath enhances or suppresses post-pulse population.; M3: Correctly distinguish the real decohering bath-correlation contribution from the phase-bearing finite-memory contribution within the stated spectral convention.; M7: State the physically defensible boundary for adequacy of a single relaxation-time surrogate; the high-temperature Debye limit is not globally equivalent.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M2, M4, M5, M6 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The final conclusion requires a valid regime decision, principal mechanism and surrogate boundary.",
        "Correct independent subclaims retain their atomic credit even when the integrated conclusion does not close."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 2-3, equilibrium initial-state, second-order and high-temperature/multi-boson limitations; p. 5, discussion: The evidence supports the stated equilibrium longitudinal bosonic-bath approximation; it does not establish heating, melting, fermionic scattering or experimental readout."
      ],
      "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "V1",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Assess relaxation-time adequacy against the bath-resolved result using evidence, accepting functionally equivalent comparisons that preserve the physical object and isolate the surrogate boundary.",
      "award_conditions": [
        "Relaxation-time adequacy is substantively compared with bath-resolved physics using equivalent evidence; a complete hidden alternative-bath curve is unnecessary."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "F3: Derive or correctly instantiate the bath-traced second-order momentum-resolved population with dressed action, thermal correlation, causal time ordering and Brillouin-zone integration for the visible final observable. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O1, I1, V2, V3, M3, M4, M5, M6 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The adequacy assessment must preserve the same bath-resolved formulation; V1 itself judges whether the submitted functionally equivalent comparison supplies discriminating evidence.",
        "An incomplete mandatory matrix does not erase a valid same-object surrogate comparison, and weak surrogate validation does not erase independently correct matrix, risk-response, scope or bath-mechanism work.",
        "Surrogate adequacy is an unconditional commissioned scientific question, not the risk-triggered V2 atom. An evidenced boundary need not include every source alternative-bath curve."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 3-4, paragraph following Eq. (5), Fig. 2(b,c) and Debye-limit discussion: The high-temperature Debye limit gives a relaxation-time form, not global equivalence for arbitrary bath spectra or low temperature."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "When candidate method, data, anomaly or claim raises a concrete material alternative threatening the central conclusion, supply discriminating evidence capable of exposing it or explicitly leave the outcome unresolved for adjudication.",
      "award_conditions": [
        "When the actual calculation raises a material alternative, supply discriminatory evidence or explicitly preserve the unresolved issue for adjudication, subject to the existing applicability rule."
      ],
      "applicability_and_na": [
        "Activate only for a concrete material risk arising from the candidate method, data, anomaly or claim; no fixed test is required in the absence of a trigger.",
        "Without a triggered risk record N/A and award 0.5 without positive validation evidence; this neither blocks RC4 nor triggers RC3.",
        "When triggered, accept functionally equivalent discriminating evidence or a justified restriction of the threatened claim."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Evaluate the trigger and its evidence independently of the atomic award.",
        "No untriggered preferred check may reduce other item credit; one defect is charged only where it damages evidence or claim."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint p. 3, Eqs. (3)-(6); stated task observable and evidence commission: Normalization, causal ordering and intervention identity provide the scientific basis for actual material risks. Validation is conditional; the source does not prescribe an extra numerical checklist."
      ],
      "rc_relation": "RC3: an unresolved applicable material risk, only after signals and principal mechanisms are substantially supported and all six risk-proof requirements are met. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "V3",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Limit conclusions to the stated two-band, equilibrium bosonic-bath, longitudinal-coupling and second-order setting; do not claim unsupported dynamic heating, fermionic scattering, damage, melting or experimental observability.",
      "award_conditions": [
        "The conclusion remains second-order, two-band, equilibrium-bosonic and longitudinal; uncomputed heating, fermionic scattering, damage or experimental observability are not established."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Honest scope is independently judgeable and is not conditioned on upstream success.",
        "A correct scope restriction retains credit even if an upstream object or mechanism fails."
      ],
      "equivalent_evidence": [
        "Gauge, representation, frequency-integration convention and numerical method may differ with exact bath-influence conversion, matching causal second-order content, initial state and final ratio.",
        "Any same-object contribution-isolating intervention with demonstrated discriminating function can replace an imaginary-correlation switch. Preserve mandatory-case coverage, sign, ordering and magnitude classes.",
        "Accept evidence-based surrogate-boundary comparisons without a full Debye/T2 curve or hidden intermediate scan; alternative displays, quadratures and grids are allowed when the claimed physical structures remain reconstructible."
      ],
      "source_support": [
        "Boroumand et al. (2025), preprint pp. 2-3, equilibrium initial-state, second-order and high-temperature/multi-boson limitations; p. 5, discussion: The evidence supports the stated equilibrium longitudinal bosonic-bath approximation; it does not establish heating, melting, fermionic scattering or experimental readout."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    }
  ],
  "case_scientific_rules": [
    "The canonical second-order population is nc(K,t) = (1/2) Re integral_{-infinity}^t dt1 integral_{-infinity}^{t1} dt2 Omega*(K_t1,t1) Omega(K_t2,t2) exp[i S(t1,t2) + C(t1-t2)]. S = (1/hbar) integral_{t2}^{t1} sqrt(E(K_tau)^2 + hbar^2 Omega(K_tau,tau)^2) d tau. Integrate over the one-dimensional Brillouin zone and use the specified long-time bath/no-bath ratio eta.",
    "C(dt) = integral_{-infinity}^{infinity} J(omega) {i sin(omega dt) - [1-cos(omega dt)] coth[hbar omega/(2 kB T)]} d omega. The positive-frequency convention is J_plus(omega) = 2 sum_q |g_q/(hbar omega_q)|^2 delta(omega-omega_q), with odd all-frequency extension. J has inverse-angular-frequency units and j0 is dimensionless. Positive-only or other conventions require all factors and thermal terms converted to preserve C.",
    "The dominant main-text formula and full supplemental source correction/dressed-state factor are equivalent only when predictions agree at the resolution material to the claim. The small correction is not a compulsory separate calculation.",
    "The eight mandatory cases are the Cartesian corners omega_c/omega0 = 0.1 or 3.4, T = 300 or 20000 K, and j0 = 0.1 or 5, with no-bath reference. Optional cases do not replace a missing mandatory corner. Grade robust sign, ordering and magnitude class within demonstrated uncertainty, not reference digits.",
    "The no-bath post-pulse population is of order 2e-6. For T = 300 K, log10 eta at (cutoff,j0) = (0.1,0.1),(3.4,0.1),(0.1,5),(3.4,5) is approximately -0.02,-0.08,-1.14,-4.23. At T = 20000 K the corresponding classes are approximately 0.24,3.46,3.75,2.70. These indicate robust regime structure, not exact numerical targets or a required table format.",
    "For the stated Ohmic convention, Im C(t) = 4 j0 omega_c t/[1+(omega_c t)^2]^2 up to a declared transform/sign convention. Distinguish real decoherence, which can retain transient population, from finite-memory phase, which modifies effective action/gap.",
    "Removing Im C in one mandatory case is an accepted diagnostic, not the only route. An intervention must preserve the same population and physical case while isolating its claimed contribution; simultaneous changes of temperature, coupling, cutoff, spectrum and diagnostic are not discriminating.",
    "A simple relaxation-time form emerges in the high-temperature Debye limit, not for every spectral density or temperature. A full Debye-versus-T2 curve is optional, but the adequacy boundary must be evidenced, not merely a fitted T2 asserted to reproduce bath physics.",
    "Exact direct Hamiltonian propagation is accepted only with demonstrated matching thermal state, longitudinal coupling, spectral convention, weak-drive/second-order scope and final observable. An imposed Markovian rate is not the same bath-resolved branch.",
    "Concrete risks include bath/state/normalization misbinding, under-resolved Brillouin-zone cancellation, multi-factor interventions, finite-time transients mistaken for post-pulse populations and overextension to dynamic heating or experiment. Unresolved material comparisons remain bounded adjudication issues rather than hidden full sweeps.",
    "The score is the sum of twenty material-core criteria, each worth either 0 or 0.5, for a maximum of 10.0. Research Closure is descriptive and never caps, floors, rescales or repairs the score.",
    "Judge physical object identity and correctness before display similarity. For each output record object_valid, presentation_adequate and claim_adequate separately; all three must hold for its atomic award. A presentation or claim defect alone is not evidence that an existing physical object is absent or invalid.",
    "Candidate-created data, candidate presentation, candidate identification, physical inference and validation are distinct evidential acts. Examiner inspection or reconstruction may verify an object but cannot create missing candidate identification, reasoning or risk resolution.",
    "A dependency propagates only the failed necessary physical fact, not the whole upstream atomic verdict or unrelated missing detail. Name the failed premise, the downstream obligation needing it, and why independent candidate-presented evidence does not establish it. Preserve unaffected branches, independent work and honest scope.",
    "Numerical reliability has no separate generic penalty. Charge a defect where it materially damages a physical object or evidence, and a dependent conclusion only when that same defect makes the conclusion false or unsupported. Missing a preferred convergence study, control, solver or named self-check is not itself a failure.",
    "Risk-triggered validation applies only to a concrete material risk arising from the candidate method, data, anomaly or claim. With no such risk record N/A and award the fixed atomic credit without treating it as positive validation evidence; N/A does not block RC4. Unconditional scope obligations cannot be N/A.",
    "Before assigning RC3 establish all six: the concrete failure mode; its origin in candidate work; the fair task or standard-knowledge basis; the threatened central conclusion; why submitted evidence cannot expose or exclude it; and examples of functionally equivalent discriminating evidence or an honest scope restriction that would resolve it. A generic possibility of further testing is insufficient.",
    "Use bounded examiner-side source/reference readback only to resolve a material scientific uncertainty, not to demand pixels, an undeclared tolerance or additional candidate deliverables. A provisional score of at least 9.0 or provisional RC4 triggers one bounded central-output-anchor check and one principal-mechanism-link check. Reference conflict or insufficiency remains an explicit unresolved decision, not an invented target.",
    "Evaluate closure-role trigger facts independently of atomic awards and select the most severe failed required role across all indispensable and co-primary claims. Supporting claims do not independently set overall closure. A point loss alone is not a closure-gate fact.",
    "A valid candidate-caused incomplete or timeout attempt with no scientifically assessable required submission has score 0.0 and RC0 before N/A bookkeeping. Assessable incomplete work is graded from the submitted evidence; unsubmitted scratch or logs do not become scientific answers.",
    "At accelerated momentum $K_t=K+eA(t)/\\hbar$, $\\Omega=2ed(K_t)E(t)/\\hbar$ and $E_s=\\sqrt{E(K_t)^2+\\hbar^2|\\Omega|^2}$. The population is $n_c(K,t)=\\tfrac12\\operatorname{Re}\\int_{-\\infty}^t dt_1\\int_{-\\infty}^{t_1}dt_2\\,\\Omega^*(t_1)\\Omega(t_2)e^{iS(t_1,t_2)+C(t_1-t_2)}$, with $S=\\hbar^{-1}\\int_{t_2}^{t_1}E_s(K_\\tau)d\\tau$ (Eqs. (3)-(4)); keep causal order and the chosen normalization.",
    "The correlation is $C(s)=\\int_{-\\infty}^{\\infty}d\\omega\\,J(\\omega)\\{i\\sin(\\omega s)-[1-\\cos(\\omega s)]\\coth[\\hbar\\omega/(2k_BT)]\\}$ (Eq. (5)), using the stated odd all-frequency extension. Its real and imaginary parts have distinct decohering and phase-bearing roles. $\\eta=\\int_{\\rm BZ}n_c(K,\\infty;j_0)dK/\\int_{\\rm BZ}n_c(K,\\infty;0)dK$ (Eq. (6)); compare all mandatory cases to that same no-bath object.",
    "In the high-temperature Debye limit only, $C(s)\\to-s/T_2$ for causal $s\\ge0$, with $T_2=\\hbar/(2\\pi k_BTj_0)$ in the source convention. This does not replace the finite-memory correlation for the other spectral densities.",
    "The task spectral annex fixes $J_+(\\omega)=2\\sum_q|g_q/(\\hbar\\omega_q)|^2\\delta(\\omega-\\omega_q)$ for $\\omega>0$, its odd all-frequency extension, and $J(\\omega)=j_0\\omega\\exp(-|\\omega|/\\omega_c)/\\omega_c^2$. Thus J has units of inverse angular frequency and j0 is dimensionless. This normalization is task-defined; the source Eq. (5) supplies the correlation structure, not permission to change the coupling without conversion."
  ],
  "closure_requirements": {
    "RC0": [
      "Required claim CL1, central object: All of [F1: Bind the implementation to the visible one-dimensional driven two-band Hamiltonian, band/dipole functions, pulse, accelerated momentum, initial electronic state and equilibrium longitudinal bosonic bath with consistent units and signs.; F2: Implement the visible positive-frequency spectral-density normalization, odd all-frequency extension and dimensionless coupling consistently, or provide an exact conversion preserving the same bath influence.; F3: Derive or correctly instantiate the bath-traced second-order momentum-resolved population with dressed action, thermal correlation, causal time ordering and Brillouin-zone integration for the visible final observable.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Apply for a missing or materially invalid required central object; a presentation-only or claim-only defect does not establish object invalidity.",
      "No scientifically assessable required submission gives the terminal 0.0/RC0 disposition."
    ],
    "RC1": [
      "Required claim CL1, indispensable component: All of [O1: Define the stated long-time integrated-population ratio, no-bath normalization and representation metadata, and submit a valid reconstructible bath/no-bath comparison covering all eight visible mandatory cases.; O2: Submit a physically well-defined same-object intervention or functionally equivalent discriminating output for at least one mandatory case capable of isolating the claimed phase/memory or decohering contribution.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "The central object is established but a required physical component is absent or materially invalid. Preserve independent valid branches; do not invent a hidden canonical plot, sampling grid or implementation duty."
    ],
    "RC2": [
      "Required claim CL2, principal mechanism: All of [M3: Correctly distinguish the real decohering bath-correlation contribution from the phase-bearing finite-memory contribution within the stated spectral convention.; M8: Integrate mandatory-case signals, bath mechanism, parameter dependence and surrogate boundary into the strongest conclusion supported by reconstructible evidence.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required signal objects/components exist, but an indispensable principal mechanism or co-primary scientific conclusion is missing, wrong or unsupported by candidate-presented and identified evidence. Correct data do not let an examiner supply missing reasoning."
    ],
    "RC3": [
      "Required claim CL3, material validation: V2: When candidate method, data, anomaly or claim raises a concrete material alternative threatening the central conclusion, supply discriminating evidence capable of exposing it or explicitly leave the outcome unresolved for adjudication.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "All indispensable signal and principal-mechanism roles are substantially supported, but a concrete triggered material risk remains unresolved and inadequately restricted.",
      "Establish the failure mode, candidate origin, fair task/knowledge basis, threatened central conclusion, insufficiency of submitted evidence, and equivalent resolution or scope restriction. Missing an examiner-preferred check alone never suffices."
    ],
    "RC4": [
      "Every nonempty required role in every indispensable and co-primary claim above is scientifically established from candidate evidence, with the correct case/model/observable identities and evidence-bounded conclusion.",
      "All applicable material risks are discriminated or honestly restricted; no unresolved material ambiguity remains. Risk N/A does not block closure or supply positive validation evidence. Honest limitations cannot repair a false signal or mechanism.",
      "Select the most severe failed required role if any; otherwise RC4. No score threshold, score ceiling or required display/solver checklist determines this classification."
    ]
  },
  "references": [
    {
      "citation": "Neda Boroumand, Adam Thorpe, Graeme Bart, Andrew Parks, Mohamad Toutounji, Giulio Vampa, Thomas Brabec, and Lu Wang. 2025. Strong field physics in open quantum systems. arXiv, 2502.10240.",
      "url": "https://arxiv.org/abs/2502.10240v1",
      "scientific_scope": "Bath-resolved second-order post-pulse population, spectral normalization, mandatory temperature/coupling/cutoff regimes, contribution-isolating mechanism and relaxation-time adequacy. No hidden full sweep or globally exact surrogate is implied.",
      "anchors": [
        "preprint p. 2, Eqs. (1)-(2), Theory; p. 3, Results pulse/model paragraph",
        "preprint p. 3, Eq. (5); Supplement Sec. IV spectral-density convention; stated task spectral-density annex",
        "preprint p. 3, Eqs. (3)-(5)",
        "preprint pp. 3-5, Eqs. (4)-(6), Fig. 3(a)(i-iii) and Fig. 4(a); stated task eight-case matrix",
        "preprint p. 4, Fig. 3(b,c), especially caption identifying removal of Im C; Eq. (5)",
        "preprint pp. 3-5, Eq. (5), Fig. 3(b,c) and following physical-interpretation paragraphs",
        "preprint pp. 3-4, paragraph following Eq. (5), Fig. 2(b,c) and Debye-limit discussion",
        "preprint pp. 2-3, equilibrium initial-state, second-order and high-temperature/multi-boson limitations; p. 5, discussion",
        "preprint p. 3, Eqs. (3)-(6); stated task observable and evidence commission"
      ]
    }
  ]
}