cases/case10/grading_rubric.json

{
  "case_id": "Case10",
  "title": "Case10 — Phase structure of below-threshold harmonics in aligned molecules: A few-level model system",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Establish both specified few-level TDSEs and construct complex harmonic observables retaining intensity and phase from complex dipole/radiation response; preserve both orthogonal components in System B.",
      "award_conditions": [
        "Both specified TDSEs yield complex intensity-and-phase-bearing radiation observables, retaining both orthogonal System-B components."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F2, F3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-1-2, Eqs.(1)-(6): TLS dynamics, dipole, complex transform and finite Gaussian pulse; pp.L022022-3-4, Eqs.(8)-(11) for the orthogonal four-level extension."
      ],
      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Derive a System-A theoretical relation connecting complex harmonic coefficients, odd-harmonic phases and organization on both sides of the transition frequency; recurrence, perturbative or strictly equivalent routes are accepted.",
      "award_conditions": [
        "A theoretical recurrence, perturbative relation or equivalent derivation explains odd-harmonic phases on both sides of the transition."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F3, O1, O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article p.L022022-3, Eq.(7) and denominator-sign explanation; Supplemental Material pp.1-4, Eqs.(10),(12),(16)-(22): monochromatic adiabatic weaker-successive-harmonic recurrence and nonresonant phase organization."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Correctly assemble System B's two uncoupled orthogonal-transition TLS blocks, coherent equal-weight lower-state preparation and drive-angle-dependent complex x/y response, defining a line-polarization axis or strictly equivalent observable.",
      "award_conditions": [
        "System B consists of the correct uncoupled orthogonal TLS blocks with coherent equal-weight lower-state preparation and a reconstructible complex-vector/line-axis observable."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F2, O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-3-4, Eqs.(8)-(11), Fig.5 and paragraph defining linear polarization from relative 0/pi component phase. A normalized coherent equal-weight lower-state preparation and modulo-pi line axis are task-explicit conventions."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present System-A complex harmonic response and intensity over a chosen frequency domain spanning the transition, resolving odd harmonics and the finite-pulse resonant neighborhood.",
      "award_conditions": [
        "System-A complex response and intensity span the transition and resolve odd harmonics plus the finite-pulse resonant neighborhood.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F1 (Establish both specified few-level TDSEs and construct complex harmonic observables retaining intensity and phase from complex dipole/radiation response; preserve both orthogonal components in System B.)",
        "Preserve independently valid work in O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present System-A phase organization across the transition, exposing alternating real phase classes below it, a common real phase class above it, and the resonant neighborhood.",
      "award_conditions": [
        "System-A phase evidence exposes amplitude-supported alternating real classes below and common real class above transition, with resonance separately resolved.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O1 (Present System-A complex harmonic response and intensity over a chosen frequency domain spanning the transition, resolving odd harmonics and the finite-pulse resonant neighborhood.)",
        "Preserve independently valid work in O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present complex x/y response or equivalent polarization evidence for System B's lower odd-harmonic family over a sufficient chosen angular/frequency domain to assess its line-axis relation to drive angle.",
      "award_conditions": [
        "System-B complex-vector or equivalent polarization evidence exposes the lower odd family's line-axis relation over a sufficient angular/frequency domain.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F3 (Correctly assemble System B's two uncoupled orthogonal-transition TLS blocks, coherent equal-weight lower-state preparation and drive-angle-dependent complex x/y response, defining a line-polarization axis or strictly equivalent observable.)",
        "Preserve independently valid work in O4, O1, O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article p.L022022-4, Fig.5 lower odd family (orders 1-7), Fig.4 and same-phase subsystem discussion: co-rotating polarization with nonlinear amplitude-dependent axis, not necessarily equal to the driver angle."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present complex x/y response or equivalent polarization evidence for System B's higher odd-harmonic family beyond the higher transition, exposing its changed relation relative to the lower family.",
      "award_conditions": [
        "The higher odd family's complex polarization beyond the higher transition exposes the changed relation relative to the lower family.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F3 (Correctly assemble System B's two uncoupled orthogonal-transition TLS blocks, coherent equal-weight lower-state preparation and drive-angle-dependent complex x/y response, defining a line-polarization axis or strictly equivalent observable.)",
        "Preserve independently valid work in O3, O1, O2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article p.L022022-4, Fig.5 higher family (beginning at 9), Fig.3 reference frequency lines and counterrotation paragraph: relative pi phase mirrors the harmonic line axis."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Explicitly identify System-A odd harmonics, transition/resonance neighborhood and amplitude-supported alternating-below/common-above real phase classes.",
      "award_conditions": [
        "The candidate identifies odd orders, resonance neighborhood and supported alternating-below/common-above phase classes in their own data."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: O1 (Present System-A complex harmonic response and intensity over a chosen frequency domain spanning the transition, resolving odd harmonics and the finite-pulse resonant neighborhood.); O2 (Present System-A phase organization across the transition, exposing alternating real phase classes below it, a common real phase class above it, and the resonant neighborhood.)",
        "Preserve independently valid work in I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify the co-directional/co-rotating or physically equivalent polarization relation of System B's lower odd-harmonic family to the driver.",
      "award_conditions": [
        "The candidate identifies the lower family's co-directional/co-rotating relation, allowing nonlinear deviation from exact driver alignment."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O3 (Present complex x/y response or equivalent polarization evidence for System B's lower odd-harmonic family over a sufficient chosen angular/frequency domain to assess its line-axis relation to drive angle.)",
        "Preserve independently valid work in I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article p.L022022-4, Fig.5 lower odd family (orders 1-7), Fig.4 and same-phase subsystem discussion: co-rotating polarization with nonlinear amplitude-dependent axis, not necessarily equal to the driver angle."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify the counterrotating/mirrored or physically equivalent higher-family polarization relation, its change from the lower family and its association with transition scale.",
      "award_conditions": [
        "The candidate identifies the higher family's mirrored/counterrotating relation and its connection to the transition scale."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O4 (Present complex x/y response or equivalent polarization evidence for System B's higher odd-harmonic family beyond the higher transition, exposing its changed relation relative to the lower family.)",
        "Preserve independently valid work in I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article p.L022022-4, Fig.5 higher family (beginning at 9), Fig.3 reference frequency lines and counterrotation paragraph: relative pi phase mirrors the harmonic line axis."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain the change of odd-harmonic real phase organization across System A's transition through the sign of the theoretical denominator/recurrence factor or a strictly equivalent mechanism.",
      "award_conditions": [
        "The theoretical prefactor/denominator sign or equivalent mechanism explains the phase-organization change across transition."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: F2 (Derive a System-A theoretical relation connecting complex harmonic coefficients, odd-harmonic phases and organization on both sides of the transition frequency; recurrence, perturbative or strictly equivalent routes are accepted.); I1 (Explicitly identify System-A odd harmonics, transition/resonance neighborhood and amplitude-supported alternating-below/common-above real phase classes.)",
        "Preserve independently valid work in M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article p.L022022-3, Eq.(7) and denominator-sign explanation; Supplemental Material pp.1-4, Eqs.(10),(12),(16)-(22): monochromatic adiabatic weaker-successive-harmonic recurrence and nonresonant phase organization."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Distinguish the finite Gaussian pulse's resonant neighborhood from monochromatic/infinite-time theory, explain unreliable phase at unresolved weak coefficients and do not force exact-resonance agreement.",
      "award_conditions": [
        "Finite-pulse resonance and weak-coefficient phase reliability are distinguished from monochromatic adiabatic theory; exact-resonance agreement is not forced."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I1 (Explicitly identify System-A odd harmonics, transition/resonance neighborhood and amplitude-supported alternating-below/common-above real phase classes.)",
        "Preserve independently valid work in M1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Match System-A numerical complex response to the theoretical phase relation, reaching a self-consistent transition-structure inference from harmonic intensity/phase rather than merely listing lines.",
      "award_conditions": [
        "Numerical intensity and complex phase are matched to the theory to support a transition-structure inference rather than a line list."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: I1 (Explicitly identify System-A odd harmonics, transition/resonance neighborhood and amplitude-supported alternating-below/common-above real phase classes.); M1 (Explain the change of odd-harmonic real phase organization across System A's transition through the sign of the theoretical denominator/recurrence factor or a strictly equivalent mechanism.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Construct the line-polarization axis or strictly equivalent quantity from complex x/y harmonic components, correctly treating the modulo-pi axis branch and relative complex phase.",
      "award_conditions": [
        "The candidate derives the line axis from complex x/y components with relative phase and modulo-pi branch handled consistently."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F3 (Correctly assemble System B's two uncoupled orthogonal-transition TLS blocks, coherent equal-weight lower-state preparation and drive-angle-dependent complex x/y response, defining a line-polarization axis or strictly equivalent observable.)",
        "Preserve independently valid work in M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-3-4, Eqs.(8)-(11), Fig.5 and paragraph defining linear polarization from relative 0/pi component phase. A normalized coherent equal-weight lower-state preparation and modulo-pi line axis are task-explicit conventions."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain lower-family co-directional/co-rotating polarization by connecting the two orthogonal TLS complex amplitude/phase contributions.",
      "award_conditions": [
        "The lower-family explanation connects its orthogonal TLS amplitudes and relative phases to co-rotation."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: I2 (Identify the co-directional/co-rotating or physically equivalent polarization relation of System B's lower odd-harmonic family to the driver.); M4 (Construct the line-polarization axis or strictly equivalent quantity from complex x/y harmonic components, correctly treating the modulo-pi axis branch and relative complex phase.)",
        "Preserve independently valid work in M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article p.L022022-4, Fig.5 lower odd family (orders 1-7), Fig.4 and same-phase subsystem discussion: co-rotating polarization with nonlinear amplitude-dependent axis, not necessarily equal to the driver angle."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain higher-family counterrotating/mirrored polarization beyond the higher transition through transition-dependent amplitude/phase reorganization of the two TLS responses.",
      "award_conditions": [
        "Transition-dependent amplitude/phase reorganization explains higher-family mirroring beyond the upper transition."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: I3 (Identify the counterrotating/mirrored or physically equivalent higher-family polarization relation, its change from the lower family and its association with transition scale.); M4 (Construct the line-polarization axis or strictly equivalent quantity from complex x/y harmonic components, correctly treating the modulo-pi axis branch and relative complex phase.)",
        "Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article p.L022022-4, Fig.5 higher family (beginning at 9), Fig.3 reference frequency lines and counterrotation paragraph: relative pi phase mirrors the harmonic line axis."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use submitted numerical evidence to establish that phase/polarization structures are not artefacts of unresolved weak coefficients, line-axis branches, chosen frequency/angle domains or fragile reduction, and define the supported harmonic range.",
      "award_conditions": [
        "Actual numerical evidence excludes unresolved weak coefficients, axis wrapping, domain truncation or fragile reduction as the source of the claimed pattern."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in M8. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-3-4, Eq.(7) approximation/resonance limitation and final realistic-molecule discussion. Amplitude-supported phase, axis-branch stability and bounded spectral inference are task-defined scientific safeguards, not fixed plotting domains."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M8",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Synthesize System-A cross-transition phases and System-B polarization families to determine inferable transition information, diagnostic domain and their shared physical basis.",
      "award_conditions": [
        "Both systems' phase/polarization evidence supports the stated transition information, diagnostic domain and common mechanism."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: M1 (Explain the change of odd-harmonic real phase organization across System A's transition through the sign of the theoretical denominator/recurrence factor or a strictly equivalent mechanism.); M5 (Explain lower-family co-directional/co-rotating polarization by connecting the two orthogonal TLS complex amplitude/phase contributions.); M6 (Explain higher-family counterrotating/mirrored polarization beyond the higher transition through transition-dependent amplitude/phase reorganization of the two TLS responses.)",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-3-4, Eq.(7) approximation/resonance limitation and final realistic-molecule discussion. Amplitude-supported phase, axis-branch stability and bounded spectral inference are task-defined scientific safeguards, not fixed plotting domains."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "V1",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "When weak-coefficient phase, insufficient frequency/angle domain, finite-pulse/monochromatic mismatch, axis branches or reduction artefacts threaten conclusions, provide discriminating evidence or narrow the threatened claim.",
      "award_conditions": [
        "Only a concrete triggered phase, resonance, branch, domain or reduction risk requires discriminating evidence or narrowed claims; otherwise N/A."
      ],
      "applicability_and_na": [
        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-3-4, Eq.(7) approximation/resonance limitation and final realistic-molecule discussion. Amplitude-supported phase, axis-branch stability and bounded spectral inference are task-defined scientific safeguards, not fixed plotting domains."
      ],
      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Positively restrict conclusions to the specified closed few-level systems, coherent preparation, finite Gaussian pulses and calculated harmonic/angular domain; do not extrapolate to general multilevel materials or arbitrary strong-field limits.",
      "award_conditions": [
        "The candidate positively limits conclusions to closed few-level systems, coherent preparation, finite Gaussian pulses and actual calculated harmonic/angular support."
      ],
      "applicability_and_na": [
        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied."
      ],
      "equivalent_evidence": [
        "Consistent Fourier, derivative, global-phase and state-ordering conventions are accepted. Absolute scale is not graded, but complex phase and component coherence must survive the mapping.",
        "A recurrence, perturbative or alternative derivation is accepted if it explains the same two nonresonant phase organizations and its applicability boundary. The monochromatic approximation cannot replace finite-pulse propagation or be forced through strict resonance.",
        "A Stokes, complex-vector or equivalent polarization construction is accepted when it retains relative phase and handles the line-axis modulo-pi ambiguity. No particular phase mask or Stokes formula is compulsory."
      ],
      "source_support": [
        "Schopa et al. (2026), article pp.L022022-3-4, Eq.(7) approximation/resonance limitation and final realistic-molecule discussion. Amplitude-supported phase, axis-branch stability and bounded spectral inference are task-defined scientific safeguards, not fixed plotting domains."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    }
  ],
  "case_scientific_rules": [
    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
    "The canonical System-B preparation is proportional to (1,1,0,0)^T in one ordering, with simultaneous Ex d and Ey d couplings. Separate runs or unsigned intensity components do not preserve the required coherent response.",
    "Canonical lower orders 1,3,5,7 co-rotate and higher orders beginning at 9 through 11,13 mirror/counterrotate. These recognize the two families, not a fixed required frequency or angle grid.",
    "The relative 0/pi component phase carries the family change; nonlinear amplitude differences determine detailed curves. Weak unresolved coefficients cannot support phase assertions.",
    "The simplified uncoupled bound-bound model does not establish survival in realistic aligned molecules with additional states, collective response, continuum emission or imperfect alignment.",
    "A standard field-free basis gives",
    "$$\nH_A(t)=\n\\begin{pmatrix}\n-\\omega_{10}/2&E(t)d\\\\\nE(t)d&\\omega_{10}/2\n\\end{pmatrix},\n$$",
    "with lower-state initial amplitude. The canonical dipole is",
    "$$\nD(t)=d\\left(C_0^*C_1+C_1^*C_0\\right).\n$$",
    "The source intensity is constructed from the transformed dipole acceleration, whereas transition-dependent phase information requires a declared complex coefficient. Fourier-, derivative- and global-phase-equivalent conventions are accepted when treated consistently. Absolute scale is not graded.",
    "Canonical evidence contains resolved odd harmonics, localized resonant enhancement, alternating real phase classes below the transition, one common real phase class above it, and a distinct finite-pulse response near strict resonance. A weak coefficient cannot support a phase claim.",
    "With $w=|C_1|^2-|C_0|^2$, the source relations include",
    "$$\n\\ddot D+\\omega_{10}^2D=2\\omega_{10}E(t)d^2w,\n\\qquad\n\\dot w=-\\frac{2E(t)}{\\omega_{10}}\\dot D.\n$$",
    "For a monochromatic field, adiabatic occupation of one Floquet state and the successively weaker-harmonic approximation give",
    "$$\nd_n=-e^{-2i\\varphi_L}\\frac{n-2}{n-1}\n\\left[\n\\frac{2n^2}{n^2-1}\n+\\frac{\\omega_{10}^2-n^2\\omega_L^2}{E_0^2d^2}\n\\right]^{-1}d_{n-2}.\n$$",
    "Its real prefactor changes sign across the transition and explains the two nonresonant phase organizations. The approximation does not replace the finite-pulse propagation and must not be forced through strict resonance. A different derivation can earn full credit if it explains the same physical organization and applicability boundary.",
    "The canonical four-level Hamiltonian is the direct sum of the two stated TLS blocks, with simultaneous couplings $E_xd$ and $E_yd$. The coherent lower- state preparation is proportional to $(1,1,0,0)^{\\mathsf T}$ in one canonical ordering. Equivalent state orderings and global phases are accepted.",
    "The computed complex harmonic vector defines its polarization. A standard line-axis representative in a sufficiently linear region is",
    "$$\n\\alpha_N=\\frac12\\operatorname{atan2}\\!\\left(\n2\\operatorname{Re}[\\widetilde D_x\\widetilde D_y^*],\n|\\widetilde D_x|^2-|\\widetilde D_y|^2\n\\right)\\pmod\\pi.\n$$",
    "Canonical evidence separates a co-rotating family for orders 1, 3, 5 and 7 from a counterrotating or mirrored family beginning at order 9 and continuing through 11 and 13. The relative $0/\\pi$ component phase carries the family change; nonlinear amplitude differences determine the detailed curves.",
    "The result is a phase-sensitive polarization effect in a deliberately simplified uncoupled bound-bound model. It does not prove that a realistic aligned molecule preserves it in the presence of additional states, collective response, continuum emission or imperfect alignment.",
    "The System-A recurrence and System-B line-axis formula are tied respectively to article p.L022022-3, Eq.(7), and the complex-vector interpretation of Eqs.(10),(11)/Fig.5. The latter is a derived Stokes-axis representation, not a separately printed article equation. For $D_x,D_y$ at one harmonic, line polarization requires a negligible ellipticity invariant $2\\Im(D_xD_y^*)$ relative to total power; an axis cannot be assigned physical certainty at vanishing amplitude. The shared real component phases $0/\\pi$ cause co-rotation/mirroring, while unequal nonlinear amplitudes mean the lower-family axis need not exactly equal the driver angle. No particular angle grid or line-axis display branch is required."
  ],
  "closure_requirements": {
    "RC0": [
      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
      "Required indispensable claim CL0, central physical object: F1 (Establish both specified few-level TDSEs and construct complex harmonic observables retaining intensity and phase from complex dipole/radiation response; preserve both orthogonal components in System B.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC1": [
      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
      "Required co primary claim CL1, indispensable material component: all of: O1 (Present System-A complex harmonic response and intensity over a chosen frequency domain spanning the transition, resolving odd harmonics and the finite-pulse resonant neighborhood.); O2 (Present System-A phase organization across the transition, exposing alternating real phase classes below it, a common real phase class above it, and the resonant neighborhood.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL2, indispensable material component: all of: O3 (Present complex x/y response or equivalent polarization evidence for System B's lower odd-harmonic family over a sufficient chosen angular/frequency domain to assess its line-axis relation to drive angle.); O4 (Present complex x/y response or equivalent polarization evidence for System B's higher odd-harmonic family beyond the higher transition, exposing its changed relation relative to the lower family.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC2": [
      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
      "Required co primary claim CL1, principal mechanism or commissioned conclusion: M1 (Explain the change of odd-harmonic real phase organization across System A's transition through the sign of the theoretical denominator/recurrence factor or a strictly equivalent mechanism.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M5 (Explain lower-family co-directional/co-rotating polarization by connecting the two orthogonal TLS complex amplitude/phase contributions.); M6 (Explain higher-family counterrotating/mirrored polarization beyond the higher transition through transition-dependent amplitude/phase reorganization of the two TLS responses.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL3, principal mechanism or commissioned conclusion: M8 (Synthesize System-A cross-transition phases and System-B polarization families to determine inferable transition information, diagnostic domain and their shared physical basis.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC3": [
      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
      "Required co primary claim CL4, material validation/scope: V1 (When weak-coefficient phase, insufficient frequency/angle domain, finite-pulse/monochromatic mismatch, axis branches or reduction artefacts threaten conclusions, provide discriminating evidence or narrow the threatened claim.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC4": [
      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
      "Close CL0 central physical object: F1 (Establish both specified few-level TDSEs and construct complex harmonic observables retaining intensity and phase from complex dipole/radiation response; preserve both orthogonal components in System B.).",
      "Close CL1 indispensable material component: all of: O1 (Present System-A complex harmonic response and intensity over a chosen frequency domain spanning the transition, resolving odd harmonics and the finite-pulse resonant neighborhood.); O2 (Present System-A phase organization across the transition, exposing alternating real phase classes below it, a common real phase class above it, and the resonant neighborhood.).",
      "Close CL1 principal mechanism or commissioned conclusion: M1 (Explain the change of odd-harmonic real phase organization across System A's transition through the sign of the theoretical denominator/recurrence factor or a strictly equivalent mechanism.).",
      "Close CL2 indispensable material component: all of: O3 (Present complex x/y response or equivalent polarization evidence for System B's lower odd-harmonic family over a sufficient chosen angular/frequency domain to assess its line-axis relation to drive angle.); O4 (Present complex x/y response or equivalent polarization evidence for System B's higher odd-harmonic family beyond the higher transition, exposing its changed relation relative to the lower family.).",
      "Close CL2 principal mechanism or commissioned conclusion: all of: M5 (Explain lower-family co-directional/co-rotating polarization by connecting the two orthogonal TLS complex amplitude/phase contributions.); M6 (Explain higher-family counterrotating/mirrored polarization beyond the higher transition through transition-dependent amplitude/phase reorganization of the two TLS responses.).",
      "Close CL3 principal mechanism or commissioned conclusion: M8 (Synthesize System-A cross-transition phases and System-B polarization families to determine inferable transition information, diagnostic domain and their shared physical basis.).",
      "Close CL4 material validation/scope: V1 (When weak-coefficient phase, insufficient frequency/angle domain, finite-pulse/monochromatic mismatch, axis branches or reduction artefacts threaten conclusions, provide discriminating evidence or narrow the threatened claim.)."
    ]
  },
  "references": [
    {
      "citation": "Samuel Schöpa, Lina Bielke, Falk-Erik Wiechmann, Franziska Fennel, and Dieter Bauer. 2026. *Phase structure of below-threshold harmonics in aligned molecules: A few-level model system*. *Physical Review Research*, 8, L022022.",
      "url": "https://doi.org/10.1103/5fjm-8ps7",
      "scientific_scope": "Phase structure of below-threshold harmonics in aligned molecules: A few-level model system",
      "anchors": [
        "Schopa et al. (2026), article pp.L022022-1-2, Eqs.(1)-(6): TLS dynamics, dipole, complex transform and finite Gaussian pulse; pp.L022022-3-4, Eqs.(8)-(11) for the orthogonal four-level extension.",
        "Schopa et al. (2026), article p.L022022-3, Eq.(7) and denominator-sign explanation; Supplemental Material pp.1-4, Eqs.(10),(12),(16)-(22): monochromatic adiabatic weaker-successive-harmonic recurrence and nonresonant phase organization.",
        "Schopa et al. (2026), article pp.L022022-3-4, Eqs.(8)-(11), Fig.5 and paragraph defining linear polarization from relative 0/pi component phase. A normalized coherent equal-weight lower-state preparation and modulo-pi line axis are task-explicit conventions.",
        "Schopa et al. (2026), article pp.L022022-2-3, Figs.1-3, Eq.(7) and exact-resonance paragraph: odd spectra, resonance neighborhood, alternating-below/common-above real phase; finite-pulse resonant phase need not obey the adiabatic recurrence.",
        "Schopa et al. (2026), article p.L022022-4, Fig.5 lower odd family (orders 1-7), Fig.4 and same-phase subsystem discussion: co-rotating polarization with nonlinear amplitude-dependent axis, not necessarily equal to the driver angle.",
        "Schopa et al. (2026), article p.L022022-4, Fig.5 higher family (beginning at 9), Fig.3 reference frequency lines and counterrotation paragraph: relative pi phase mirrors the harmonic line axis.",
        "Schopa et al. (2026), article pp.L022022-3-4, Eq.(7) approximation/resonance limitation and final realistic-molecule discussion. Amplitude-supported phase, axis-branch stability and bounded spectral inference are task-defined scientific safeguards, not fixed plotting domains."
      ]
    },
    {
      "citation": "Samuel Schopa, Lina Bielke, Falk-Erik Wiechmann, Franziska Fennel, and Dieter Bauer. 2026. *Supplemental Material: Analytical derivation for the phase of the below-threshold harmonics in a two-level model system*, accompanying Physical Review Research 8, L022022.",
      "url": "https://journals.aps.org/prresearch/supplemental/10.1103/5fjm-8ps7",
      "scientific_scope": "Analytical dipole/population equations and adiabatic monochromatic harmonic recurrence.",
      "anchors": [
        "Supplemental Material pp.1-4, Eqs.(10),(12),(16)-(22); Eq.(22) corresponds to main-text Eq.(7)."
      ]
    }
  ]
}