cases/case18/grading_rubric.json

{
  "case_id": "Case18",
  "title": "High-harmonic generation from two weakly coupled molecules: A simple tight-binding model",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Establish the shared physical identity of the half-filled four-site tight-binding model, its geometry and spin-degenerate occupation, weak-coupling variable, length-gauge interaction and drive fixed by the reference-coupling gap.",
      "award_conditions": [
        "The four-site geometry, two doubly occupied lowest orbitals and weak-coupling variable identify one common model; the drive frequency is fixed at the reference gap rather than recomputed at every coupling."
      ],
      "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 obligation is independently judgeable; no upstream failure is propagated into it.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article p. 043106-2, Eqs. (1)-(8), Fig. 1(a,b): Four-site geometry, half-filled spin-degenerate occupation and the reference-gap drive define the target; frequency stays fixed during the coupling sweep."
      ],
      "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": "Propagate both initially occupied orbitals, each doubly occupied, in the exact branch and construct a valid reconstructible harmonic-order-resolved total-acceleration HHG spectrum.",
      "award_conditions": [
        "Both occupied orbitals are actually propagated in the exact branch and summed with spin before acceleration-spectrum power is formed; the harmonic-order reduction is reconstructible."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "F1: Establish the shared physical identity of the half-filled four-site tight-binding model, its geometry and spin-degenerate occupation, weak-coupling variable, length-gauge interaction and drive fixed by the reference-coupling gap. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article p. 043106-3, Eqs. (9)-(13): Both doubly occupied orbitals contribute coherently to the total acceleration before spectral power is formed."
      ],
      "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": "Implement the supplied instantaneous-state adia-intra identity 2 r00 + 2 r11 and preserve it as an independent like-for-like approximation branch under the same inputs and observable convention.",
      "award_conditions": [
        "Instantaneous occupied-state matrix elements implement 2r00+2r11 without transition terms, and feed the same spectral construction and physical inputs as the exact comparison."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "F1: Establish the shared physical identity of the half-filled four-site tight-binding model, its geometry and spin-degenerate occupation, weak-coupling variable, length-gauge interaction and drive fixed by the reference-coupling gap. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in F2 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-5-6, Eqs. (14)-(20): Instantaneous eigenstates define the adia-intra position; it is not the exact time propagation."
      ],
      "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": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide a physically valid reconstructible exact order-resolved HHG output family over informative weak-coupling and polarization variation, with correct case/order binding and nonnegative yields.",
      "award_conditions": [
        "The submitted exact data form nonnegative, case/order-bound HHG yields over an informative weak-coupling/polarization domain; the object cannot be an adiabatic surrogate.",
        "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": [
        "F2: Propagate both initially occupied orbitals, each doubly occupied, in the exact branch and construct a valid reconstructible harmonic-order-resolved total-acceleration HHG spectrum. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-3-5, Figs. 2, 3 and 5; paragraph following Fig. 5: The molecular-direction family is nearly coupling independent; cancellation of linear acceleration terms leaves an intermolecular yield proportional to the fourth power of weak coupling."
      ],
      "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": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present computed exact angular reorganization jointly resolved in coupling, polarization and harmonic order; coverage must expose the order-dependent competition and strongest-emission direction.",
      "award_conditions": [
        "The computed coverage resolves coupling, polarization and harmonic order jointly, exposing the change of the maximizing direction rather than an isolated angle dependence.",
        "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: Provide a physically valid reconstructible exact order-resolved HHG output family over informative weak-coupling and polarization variation, with correct case/order binding and nonnegative yields. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Only the exact response facts needed for coupling/order/angular reorganization propagate here; independent adiabatic construction is not erased by a failed exact branch."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-4-5, Fig. 4(b) and Fig. 5: Order-dependent competition switches the maximizing polarization, with higher orders switching at weaker coupling."
      ],
      "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 genuinely retained qualitative organization in a same-input, common-observable exact versus adia-intra comparison.",
      "award_conditions": [
        "A same-input exact/adia-intra comparison visibly retains a genuine angular/coupling organization on a common observable 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": [
        "All of [F2: Propagate both initially occupied orbitals, each doubly occupied, in the exact branch and construct a valid reconstructible harmonic-order-resolved total-acceleration HHG spectrum.; F3: Implement the supplied instantaneous-state adia-intra identity 2 r00 + 2 r11 and preserve it as an independent like-for-like approximation branch under the same inputs and observable convention.] 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.",
        "All named physical premises are necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Exact/adia-intra comparison needs the same model inputs and common observable scale. Retained qualitative organization and a concrete quantitative departure remain separately judgeable; failure of one does not mechanically erase the other."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-7-8, Figs. 7-9 and adjacent comparison with Figs. 2, 4(b) and 5: Adiabatic following retains broad angular organization and ordered competition, not quantitative equality."
      ],
      "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": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present one concrete quantitative departure in that same like-for-like exact versus adia-intra comparison.",
      "award_conditions": [
        "That like-for-like comparison exposes an auditable quantitative yield or competition/crossover departure; arbitrary independent rescaling cannot manufacture it.",
        "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": [
        "All of [F2: Propagate both initially occupied orbitals, each doubly occupied, in the exact branch and construct a valid reconstructible harmonic-order-resolved total-acceleration HHG spectrum.; F3: Implement the supplied instantaneous-state adia-intra identity 2 r00 + 2 r11 and preserve it as an independent like-for-like approximation branch under the same inputs and observable convention.] 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.",
        "All named physical premises are necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Exact/adia-intra comparison needs the same model inputs and common observable scale. Retained qualitative organization and a concrete quantitative departure remain separately judgeable; failure of one does not mechanically erase the other."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-6-8, Fig. 6, Fig. 8 white comparison marks and Fig. 9; Eqs. (18)-(21): Omitted instantaneous-state transitions reduce the intermolecular response and displace crossovers toward stronger coupling. The half-frequency Fig. 6 is explanatory context, not a compulsory input case."
      ],
      "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 intramolecular and intermolecular response families and their different weak-coupling dependences in the candidate's exact evidence.",
      "award_conditions": [
        "The candidate identifies the nearly coupling-independent molecular response and the growing intermolecular response in their own exact 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: Provide a physically valid reconstructible exact order-resolved HHG output family over informative weak-coupling and polarization variation, with correct case/order binding and nonnegative yields. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-3-5, Figs. 2, 3 and 5; paragraph following Fig. 5: The molecular-direction family is nearly coupling independent; cancellation of linear acceleration terms leaves an intermolecular yield proportional to the fourth power of weak coupling."
      ],
      "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 the candidate's evidence the joint signal that the strongest-emission direction reorganizes with harmonic order.",
      "award_conditions": [
        "The candidate explicitly locates the order-dependent reorganization of the strongest-emission direction in their computed evidence.",
        "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: Present computed exact angular reorganization jointly resolved in coupling, polarization and harmonic order; coverage must expose the order-dependent competition and strongest-emission direction. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Only the exact response facts needed for coupling/order/angular reorganization propagate here; independent adiabatic construction is not erased by a failed exact branch."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-4-5, Fig. 4(b) and Fig. 5: Order-dependent competition switches the maximizing polarization, with higher orders switching at weaker coupling."
      ],
      "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": "Explicitly identify a genuinely retained qualitative feature in the like-for-like exact/adia-intra evidence.",
      "award_conditions": [
        "The candidate names and binds a retained qualitative feature to both correctly identified comparison branches.",
        "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 genuinely retained qualitative organization in a same-input, common-observable exact versus adia-intra comparison. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Exact/adia-intra comparison needs the same model inputs and common observable scale. Retained qualitative organization and a concrete quantitative departure remain separately judgeable; failure of one does not mechanically erase the other."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-7-8, Figs. 7-9 and adjacent comparison with Figs. 2, 4(b) and 5: Adiabatic following retains broad angular organization and ordered competition, not quantitative equality."
      ],
      "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": "I4",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Explicitly identify a concrete quantitative departure in the like-for-like exact/adia-intra evidence.",
      "award_conditions": [
        "The candidate identifies a concrete quantitative departure from the common-scale comparison, not merely that two curves differ.",
        "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": [
        "O4: Present one concrete quantitative departure in that same like-for-like exact versus adia-intra comparison. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Exact/adia-intra comparison needs the same model inputs and common observable scale. Retained qualitative organization and a concrete quantitative departure remain separately judgeable; failure of one does not mechanically erase the other."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-6-8, Fig. 6, Fig. 8 white comparison marks and Fig. 9; Eqs. (18)-(21): Omitted instantaneous-state transitions reduce the intermolecular response and displace crossovers toward stronger coupling. The half-frequency Fig. 6 is explanatory context, not a compulsory input case."
      ],
      "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": "Explain the physical origins of the two response families and their different dependence on weak intermolecular coupling.",
      "award_conditions": [
        "The physical argument explains the different weak-coupling dependence of the two families and is supported by the candidate exact-response identification.",
        "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.",
        "Explain the cancellation of the linear occupied-orbital acceleration contributions, or an equivalent derivation of the leading fourth-power intermolecular yield, while the molecular response remains nearly coupling independent."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "I1: Identify intramolecular and intermolecular response families and their different weak-coupling dependences in the candidate's exact evidence. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-3-5, Figs. 2, 3 and 5; paragraph following Fig. 5: The molecular-direction family is nearly coupling independent; cancellation of linear acceleration terms leaves an intermolecular yield proportional to the fourth power of weak coupling."
      ],
      "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": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use the exact/adia-intra comparison to bound the approximation conclusion to qualitative retention rather than unsupported quantitative equivalence.",
      "award_conditions": [
        "The approximation conclusion follows from both retained structure and quantitative departure, supporting qualitative retention rather than claiming numerical identity.",
        "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 [I3: Explicitly identify a genuinely retained qualitative feature in the like-for-like exact/adia-intra evidence.; I4: Explicitly identify a concrete quantitative departure in the like-for-like exact/adia-intra evidence.] 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Exact/adia-intra comparison needs the same model inputs and common observable scale. Retained qualitative organization and a concrete quantitative departure remain separately judgeable; failure of one does not mechanically erase the other."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-6-8, Fig. 6, Fig. 8 white comparison marks and Fig. 9; Eqs. (18)-(21): Omitted instantaneous-state transitions reduce the intermolecular response and displace crossovers toward stronger coupling. The half-frequency Fig. 6 is explanatory context, not a compulsory input case."
      ],
      "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": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain why competition between the two response families changes with harmonic order.",
      "award_conditions": [
        "The argument connects different order dependence/spacing of the competing families to their differently placed competition thresholds.",
        "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 intramolecular and intermolecular response families and their different weak-coupling dependences in the candidate's exact evidence.; I2: Identify from the candidate's evidence the joint signal that the strongest-emission direction reorganizes with harmonic order.] 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.",
        "All named physical premises are necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Only the exact response facts needed for coupling/order/angular reorganization propagate here; independent adiabatic construction is not erased by a failed exact branch."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-4-5, Fig. 4(b) and Fig. 5: Order-dependent competition switches the maximizing polarization, with higher orders switching at weaker coupling."
      ],
      "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": "Causally connect the order-dependent competition to the reorganization of the polarization direction of strongest emission.",
      "award_conditions": [
        "The identified competition is causally linked to which physical polarization direction maximizes each order as coupling changes.",
        "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 the candidate's evidence the joint signal that the strongest-emission direction reorganizes with harmonic order.; M3: Explain why competition between the two response families changes with harmonic order.] 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.",
        "All named physical premises are necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Only the exact response facts needed for coupling/order/angular reorganization propagate here; independent adiabatic construction is not erased by a failed exact branch."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-4-5, Fig. 4(b) and Fig. 5: Order-dependent competition switches the maximizing polarization, with higher orders switching at weaker coupling."
      ],
      "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": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain which qualitative organization is already encoded in, and retained by, adiabatic following.",
      "award_conditions": [
        "The argument explains why instantaneous-state following already carries the observed qualitative angular/coupling organization.",
        "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": [
        "I3: Explicitly identify a genuinely retained qualitative feature in the like-for-like exact/adia-intra evidence. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Exact/adia-intra comparison needs the same model inputs and common observable scale. Retained qualitative organization and a concrete quantitative departure remain separately judgeable; failure of one does not mechanically erase the other."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-7-8, Figs. 7-9 and adjacent comparison with Figs. 2, 4(b) and 5: Adiabatic following retains broad angular organization and ordered competition, not quantitative equality."
      ],
      "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": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain that adia-intra omits transitions/coherences between instantaneous states, or a physically equivalent transition-assisted response description.",
      "award_conditions": [
        "The candidate correctly identifies the absent instantaneous-state transitions/coherences or an equivalent transition-assisted contribution.",
        "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: Implement the supplied instantaneous-state adia-intra identity 2 r00 + 2 r11 and preserve it as an independent like-for-like approximation branch under the same inputs and observable convention. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Exact/adia-intra comparison needs the same model inputs and common observable scale. Retained qualitative organization and a concrete quantitative departure remain separately judgeable; failure of one does not mechanically erase the other."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-6-8, Fig. 6, Fig. 8 white comparison marks and Fig. 9; Eqs. (18)-(21): Omitted instantaneous-state transitions reduce the intermolecular response and displace crossovers toward stronger coupling. The half-frequency Fig. 6 is explanatory context, not a compulsory input case."
      ],
      "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": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Causally connect the omitted transition-assisted response to the observed quantitative departure.",
      "award_conditions": [
        "The missing transition-assisted response explains the measured yield imbalance or shifted crossover in the candidate comparison.",
        "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.",
        "Connect omitted transition-assisted response to the observed quantitative yield or crossover departure; saying only that the approximation differs is insufficient."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [I4: Explicitly identify a concrete quantitative departure in the like-for-like exact/adia-intra evidence.; M6: Explain that adia-intra omits transitions/coherences between instantaneous states, or a physically equivalent transition-assisted response description.] 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.",
        "All named physical premises are necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Exact/adia-intra comparison needs the same model inputs and common observable scale. Retained qualitative organization and a concrete quantitative departure remain separately judgeable; failure of one does not mechanically erase the other."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article pp. 043106-6-8, Fig. 6, Fig. 8 white comparison marks and Fig. 9; Eqs. (18)-(21): Omitted instantaneous-state transitions reduce the intermolecular response and displace crossovers toward stronger coupling. The half-frequency Fig. 6 is explanatory context, not a compulsory input case."
      ],
      "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": "Limit conclusions to the weak-coupling four-level model, its interpretable parameter domain and the candidate's evidence, separating qualitative mechanism support from quantitative agreement.",
      "award_conditions": [
        "The conclusion positively states the interpretable weak-coupling four-level domain and distinguishes supported qualitative mechanism from quantitative agreement."
      ],
      "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 obligation is independently judgeable; no upstream failure is propagated into it.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article p. 043106-5, paragraph beginning with the strong-coupling regime; p. 043106-8, Conclusion: The four-level model loses quantitative interpretability at strong coupling; the task imposes the weak-coupling scope."
      ],
      "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": "Only when the candidate method, data, anomaly or scope/quantitative claim triggers a concrete material alternative, exclude it with discriminating evidence or honestly restrict the claim.",
      "award_conditions": [
        "If a material alternative arises from the actual comparison, such as scale erasure or state mis-tracking, the candidate discriminates it or restricts the affected conclusion; otherwise use the existing N/A 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.",
        "This obligation is independently judgeable; no upstream failure is propagated into it.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept coordinate translations preserving relative geometry, declared coupling-sign or magnitude conventions g = |t1/t0|, polarization modulo 180 degrees, and one common spectrum factor.",
        "Accept physically reasonable reconstructible finite-pulse transforms, windows, order reductions, propagators, grids and angular argmax representatives; no source implementation or pixel identity is required.",
        "Angular distributions, response decompositions, crossing analyses, phase-space summaries or other evidence can replace the canonical plots when they establish the same joint dependence and approximation boundary."
      ],
      "source_support": [
        "Bielke et al. (2026), article p. 043106-3, Eqs. (10)-(13), and p. 043106-6, Eqs. (18)-(20): These definitions explain why relative scales, harmonic assignment and instantaneous-state tracking can threaten the comparison. Validation is task-defined and risk-triggered, not an extra figure obligation."
      ],
      "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."
    }
  ],
  "case_scientific_rules": [
    "Diagonalize the four-site H0, doubly occupy the two lowest one-electron states, and propagate both under H0 + Hlaser(t). The drive frequency remains fixed from the default-coupling gap throughout the coupling sweep; recomputing it at every coupling changes the physical problem.",
    "The adia-intra position is 2 r00 + 2 r11 in consistently tracked instantaneous eigenstates, followed by the same acceleration and spectral construction. It is not exact propagation and cannot replace the central exact branch. Merely restating the supplied identity does not establish its computational implementation.",
    "In weak coupling the exact family perpendicular to the intermolecular axis (phi = 110 degrees modulo 180 degrees) is nearly coupling independent. The family perpendicular to the molecular axes (phi = 0 degrees modulo 180 degrees) grows with leading g^4 intensity: acceleration terms linear in t1 cancel, leaving a quadratic total acceleration. The g^4 detail is depth diagnostic, not a standalone atomic requirement; its omission alone cannot fail M1 and M3.",
    "The response families exchange ordering at harmonic-order-dependent couplings, with higher orders crossing first. The maximizing direction reorganizes from molecular toward intermolecular alignment; maxima may deviate from the nominal axis by several degrees. Coupling/polarization/order structure, not exact angle coordinates, is the correctness anchor.",
    "Adia-intra retains the broad response families and ordered competition but omits instantaneous-state transitions. It underestimates transition-assisted intermolecular response, especially near and above the middle-level gap, shifting crossover toward stronger coupling. This supports qualitative retention, not equal yields or crossover locations.",
    "The interpretable weak-coupling domain is g <= 0.1. Strong-coupling fluctuations outside this model domain are not quantitative grading targets. A common arbitrary spectral scale is allowed; independent rescaling of compared branches that destroys relative evidence is not.",
    "No specific split propagator, time step, Hann window, harmonic bin, angular/coupling grid, fixed-direction sweep or maximizing-angle map is required. Alternative declared finite-pulse spectral treatments must be physically valid, reconstructible and consistently applied.",
    "Concrete risks can include branch-dependent normalization, harmonic-band misassignment, angular/coupling aliasing and instantaneous-state mistracking masquerading as approximation failure. These possibilities do not require fixed controls without a candidate-specific trigger.",
    "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.",
    "Total position is $\\mathbf r(t)=2\\langle u_0(t)|\\hat{\\mathbf r}|u_0(t)\\rangle+2\\langle u_1(t)|\\hat{\\mathbf r}|u_1(t)\\rangle$. With $\\mathbf a=\\ddot{\\mathbf r}$, $I(\\omega)\\propto|\\int w(t)\\mathbf a(t)e^{i\\omega t}dt|^2$ and $I_n=\\int_{B_n}I(\\omega)d\\omega$. The spin factors and coherent sum are physical; a declared equivalent window and order band $B_n$ are allowed (Eqs. (10)-(13)).",
    "For instantaneous eigenstates $\\mu_n(t)$, $\\mathbf r_{mn}=\\langle\\mu_m|\\hat{\\mathbf r}|\\mu_n\\rangle$ and $\\mathbf r_{\\rm adia-intra}=2\\mathbf r_{00}+2\\mathbf r_{11}$ (Eq. (20)). Use the same acceleration/spectrum convention for comparison. Weak-coupling cancellation gives $\\mathbf a_{\\rm inter}=O(g^2)$ and $I_{\\rm inter}=O(g^4)$, $g=|t_1/t_0|$; this is not a universal strong-coupling law."
  ],
  "closure_requirements": {
    "RC0": [
      "Required claim CL1, central object: All of [F1: Establish the shared physical identity of the half-filled four-site tight-binding model, its geometry and spin-degenerate occupation, weak-coupling variable, length-gauge interaction and drive fixed by the reference-coupling gap.; F2: Propagate both initially occupied orbitals, each doubly occupied, in the exact branch and construct a valid reconstructible harmonic-order-resolved total-acceleration HHG spectrum.; O1: Provide a physically valid reconstructible exact order-resolved HHG output family over informative weak-coupling and polarization variation, with correct case/order binding and nonnegative yields.]. 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 CL2, indispensable component: O2: Present computed exact angular reorganization jointly resolved in coupling, polarization and harmonic order; coverage must expose the order-dependent competition and strongest-emission direction.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL3, indispensable component: F3: Implement the supplied instantaneous-state adia-intra identity 2 r00 + 2 r11 and preserve it as an independent like-for-like approximation branch under the same inputs and observable convention.. 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 [M1: Explain the physical origins of the two response families and their different dependence on weak intermolecular coupling.; M3: Explain why competition between the two response families changes with harmonic order.; M4: Causally connect the order-dependent competition to the reorganization of the polarization direction of strongest emission.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL3, principal mechanism: All of [M2: Use the exact/adia-intra comparison to bound the approximation conclusion to qualitative retention rather than unsupported quantitative equivalence.; M5: Explain which qualitative organization is already encoded in, and retained by, adiabatic following.; M6: Explain that adia-intra omits transitions/coherences between instantaneous states, or a physically equivalent transition-assisted response description.; M7: Causally connect the omitted transition-assisted response to the observed quantitative departure.]. 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 CL4, material validation: V2: Only when the candidate method, data, anomaly or scope/quantitative claim triggers a concrete material alternative, exclude it with discriminating evidence or honestly restrict the claim.. 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": "Lina Bielke, Samuel Schöpa, Falk-Erik Wiechmann, Franziska Fennel, and Dieter Bauer. 2026. High-harmonic generation from two weakly coupled molecules: A simple tight-binding model. Physical Review A, 113, 043106.",
      "url": "https://doi.org/10.1103/7ljs-sbpy",
      "scientific_scope": "Four-site exact and adia-intra HHG identities, weak-coupling response reorganization, transition-assisted departures and qualitative/quantitative scope. Source numerical implementation and display choices are examples, not required deliverables.",
      "anchors": [
        "article p. 043106-2, Eqs. (1)-(8), Fig. 1(a,b)",
        "article p. 043106-3, Eqs. (9)-(13)",
        "article pp. 043106-5-6, Eqs. (14)-(20)",
        "article pp. 043106-3-5, Figs. 2, 3 and 5; paragraph following Fig. 5",
        "article pp. 043106-4-5, Fig. 4(b) and Fig. 5",
        "article pp. 043106-7-8, Figs. 7-9 and adjacent comparison with Figs. 2, 4(b) and 5",
        "article pp. 043106-6-8, Fig. 6, Fig. 8 white comparison marks and Fig. 9; Eqs. (18)-(21)",
        "article p. 043106-5, paragraph beginning with the strong-coupling regime; p. 043106-8, Conclusion",
        "article p. 043106-3, Eqs. (10)-(13), and p. 043106-6, Eqs. (18)-(20)"
      ]
    }
  ]
}