{
  "case_id": "Case29",
  "title": "Attosecond Rabi oscillations in high harmonic generation resonantly driven by extreme ultraviolet laser fields",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Instantiate the specified correlated two-electron soft-core Hamiltonian, field-free ground state and 32-cycle central pulse under consistent gauge and units.",
      "award_conditions": [
        "The correlated two-electron soft-core Hamiltonian, field-free ground state and 32-cycle central pulse have consistent gauge/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.",
        "The production-model identity is independently judgeable.",
        "A failure here propagates only to claims requiring this production object; independent standard reasoning is not separately charged."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-3, Eq. (1), methodology and 32-cycle field definition: The two-active-electron soft-core target and ground state under the specified finite EUV pulse define production, not a standalone two-level propagation."
      ],
      "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": "Define named-state coherent-exchange accounting and survival/leakage of the same two-state subspace from the propagated state, preserving specified state content and inside/outside boundary.",
      "award_conditions": [
        "Named-state population/coherence and survival/leakage account for the same two-state subspace, not total norm alone."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "F1: Instantiate the specified correlated two-electron soft-core Hamiltonian, field-free ground state and 32-cycle central pulse under consistent gauge and units. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in F3 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 accounting must be constructed from the required propagated production state.",
        "A state-accounting defect does not by itself erase an independently correct radiation-observable derivation; downstream exchange claims alone lose their premise.",
        "Named-state exchange and survival use the same specified two-state subspace. A correct exchange trace does not establish survival from total norm alone, while a local survival weakness does not erase established exchange."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-3, Eq. (3), Fig. 1(c) and population discussion: Named ground/excited populations and their sum identify coherent exchange and actual two-state survival/leakage; total norm is not a replacement."
      ],
      "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": "Construct the full radiation observable and HHG spectrum from the correlated TDSE production state, declaring transform, frequency weighting, normalization and case binding relevant to identity.",
      "award_conditions": [
        "The full correlated-TDSE radiation spectrum has a defined transform, frequency weighting, normalization and case binding."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "F1: Instantiate the specified correlated two-electron soft-core Hamiltonian, field-free ground state and 32-cycle central pulse under consistent gauge and units. 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.",
        "The full radiation observable must arise from the required correlated production state.",
        "A radiation-construction defect does not erase independently correct named-state/subspace accounting."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-4, Eq. (2), Fig. 1(d), Fig. 3(a,b): Full correlated-TDSE radiation carries material high-order split branches. A two-state component is not the full production observable."
      ],
      "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": "F4",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Establish an identity-preserving comparison distinguishing isolated bound two-state capture from continuum contributions; distinguish an exact transition component, standalone two-level coherence and any fit from the full TDSE observable and from prediction.",
      "award_conditions": [
        "The comparison distinguishes full radiation, exact transition component, standalone two-level coherence and fit/prediction identity."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [F1: Instantiate the specified correlated two-electron soft-core Hamiltonian, field-free ground state and 32-cycle central pulse under consistent gauge and units.; F3: Construct the full radiation observable and HHG spectrum from the correlated TDSE production state, declaring transform, frequency weighting, normalization and case binding relevant to identity.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in F2, O1 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.",
        "A like-for-like comparison requires both the production-model identity and the full-radiation observable mapping.",
        "Failure of the comparison identity does not erase independently correct state/subspace work or time-domain evidence.",
        "Exact-TDSE component, standalone two-level coherence and fitted dynamics remain distinct physical comparisons. Local agreement can establish captured structure without proving the full response is isolated two-state emission."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-3, Eqs. (2)-(3), Fig. 1(d); pp. 023268-5-7, Appendices A-B and comparison discussion: An exact TDSE two-state transition component, standalone two-level coherence and fitted loss/return model are distinct. Their comparison exposes captured satellites versus continuum/other-state response."
      ],
      "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 valid reconstructible adequately presented central named-state/retained-subspace time evidence resolving coherent exchange, its timescale and material survival/leakage.",
      "award_conditions": [
        "Reconstructible named-state and retained-subspace time data resolve coherent exchange, its timescale and material survival/leakage.",
        "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: Define named-state coherent-exchange accounting and survival/leakage of the same two-state subspace from the propagated state, preserving specified state content and inside/outside boundary. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O2, O3 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 displayed time-domain evidence must instantiate the correct named-state/subspace object.",
        "A failed time-domain output does not erase independently valid frequency-domain or comparison outputs.",
        "Named-state exchange and survival use the same specified two-state subspace. A correct exchange trace does not establish survival from total norm alone, while a local survival weakness does not erase established exchange."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-3, Eq. (3), Fig. 1(c) and population discussion: Named ground/excited populations and their sum identify coherent exchange and actual two-state survival/leakage; total norm is not a replacement."
      ],
      "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": "Provide valid reconstructible adequately presented full correlated-TDSE HHG evidence over the central/comparison domain resolving resonance-specific material high-order branch families.",
      "award_conditions": [
        "Full correlated-TDSE spectra resolve resonance-specific high-order branch families over a central/comparison domain adequate for the claim.",
        "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: Construct the full radiation observable and HHG spectrum from the correlated TDSE production state, declaring transform, frequency weighting, normalization and case binding relevant to identity. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O1, O3 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 claim-bearing spectrum requires the correct full-radiation observable identity.",
        "A failed HHG output leaves independently correct time-domain and comparison-family work creditable."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-4, Eq. (2), Fig. 1(d), Fig. 3(a,b): Full correlated-TDSE radiation carries material high-order split branches. A two-state component is not the full production observable."
      ],
      "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": "Provide valid reconstructible adequately presented component, reduced-model, time-resolved or equivalent comparison evidence that actually distinguishes two-state capture from continuum-dependent response.",
      "award_conditions": [
        "A component, reduced-model, time-frequency or equivalent comparison actually distinguishes two-state capture from continuum-dependent response.",
        "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": [
        "F4: Establish an identity-preserving comparison distinguishing isolated bound two-state capture from continuum contributions; distinguish an exact transition component, standalone two-level coherence and any fit from the full TDSE observable and from prediction. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O1, O2 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 comparison output must preserve exact/component/reduced object identity.",
        "A failed comparison output does not erase valid production time traces or full spectra.",
        "Exact-TDSE component, standalone two-level coherence and fitted dynamics remain distinct physical comparisons. Local agreement can establish captured structure without proving the full response is isolated two-state emission."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-3, Eqs. (2)-(3), Fig. 1(d); pp. 023268-5-7, Appendices A-B and comparison discussion: An exact TDSE two-state transition component, standalone two-level coherence and fitted loss/return model are distinct. Their comparison exposes captured satellites versus continuum/other-state response."
      ],
      "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": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Explicitly identify coherent population exchange and a subfemtosecond scale consistent with the candidate's timing definition, resolution and uncertainty.",
      "award_conditions": [
        "The candidate identifies coherent population exchange and a subfemtosecond scale consistent with their timing definition and resolution.",
        "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 valid reconstructible adequately presented central named-state/retained-subspace time evidence resolving coherent exchange, its timescale and material survival/leakage. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I2, I3 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.",
        "Candidate identification requires valid and adequately presented time-domain evidence.",
        "Failure to identify the time-domain signal does not erase independent frequency-domain or comparison identifications.",
        "Named-state exchange and survival use the same specified two-state subspace. A correct exchange trace does not establish survival from total norm alone, while a local survival weakness does not erase established exchange."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-3, Eq. (3), Fig. 1(c) and population discussion: Named ground/excited populations and their sum identify coherent exchange and actual two-state survival/leakage; total norm is not a replacement."
      ],
      "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": "Explicitly identify resonance-specific high-order splitting/branch families in the candidate's full HHG evidence; arrays alone or examiner readback do not create identification.",
      "award_conditions": [
        "The candidate explicitly identifies resonance-specific material splitting/branch families in their full HHG 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: Provide valid reconstructible adequately presented full correlated-TDSE HHG evidence over the central/comparison domain resolving resonance-specific material high-order branch families. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I1, I3 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.",
        "Candidate identification requires a valid full-HHG output family.",
        "A missing HHG identification does not erase independent exchange or comparison identification."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-4, Eq. (2), Fig. 1(d), Fig. 3(a,b): Full correlated-TDSE radiation carries material high-order split branches. A two-state component is not the full production observable."
      ],
      "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 from the candidate's comparison the structure actually captured by isolated two-state physics and material continuum/other-state differences.",
      "award_conditions": [
        "The candidate identifies both structure captured by isolated two-state physics and material continuum/other-state differences.",
        "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: Provide valid reconstructible adequately presented component, reduced-model, time-resolved or equivalent comparison evidence that actually distinguishes two-state capture from continuum-dependent response. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I1, I2 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.",
        "Candidate identification requires valid comparison evidence.",
        "Failure in the comparison identification does not erase independent time/frequency signal identification.",
        "Exact-TDSE component, standalone two-level coherence and fitted dynamics remain distinct physical comparisons. Local agreement can establish captured structure without proving the full response is isolated two-state emission."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-3, Eqs. (2)-(3), Fig. 1(d); pp. 023268-5-7, Appendices A-B and comparison discussion: An exact TDSE two-state transition component, standalone two-level coherence and fitted loss/return model are distinct. Their comparison exposes captured satellites versus continuum/other-state response."
      ],
      "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": "Attribute identified temporal exchange physically to coherent Rabi dynamics with its scale consistent with the candidate's timing evidence.",
      "award_conditions": [
        "The temporal exchange is physically attributed to Rabi dynamics with a scale consistent with the submitted 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": [
        "I1: Explicitly identify coherent population exchange and a subfemtosecond scale consistent with the candidate's timing definition, resolution and uncertainty. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in 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.",
        "Rabi attribution requires the candidate to identify a valid exchange-timescale signal.",
        "Failure of the Rabi attribution does not erase independent two-state capture/failure reasoning.",
        "Named-state exchange and survival use the same specified two-state subspace. A correct exchange trace does not establish survival from total norm alone, while a local survival weakness does not erase established exchange."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-3, Eq. (3), Fig. 1(c) and population discussion: Named ground/excited populations and their sum identify coherent exchange and actual two-state survival/leakage; total norm is not a replacement."
      ],
      "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 detuning, field-strength dependence or equivalent candidate-chosen contrast to establish resonance dependence; arbitrary periodic oscillations are not sufficient.",
      "award_conditions": [
        "A detuning, field-strength or equally discriminating contrast establishes resonance dependence rather than arbitrary oscillation.",
        "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": [
        "I1: Explicitly identify coherent population exchange and a subfemtosecond scale consistent with the candidate's timing definition, resolution and uncertainty. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M1, M3, M4 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 resonance-dependence inference must be tied to the candidate-identified exchange signal.",
        "A weak resonance contrast does not erase an otherwise correct exchange attribution or independently established HHG relation."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article p. 023268-4, Fig. 2(a-d), Fig. 3(a,b) and generalized-Rabi-frequency paragraph: Detuning/field-strength and spectral contrasts discriminate resonance-driven dynamics; the source scans are examples, not fixed comparison grids."
      ],
      "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": "Physically connect identified high-order splitting/branch separation to the candidate's temporal Rabi scale.",
      "award_conditions": [
        "The candidate physically relates high-order splitting or satellite separation to their temporal Rabi scale.",
        "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: Attribute identified temporal exchange physically to coherent Rabi dynamics with its scale consistent with the candidate's timing evidence.; I2: Explicitly identify resonance-specific high-order splitting/branch families in the candidate's full HHG evidence; arrays alone or examiner readback do not create identification.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in 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 cross-domain relation requires the candidate-established Rabi attribution from M1 and candidate identification of the high-order response family; an examiner-discovered time trace cannot substitute for M1.",
        "A failed cross-domain link does not erase independently correct two-state/continuum reasoning."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-3-4, Fig. 1(c-e), Fig. 3(a,b) and triplet discussion: Satellite separation is connected to the temporal Rabi scale, with a candidate-authored cross-domain causal answer rather than an examiner-supplied synthesis."
      ],
      "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": "Use time-frequency, field-strength, detuning or equivalent evidence to establish that high-order structure follows the Rabi scale, not merely similar positions.",
      "award_conditions": [
        "Time-frequency, strength, detuning or equivalent evidence tests that correspondence beyond merely similar peak positions.",
        "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 [O2: Provide valid reconstructible adequately presented full correlated-TDSE HHG evidence over the central/comparison domain resolving resonance-specific material high-order branch families.; M3: Physically connect identified high-order splitting/branch separation to the candidate's temporal Rabi scale.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M1, M2 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.",
        "Discriminating evidence must act on a valid HHG object and the asserted cross-domain scale relation.",
        "Failure of this extra discrimination does not erase independently correct time-domain attribution or resonance evidence."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article p. 023268-4, Fig. 2(a-d), Fig. 3(a,b) and generalized-Rabi-frequency paragraph: Detuning/field-strength and spectral contrasts discriminate resonance-driven dynamics; the source scans are examples, not fixed comparison grids."
      ],
      "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": "Use comparison evidence to explain why an isolated two-state picture captures major satellite positions or early coherent-exchange structure.",
      "award_conditions": [
        "Comparison evidence explains why two-state physics captures major satellites or early coherent exchange.",
        "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: Identify from the candidate's comparison the structure actually captured by isolated two-state physics and material continuum/other-state differences. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in 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 capture explanation requires the candidate-identified retained comparison feature.",
        "A failed capture explanation does not erase an independently correct failure explanation or C1 cross-domain synthesis.",
        "Exact-TDSE component, standalone two-level coherence and fitted dynamics remain distinct physical comparisons. Local agreement can establish captured structure without proving the full response is isolated two-state emission."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-3, Eqs. (2)-(3), Fig. 1(d); pp. 023268-5-7, Appendices A-B and comparison discussion: An exact TDSE two-state transition component, standalone two-level coherence and fitted loss/return model are distinct. Their comparison exposes captured satellites versus continuum/other-state response."
      ],
      "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 why continuum/other states, depletion/return or physically equivalent contributions prevent an isolated two-state picture from accounting for material full-response branches or relative yields.",
      "award_conditions": [
        "The candidate explains why continuum/other-state dynamics, depletion/return or equivalent effects prevent full isolated-two-state agreement.",
        "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: Identify from the candidate's comparison the structure actually captured by isolated two-state physics and material continuum/other-state differences. 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.",
        "The failure explanation requires the candidate-identified continuum-dependent difference.",
        "A failed continuum account does not erase a correct bounded capture explanation or independent C1 cross-domain synthesis.",
        "Exact-TDSE component, standalone two-level coherence and fitted dynamics remain distinct physical comparisons. Local agreement can establish captured structure without proving the full response is isolated two-state emission."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-3, Eqs. (2)-(3), Fig. 1(d); pp. 023268-5-7, Appendices A-B and comparison discussion: An exact TDSE two-state transition component, standalone two-level coherence and fitted loss/return model are distinct. Their comparison exposes captured satellites versus continuum/other-state response."
      ],
      "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": "Provide a candidate-authored end-to-end synthesis, founded on the local high-order-separation/Rabi-scale correspondence and discriminating detuning/strength/time-frequency evidence, explicitly showing how the same Rabi dynamics is supported by populations and high-order HHG and bounding that conclusion.",
      "award_conditions": [
        "An explicit end-to-end research answer integrates population Rabi evidence, local high-order scale correspondence and discriminating resonance 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": [
        "All of [M3: Physically connect identified high-order splitting/branch separation to the candidate's temporal Rabi scale.; M4: Use time-frequency, field-strength, detuning or equivalent evidence to establish that high-order structure follows the Rabi scale, not merely similar positions.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M2, 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 end-to-end synthesis requires both the candidate-established local cross-domain correspondence in M3 and the discriminating evidence in M4; examiner reconstruction or one isolated linking sentence cannot supply the missing premise.",
        "M3 and M4 retain independent credit when their own duties are met even if M7 synthesis is absent. Conversely, the same sentence or local correspondence used for M3 cannot by itself satisfy M7 without integrating the M4 discrimination, both evidence domains and the applicability boundary; C2 capture/failure remains independent.",
        "The end-to-end answer depends on candidate-established temporal/spectral Rabi correspondence and discriminating resonance evidence, not merely on output arrays or examiner synthesis."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-3-4, Fig. 1(c-e), Fig. 3(a,b) and triplet discussion: Satellite separation is connected to the temporal Rabi scale, with a candidate-authored cross-domain causal answer rather than an examiner-supplied synthesis."
      ],
      "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": "Positively identify the actual one-dimensional soft-core finite-pulse single-atom production model and comparison domain established by the calculation.",
      "award_conditions": [
        "The actual one-dimensional soft-core finite-pulse single-atom production and investigated comparison domain are positively stated."
      ],
      "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.",
        "Preserve independent correct work in V3 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.",
        "Positive identification of the actual model/evidence domain is independently judgeable and is not conditioned on success of a broader claim.",
        "V1 is lost only for missing or materially wrong identification of the actual model/evidence domain; do not also charge V1 for the same overclaim adjudicated at V3."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article pp. 023268-2-4, dimensional reduction and soft-core resonance-energy discussion; Sec. IV: The resonance energy of the reduced model differs from real helium; the conclusion is single-atom and finite-pulse bounded."
      ],
      "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 method, data, anomaly or high-order claim triggers a concrete risk of a material branch being a window, boundary, sampling or representation artifact, discriminate it or honestly restrict scope.",
      "award_conditions": [
        "An actual window, boundary, sampling or representation threat to a material high-order branch is discriminated or restricted; otherwise N/A."
      ],
      "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.",
        "Applicability is determined by the candidate's own method, data, anomaly or claim rather than another atomic award.",
        "When no concrete risk is triggered, fixed atomic credit is awarded without claiming evidence and RC4 is not blocked."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article p. 023268-2, Eqs. (2)-(3); pp. 023268-5-7, Appendices A-C and model/continuum discussion: Transform artifacts, component/fit identity and continuum or macroscopic extrapolation are potential claim-specific risks. The source appendices do not mandate fitted decay rates or macroscopic propagation."
      ],
      "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": "Only when comparison identity, fit/component mapping, continuum alternative, anomaly or material 3D-yield/macroscopic/domain overclaim creates a concrete validity risk to two-state capture/failure or its scope, discriminate it or honestly restrict scope.",
      "award_conditions": [
        "An actual component/fit identity, continuum alternative, 3D-yield or macroscopic overclaim risk is discriminated or restricted; otherwise N/A."
      ],
      "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.",
        "Preserve independent correct work in V1 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.",
        "Applicability is triggered by the candidate's comparison method, data, anomaly or a material 3D/macroscopic/comparison-domain overclaim, not by missing positive model/evidence-domain identification alone.",
        "No-trigger status earns fixed credit without inventing a validation claim; ordinary comparison defects are adjudicated at F/O, missing model/evidence-domain identification at V1, and the same material overclaim is charged only once at V3."
      ],
      "equivalent_evidence": [
        "Named-state projections, density matrices, subspace survival or complementary leakage can establish the same accounting with identical states and inside/outside boundary; no literal plot/notation is required.",
        "Accept correctly mapped complex-frequency or Hermitian transition components, standalone reduced models labeled as such, time-resolved diagnostics, interventions or equivalent causal comparisons preserving full/component/reduced identity.",
        "Detuning, strength, time-frequency or equally discriminating evidence can test the Rabi correspondence. No author damping fit, far-field propagation, exact scan maximum, numerical implementation or fixed window is compulsory."
      ],
      "source_support": [
        "de las Heras et al. (2025), article p. 023268-2, Eqs. (2)-(3); pp. 023268-5-7, Appendices A-C and model/continuum discussion: Transform artifacts, component/fit identity and continuum or macroscopic extrapolation are potential claim-specific risks. The source appendices do not mandate fitted decay rates or macroscopic propagation."
      ],
      "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": [
    "The required production route is correlated TDSE, not standalone two-level dynamics. For field-free orthonormal ground g = |1s^2> and lowest dipole-coupled odd e = |1s2p>, cg = <g|Psi>, ce = <e|Psi>, Pg = |cg|^2, Pe = |ce|^2 and P2L = Pg + Pe. P2L is survival within that same subspace, not continuum/other states or total box norm.",
    "Equivalent density matrices, subspace projectors and complementary leakage accounting are accepted if they preserve named-state content, coherent exchange and inside/outside boundary. Literal P2L notation or a separate plot is not compulsory.",
    "Central exchange is subfemtosecond; the approximate source 854 as scale corresponds to peak coupling Omega about 0.263 omega0 (chi0 = 0.178 a.u.), not a unique interval between finite-pulse maxima. The retained subspace shows exchange-related stepwise loss and later stabilization, with order-half survival in the source case. Judge the defined timing and uncertainty, not a forced peak-spacing algorithm.",
    "Full acceleration is a_tot = -<Psi|grad V|Psi>, grad = partial_x1 + partial_x2. The exact specified transition component is a_ge = -cg* ce <g|grad V|e>. Its literal source form is a one-direction complex component without explicit conjugate; accept the correct radiation-frequency side or a declared Hermitian real counterpart.",
    "A standalone two-level spectrum from Re(c1 c2*) is not that exact acceleration trace. Structural comparisons require explicit frequency weighting, units, normalization and observable mapping. Phenomenological damping fits must be labeled fits, not predictions; hidden gamma1(t),gamma2(t) curves are not student duties.",
    "Near resonance, material harmonic orders have a branch at q omega0 and satellites around q omega0 +/- Omega; away from resonance the structure simplifies. Satellite separation changes with field-dependent Rabi coupling. No unique source scan maximum, range or sampling is required.",
    "At the source comparison condition 18.4 eV and 1.6e15 W/cm^2, isolated two-state dynamics captures satellite positions but underestimates high-order yield and lacks or weakens the central feature. Later central full-TDSE emission is linked to continuum buildup. Local peak-position agreement does not establish continuum irrelevance.",
    "Dressed-state depletion and state-dependent damping can explain persistent exchange, while continuum/Rydberg return and bound-continuum radiation contribute to the full result. One canonical parameterization uses chi(t) = 0.178 sin^2(omega0 t/64), average gamma = (gamma1+gamma2)/2 and asymmetry (gamma2-gamma1)/(gamma2+gamma1). This is optional mechanism context, not a required fit or unique full-credit chain.",
    "A declared physically equivalent dipole/acceleration, one/two-sided Fourier, gauge, basis, common normalization or window is accepted with proper frequency factors. Do not use window-specific backgrounds, extremely weak branches, absolute yields or pointwise spectral depths as hidden standards.",
    "Triggered risks include wrong projection/subspace accounting, radiation/gauge misbinding, finite-record/window/boundary artifacts, inadequate comparison domain, fits replacing exact prediction or unexplained mapping between spectra. Ordinary domain identification and triggered claim-validity overextension are separate owners; no generic second penalty is added.",
    "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.",
    "For the named field-free states, $c_g=\\langle g|\\Psi\\rangle$, $c_e=\\langle e|\\Psi\\rangle$, $P_g=|c_g|^2$, $P_e=|c_e|^2$ and $P_{2\\rm L}=P_g+P_e$; leakage is outside this same named subspace, not mere norm loss. This projection accounting is the direct entailment underlying Fig. 1(c), with equivalent same-content representations allowed.",
    "The full acceleration is $a_{\\rm full}=-\\langle\\Psi|(\\partial_{x_1}+\\partial_{x_2})V|\\Psi\\rangle$ (Eq. (2)); the selected transition component is $a_{ge}=-c_g^*c_e\\langle g|(\\partial_{x_1}+\\partial_{x_2})V|e\\rangle$ (Eq. (3), with the declared conjugate/real-signal convention). Do not conflate its exact TDSE coefficients with an isolated two-level coherence or a fit.",
    "$S(\\omega)\\propto|\\widetilde a(\\omega)|^2$. Rabi satellites occur near $q\\omega_0\\pm\\Omega$, with $T_R=2\\pi/\\Omega$; the elementary two-level comparison has $\\Omega=\\sqrt{\\Delta^2+|\\chi|^2}$ (pp. 023268-3-4). The source central period near 854 as is a scale example, not an exact imposed timing/peak coordinate. Continuum/depletion effects bound the isolated two-state interpretation."
  ],
  "closure_requirements": {
    "RC0": [
      "Required claim CL0, central object: All of [F1: Instantiate the specified correlated two-electron soft-core Hamiltonian, field-free ground state and 32-cycle central pulse under consistent gauge and units.; F2: Define named-state coherent-exchange accounting and survival/leakage of the same two-state subspace from the propagated state, preserving specified state content and inside/outside boundary.; F3: Construct the full radiation observable and HHG spectrum from the correlated TDSE production state, declaring transform, frequency weighting, normalization and case binding relevant to identity.]. 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: O1: Provide valid reconstructible adequately presented central named-state/retained-subspace time evidence resolving coherent exchange, its timescale and material survival/leakage.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL2, indispensable component: O2: Provide valid reconstructible adequately presented full correlated-TDSE HHG evidence over the central/comparison domain resolving resonance-specific material high-order branch families.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL3, indispensable component: All of [F4: Establish an identity-preserving comparison distinguishing isolated bound two-state capture from continuum contributions; distinguish an exact transition component, standalone two-level coherence and any fit from the full TDSE observable and from prediction.; O3: Provide valid reconstructible adequately presented component, reduced-model, time-resolved or equivalent comparison evidence that actually distinguishes two-state capture from continuum-dependent response.]. 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 CL1, principal mechanism: All of [M1: Attribute identified temporal exchange physically to coherent Rabi dynamics with its scale consistent with the candidate's timing evidence.; M2: Use detuning, field-strength dependence or equivalent candidate-chosen contrast to establish resonance dependence; arbitrary periodic oscillations are not sufficient.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL2, principal mechanism: All of [M3: Physically connect identified high-order splitting/branch separation to the candidate's temporal Rabi scale.; M4: Use time-frequency, field-strength, detuning or equivalent evidence to establish that high-order structure follows the Rabi scale, not merely similar positions.; M7: Provide a candidate-authored end-to-end synthesis, founded on the local high-order-separation/Rabi-scale correspondence and discriminating detuning/strength/time-frequency evidence, explicitly showing how the same Rabi dynamics is supported by populations and high-order HHG and bounding that conclusion.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL3, principal mechanism: All of [M5: Use comparison evidence to explain why an isolated two-state picture captures major satellite positions or early coherent-exchange structure.; M6: Explain why continuum/other states, depletion/return or physically equivalent contributions prevent an isolated two-state picture from accounting for material full-response branches or relative yields.]. 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 CL2, material validation: V2: Only when method, data, anomaly or high-order claim triggers a concrete risk of a material branch being a window, boundary, sampling or representation artifact, discriminate it or honestly restrict scope.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL3, material validation: V3: Only when comparison identity, fit/component mapping, continuum alternative, anomaly or material 3D-yield/macroscopic/domain overclaim creates a concrete validity risk to two-state capture/failure or its scope, discriminate it or honestly restrict scope.. 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": "Alba de las Heras, Carlos Hernández-García, Javier Serrano, Aleksandar Prodanov, Dimitar Popmintchev, Tenio Popmintchev, and Luis Plaja. 2025. Attosecond Rabi oscillations in high harmonic generation resonantly driven by extreme ultraviolet laser fields. Physical Review Research, 7, 023268.",
      "url": "https://doi.org/10.1103/PhysRevResearch.7.023268",
      "scientific_scope": "Correlated population/subspace dynamics and full HHG linked by Rabi scales, with identity-preserving two-state/continuum discrimination. Source timing, fit and spectral conventions are bounded physical anchors rather than fixed display or fit obligations.",
      "anchors": [
        "article pp. 023268-2-3, Eq. (1), methodology and 32-cycle field definition",
        "article pp. 023268-2-3, Eq. (3), Fig. 1(c) and population discussion",
        "article pp. 023268-2-4, Eq. (2), Fig. 1(d), Fig. 3(a,b)",
        "article pp. 023268-2-3, Eqs. (2)-(3), Fig. 1(d); pp. 023268-5-7, Appendices A-B and comparison discussion",
        "article p. 023268-4, Fig. 2(a-d), Fig. 3(a,b) and generalized-Rabi-frequency paragraph",
        "article pp. 023268-3-4, Fig. 1(c-e), Fig. 3(a,b) and triplet discussion",
        "article pp. 023268-2-4, dimensional reduction and soft-core resonance-energy discussion; Sec. IV",
        "article p. 023268-2, Eqs. (2)-(3); pp. 023268-5-7, Appendices A-C and model/continuum discussion"
      ]
    }
  ]
}