{
  "case_id": "Case39",
  "title": "Atomic cavity-modified HHG and electron-mediated energy exchange",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Instantiate the visible one-dimensional soft-Coulomb electron and single cavity coordinate with the bilinear interaction, dipole self-energy, electron-only pulse, uncoupled reference and all three specified cavity cases, preserving signs, units and atomic rather than molecular branch identity.",
      "award_conditions": [
        "Instantiate the visible one-dimensional soft-Coulomb electron and single cavity coordinate with the bilinear interaction, dipole self-energy, electron-only pulse, uncoupled reference and all three specified cavity cases, preserving signs, units and atomic rather than molecular branch identity."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for F2, F3, F4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Albrecht et al. (2025), article pp. 4–7, Eqs. (1)–(7), (11)–(16). Electron-only drive, bilinear cavity coupling and positive dipole self-energy, including the atomic rather than molecular model."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Construct the full field-free polaritonic ground state for each coupled case and a stable two-coordinate propagation that retains physical norm loss, declares boundary and conditional-normalization conventions, and keeps all outputs bound to the same case/state.",
      "award_conditions": [
        "Construct the full field-free polaritonic ground state for each coupled case and a stable two-coordinate propagation that retains physical norm loss, declares boundary and conditional-normalization conventions, and keeps all outputs bound to the same case/state."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for F1, F3, F4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 7–8, Sec. III A; p. 12, Sec. IV A opening paragraph. Coupled field-free ground state and two-coordinate grid propagation; physical norm loss and conditional coordinate expectations."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Define a reconstructible HHG complex transform and intensity together with a high-order or endpoint summary, underlying data, and a common case and normalization identity.",
      "award_conditions": [
        "Define a reconstructible HHG complex transform and intensity together with a high-order or endpoint summary, underlying data, and a common case and normalization identity."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for F1, F2, F4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article p. 6, Eqs. (8)–(9) and no-renormalization paragraph. HHG complex transform and spectrum; the source fitted endpoint is an example, not a unique threshold or mandatory fitting procedure."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "F4",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Define reconstructible electronic and cavity dynamical observables plus term-resolved energy, timing, control or functionally equivalent electron-mediated-exchange evidence, with underlying data and the same case, propagated state and normalization identity; the disputed absolute photon transient peak is excluded as a unique target.",
      "award_conditions": [
        "Electronic/cavity coordinates and chosen energy, timing, control or equivalent exchange observables are reconstructible from the same propagated case/state.",
        "Norm/conditional conventions are consistent; no disputed absolute photon transient is made a unique target."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for F1, F2, F3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article p. 6, Eq. (10); pp. 12–16, Sec. IV A, Figs. 2(a,b), 3(a,b). Same-state electronic/cavity responses and energy partition. The task does not require the disputed absolute photon peak or its unique estimator."
      ],
      "rc_relation": "Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Submit valid, reconstructible HHG evidence for the uncoupled reference and all three visible cavity cases on a common comparison scale that exposes claim-bearing high-order bands, endpoint structure and lower-order exceptions.",
      "award_conditions": [
        "Submit valid, reconstructible HHG evidence for the uncoupled reference and all three visible cavity cases on a common comparison scale that exposes claim-bearing high-order bands, endpoint structure and lower-order exceptions.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for O2, O3, I2, I3, M2, M3, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 12–14, Sec. IV A, Fig. 1(a,b) and discussion of the 5th–9th harmonics. Case-resolved high-order/cutoff suppression and lower-order exceptions; fixed-coupling frequency comparisons must not be conflated with changing coupling."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Submit valid, reconstructible electronic and cavity dynamical responses from the same correctly propagated coupled states, with norm convention and case identity sufficient to compare electronic restriction, cavity excitation and persistent versus transient behavior.",
      "award_conditions": [
        "Submit valid, reconstructible electronic and cavity dynamical responses from the same correctly propagated coupled states, with norm convention and case identity sufficient to compare electronic restriction, cavity excitation and persistent versus transient behavior.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for O1, O3, I1, I3, M1, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 13–16, Fig. 2(a,b), Fig. 3(a) and adjacent persistent/transient discussion. Electronic restriction and cavity excitation under electron-only drive; normalized coordinate expectations differ from unrenormalized HHG production."
      ],
      "rc_relation": "Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Submit term-resolved energy histories, causal timing, a controlled Hamiltonian comparison, coordinate phase relations or functionally equivalent discriminating evidence from the same cases that can test electron-mediated cavity exchange without using the disputed photon peak as a target.",
      "award_conditions": [
        "Submit term-resolved energy histories, causal timing, a controlled Hamiltonian comparison, coordinate phase relations or functionally equivalent discriminating evidence from the same cases that can test electron-mediated cavity exchange without using the disputed photon peak as a target.",
        "The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for O1, O2, I1, I2, M1, M2, M3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 14–16, Fig. 3(b), energy-decomposition paragraphs; Eqs. (1), (3), (5), (6), (14)–(16). Electron-mediated exchange is physically entailed by the electron-only drive and interaction term. Source Fig. 3(b) has conflicting parameter labels/caption; it is qualitative mechanism context, never a unique numerical target."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "From the candidate's four-case HHG evidence, identify the material high-order and endpoint changes, fixed-coupling frequency relation, high-frequency case behavior and any lower-order exceptions without importing source-only cutoffs.",
      "award_conditions": [
        "From the candidate's four-case HHG evidence, identify the material high-order and endpoint changes, fixed-coupling frequency relation, high-frequency case behavior and any lower-order exceptions without importing source-only cutoffs."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O1. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for I2, I3, M2, M3, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 12–14, Sec. IV A, Fig. 1(a,b) and discussion of the 5th–9th harmonics. Case-resolved high-order/cutoff suppression and lower-order exceptions; fixed-coupling frequency comparisons must not be conflated with changing coupling."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "From the candidate's coordinate dynamics, identify electronic restriction, cavity excitation and the material persistent-versus-transient case relation under the declared norm convention.",
      "award_conditions": [
        "From the candidate's coordinate dynamics, identify electronic restriction, cavity excitation and the material persistent-versus-transient case relation under the declared norm convention."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O2. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for I1, I3, M1, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 13–16, Fig. 2(a,b), Fig. 3(a) and adjacent persistent/transient discussion. Electronic restriction and cavity excitation under electron-only drive; normalized coordinate expectations differ from unrenormalized HHG production."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "From the candidate's discriminating evidence, identify the electron-first timing, interaction/exchange and cavity-energy response or a functionally equivalent causal signature that bears on electron-mediated rather than direct cavity excitation.",
      "award_conditions": [
        "From the candidate's discriminating evidence, identify the electron-first timing, interaction/exchange and cavity-energy response or a functionally equivalent causal signature that bears on electron-mediated rather than direct cavity excitation."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: O3. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for I1, I2, M1, M2, M3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 14–16, Fig. 3(b), energy-decomposition paragraphs; Eqs. (1), (3), (5), (6), (14)–(16). Electron-mediated exchange is physically entailed by the electron-only drive and interaction term. Source Fig. 3(b) has conflicting parameter labels/caption; it is qualitative mechanism context, never a unique numerical target."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use the candidate-identified spectra to determine how each visible cavity case changes the high-order response and endpoint relative to the uncoupled atom, retaining lower-order exceptions, correctly distinguishing the fixed-coupling frequency relation from the high-frequency stronger-coupling case, and not extrapolating the finite computed cases into a universal monotonic law.",
      "award_conditions": [
        "Use the candidate-identified spectra to determine how each visible cavity case changes the high-order response and endpoint relative to the uncoupled atom, retaining lower-order exceptions, correctly distinguishing the fixed-coupling frequency relation from the high-frequency stronger-coupling case, and not extrapolating the finite computed cases into a universal monotonic law."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: I1. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M2, M3, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 12–14, Sec. IV A, Fig. 1(a,b) and discussion of the 5th–9th harmonics. Case-resolved high-order/cutoff suppression and lower-order exceptions; fixed-coupling frequency comparisons must not be conflated with changing coupling."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain the DSE-inclusive coupling contribution to electronic restriction and distinguish the positive confining self-energy from a disposable numerical correction.",
      "award_conditions": [
        "Explain the DSE-inclusive coupling contribution to electronic restriction and distinguish the positive confining self-energy from a disposable numerical correction."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F1 AND I2). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M1, M3, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Albrecht et al. (2025), article pp. 4–7, Eqs. (1)–(7), (11)–(16). Electron-only drive, bilinear cavity coupling and positive dipole self-energy, including the atomic rather than molecular model."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain how electron-only driving produces the candidate-identified cavity response and why its persistence or transience depends on the computed cavity case rather than direct laser excitation of the mode.",
      "award_conditions": [
        "Explain how electron-only driving produces the candidate-identified cavity response and why its persistence or transience depends on the computed cavity case rather than direct laser excitation of the mode."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F1 AND I2). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M1, M2, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 13–16, Fig. 2(a,b), Fig. 3(a) and adjacent persistent/transient discussion. Electronic restriction and cavity excitation under electron-only drive; normalized coordinate expectations differ from unrenormalized HHG production."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use the candidate-identified energy, timing, control or equivalent causal signature to explain electron-mediated cavity exchange and reject direct cavity driving or a DSE-omitted model as the same mechanism.",
      "award_conditions": [
        "Use the candidate-identified energy, timing, control or equivalent causal signature to explain electron-mediated cavity exchange and reject direct cavity driving or a DSE-omitted model as the same mechanism."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (F1 AND I3). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M1, M2, M3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 14–16, Fig. 3(b), energy-decomposition paragraphs; Eqs. (1), (3), (5), (6), (14)–(16). Electron-mediated exchange is physically entailed by the electron-only drive and interaction term. Source Fig. 3(b) has conflicting parameter labels/caption; it is qualitative mechanism context, never a unique numerical target."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect the candidate's case-resolved high-order spectral changes to mutually compatible DSE-inclusive electronic restriction, cavity response and electron-mediated exchange without asserting a universal one-parameter law.",
      "award_conditions": [
        "Connect the candidate's case-resolved high-order spectral changes to mutually compatible DSE-inclusive electronic restriction, cavity response and electron-mediated exchange without asserting a universal one-parameter law."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (M1 AND M4). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M2, M3, M6; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 12–16, Figs. 1(a,b), 2(a,b), 3(a,b), Sec. IV A. Task-defined synthesis of case-resolved spectra, DSE restriction and exchange; no universal one-parameter monotonic law follows from these finite cases."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use a discriminating alternative, intervention, control or functionally equivalent evidence to distinguish the DSE-inclusive electron-mediated explanation from a claim-relevant competing account; the same dual-purpose evidence may also support V2 when a material risk is triggered.",
      "award_conditions": [
        "Candidate-presented discrimination distinguishes the DSE-inclusive electron-mediated account from a material competing explanation.",
        "A dual-purpose control may also address a triggered V2 risk; no separate second control is required merely because two scientific functions are scored."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: I3. This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M1, M2, M3, M4; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 4–7, Eqs. (1), (3), (5), (6), (14)–(16); pp. 13–16, Sec. IV A. Hamiltonian terms entail discriminating controls against direct cavity driving or DSE omission. Alternative/intervention requirements are task-defined, not a prescribed source control plot."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Integrate the case-resolved HHG relation, DSE-inclusive electron/cavity dynamics, electron-mediated exchange, causal discrimination and computed-case boundary into the strongest physically consistent conclusion supported by the evidence.",
      "award_conditions": [
        "Integrate the case-resolved HHG relation, DSE-inclusive electron/cavity dynamics, electron-mediated exchange, causal discrimination and computed-case boundary into the strongest physically consistent conclusion supported by the evidence."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Necessary scientific premises: (M1 AND M4 AND M5 AND M6). This identifies facts, not prerequisite half-point awards.",
        "Preserve independently valid evidence for M2, M3, V1, V3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 12–16, Figs. 1(a,b), 2(a,b), 3(a,b), Sec. IV A. Task-defined synthesis of case-resolved spectra, DSE restriction and exchange; no universal one-parameter monotonic law follows from these finite cases."
      ],
      "rc_relation": "Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award."
    },
    {
      "criterion_id": "V1",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Provide claim-relevant evidence that common-scale HHG relations and norm-loss-aware dynamics are not manufactured by per-curve normalization, boundary reflection, transform/window choice or an under-resolved high-order tail, using any genuinely discriminating validation.",
      "award_conditions": [
        "Provide claim-relevant evidence that common-scale HHG relations and norm-loss-aware dynamics are not manufactured by per-curve normalization, boundary reflection, transform/window choice or an under-resolved high-order tail, using any genuinely discriminating validation."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for V2, V3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article p. 6, Eq. (8), window and norm-loss paragraphs; pp. 7–8, grid-model boundary treatment. Common-scale and norm-loss-aware spectral reliability; no mandatory source Hann window, grid or endpoint estimator."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "When the candidate's actual method, data, anomaly or claim raises a concrete material failure mode capable of changing the central conclusion, provide evidence that can expose it or proportionately narrow the claim; otherwise record N/A without claiming validation evidence.",
      "award_conditions": [
        "When the candidate's actual method, data, anomaly or claim raises a concrete material failure mode capable of changing the central conclusion, provide evidence that can expose it or proportionately narrow the claim; otherwise record N/A without claiming validation evidence.",
        "When triggered, award only if claim-relevant discriminating evidence resolves the threat or an evidence-based restriction makes it immaterial; merely acknowledging an unresolved material threat is not positive validation credit. With no trigger, record N/A and retain the fixed 0.5 without claiming performed validation."
      ],
      "applicability_and_na": [
        "Applies only when the submitted method, data, anomaly or conclusion creates the concrete material risk described here. If untriggered, record not_applicable and retain the fixed 0.5 contribution; this is not evidence that validation was performed, and does not block RC4."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Preserve independently valid evidence for V1, V3; failure here does not automatically erase those criteria.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 4–7, Eqs. (1), (3), (5), (6), (14)–(16); pp. 13–16, Sec. IV A. Hamiltonian terms entail discriminating controls against direct cavity driving or DSE omission. Alternative/intervention requirements are task-defined, not a prescribed source control plot."
      ],
      "rc_relation": "Material-validation role: RC3 only for a triggered, unresolved threat to a central conclusion, with all six burden-of-proof elements established. N/A does not block RC4."
    },
    {
      "criterion_id": "V3",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Limit conclusions to the specified one-dimensional, single-electron, single-mode atomic model and computed cases; do not claim a universal cavity-HHG law, molecular branch, direct cavity drive, realistic coupling or experimental conversion efficiency.",
      "award_conditions": [
        "Limit conclusions to the specified one-dimensional, single-electron, single-mode atomic model and computed cases; do not claim a universal cavity-HHG law, molecular branch, direct cavity drive, realistic coupling or experimental conversion efficiency."
      ],
      "applicability_and_na": [
        "Applies to every assessable submission; absence or failure is scored 0, not N/A."
      ],
      "dependencies": [
        "Judge this scientific obligation directly; no fixed prerequisite award.",
        "Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation."
      ],
      "equivalent_evidence": [
        "Accept stable grids/bases, absorbers, propagators, timesteps, acceleration forms, transforms/tapers, endpoint or high-order summaries and layouts preserving the same model, state, common scale and claim-relevant invariants.",
        "Term-resolved energy histories, causal timing, controlled Hamiltonian comparisons, coordinate phase relations or equally discriminating evidence may establish electron-mediated exchange. The same dual-purpose control can support causal discrimination and conclusion-level falsification; no separate second control is required."
      ],
      "source_support": [
        "Article pp. 5, 7–8, coupling-parameter qualification and Sec. III A; pp. 9–12, Sec. III B as contrast. One-dimensional single-electron single-mode atomic scope; molecular QED-CIS and realistic experimental-yield claims are not established by this task."
      ],
      "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim."
    }
  ],
  "case_scientific_rules": [
    "Use He=−(1/2)partial_z²−1/(|z|+eta), Hc=−(1/2)partial_xc²+omega_c² xc²/2, Hint=−sqrt(2 omega_c)g_c z xc, Hdse=(g_c²/omega_c)z², and electronic drive +zF(t) for dipole mu_z=−z. The laser does not directly drive xc. Each coupled case starts from the complete field-free polaritonic ground state, not an unqualified bare product.",
    "HHG is a declared complex transform of the unrenormalized dipole acceleration, e.g. I proportional to |integral w(t)exp(−i omega t)ddot mu_z dt|². Conditional coordinate/term expectations may divide by surviving norm N(t), but stepwise renormalization must not erase ionization loss from radiation.",
    "If photon number is used, the length-gauge expression is <n_c>=(<Hc+Hint+Hdse>/omega_c)−1/2 with consistent norm convention. The exact low-frequency transient maximum is unresolved and is not an answer point; deleting DSE to match it is physically inequivalent.",
    "The source-supported structural comparison is reduced high-order response/earlier endpoint in the low-frequency (omega_c,g_c)=(0.05,0.01) case relative to g_c=0; at fixed g_c=0.01 the 0.10-frequency case is less suppressed; (0.3185,0.06) retains much more high-order response despite larger coupling. Some lower harmonics need not decrease. Exact endpoints, absolute heights and tail floors are not fixed targets.",
    "Coupling restricts electronic excursions and excites the cavity; the positive DSE confines the electronic coordinate. The low-frequency response can persist beyond the pulse while the fixed-coupling 0.10 response is predominantly transient. Absolute coordinate maxima are not strict targets.",
    "Exchange evidence should support electron-first response followed by interaction/cavity response and accumulated cavity energy, or an equivalent causal signature. Source energy-panel case labels are inconsistent; judge the explicitly bound case, Hamiltonian term, timing/sign and relative exchange, not hidden curves.",
    "CAP symmetry/strength/onset, disputed photon peak, exact high-frequency floor, uncomputed full scans and source raster are not duties. Boundary, norm, normalization and window choices matter only where they actually damage evidence. Scope is the computed atomic single-electron single-mode model, not universal cavity laws or experimental efficiency.",
    "Score exactly twenty fixed 0/0.5 material-core criteria. Do not import numerical score ranges or RC score caps. A valid run with no assessable scientific work receives score 0 and RC0 before criterion summation; assessable partial work and timeouts are graded on available evidence.",
    "Object existence, candidate presentation, candidate identification, physical inference and validation are different acts. Inspect every candidate-authored claim-bearing figure. A reference, rerender or examiner reconstruction can verify an object but cannot create missing candidate reasoning.",
    "When a material decision depends on feature resolution, fine structure, component relations, formula identity, representation equivalence or suspicious morphology, perform a focused applicable source/reference check. Establish model/observable/case/component, units, basis/gauge, normalization and transformations first; do not turn source-only display choices into new duties. A provisional score at least 9.0 or provisional RC4 requires a focused check of one central output and one principal-mechanism link. Reference verification is examiner-side, not a new candidate deliverable.",
    "For the atomic coordinate $z$, cavity coordinate $x_c$ and $\\hbar=1$ conventions, $H=H_e+H_c+H_{\\rm int}+H_{\\rm dse}+zF(t)$, $H_e=p_z^2/2-Z/(|z|+\\eta)$, $H_c=p_c^2/2+\\omega_c^2x_c^2/2$, $H_{\\rm int}=-\\sqrt{2\\omega_c}g_czx_c$, $H_{\\rm dse}=g_c^2z^2/\\omega_c$ (Eqs. (11), (14)–(16)). $\\eta$ regularizes the cusp; $g_c$ is coupling, $\\omega_c$ cavity frequency and $F$ the electron-only pulse. The DSE is a positive confining term, not an optional numerical adjustment.",
    "With $N(t)=\\langle\\Psi|\\Psi\\rangle$, conditional coordinates use $\\langle z\\rangle/N$ and $\\langle x_c\\rangle/N$ when declared, while source HHG uses the norm-loss-aware dipole $\\mu_z(t)=-\\langle\\Psi|z|\\Psi\\rangle$ without propagation renormalization: $\\mathcal A(\\Omega)=\\int_0^{t_f}w(t)\\ddot\\mu_z(t)e^{-i\\Omega t}dt$, $I(\\Omega)\\propto|\\mathcal A|^2$ (Eq. (8), Sec. IV A). Independent per-curve normalization is not equivalent for common-scale spectral comparisons.",
    "Term energies satisfy $E_{\\rm tot}=E_e+E_c+E_{\\rm int}+E_{\\rm dse}$ under the same expectation/norm convention. Their timing and exchange, or a functionally equivalent causal control, test electron-mediated mode excitation. The source Eq. (10) photon expression and Fig. 3(a) absolute transient are not imposed as unique scoring targets; the stated task permits unambiguous coordinate/energy observables instead."
  ],
  "closure_requirements": {
    "RC0": [
      "The central physical object is absent or materially invalid. Establish this scientific fact independently of atomic credit; a local notation or presentation weakness is not itself RC0.",
      "(F1 AND F2 AND F3 AND F4): Instantiate the visible one-dimensional soft-Coulomb electron and single cavity coordinate with the bilinear interaction, dipole self-energy, electron-only pulse, uncoupled reference and all three specified cavity cases, preserving signs, units and atomic rather than molecular branch identity. Construct the full field-free polaritonic ground state for each coupled case and a stable two-coordinate propagation that retains physical norm loss, declares boundary and conditional-normalization conventions, and keeps all outputs bound to the same case/state. Define a reconstructible HHG complex transform and intensity together with a high-order or endpoint summary, underlying data, and a common case and normalization identity. Define reconstructible electronic and cavity dynamical observables plus term-resolved energy, timing, control or functionally equivalent electron-mediated-exchange evidence, with underlying data and the same case, propagated state and normalization identity; the disputed absolute photon transient peak is excluded as a unique target."
    ],
    "RC1": [
      "The central object exists, but a required indispensable component is absent or materially invalid. A failed presentation or overextended claim alone does not establish object absence or invalidity.",
      "O1: Submit valid, reconstructible HHG evidence for the uncoupled reference and all three visible cavity cases on a common comparison scale that exposes claim-bearing high-order bands, endpoint structure and lower-order exceptions.",
      "O2: Submit valid, reconstructible electronic and cavity dynamical responses from the same correctly propagated coupled states, with norm convention and case identity sufficient to compare electronic restriction, cavity excitation and persistent versus transient behavior."
    ],
    "RC2": [
      "Required objects are scientifically valid, but a required principal mechanism or state-dependence inference is absent or incorrect. Reference evidence cannot provide omitted candidate reasoning.",
      "M4: Use the candidate-identified energy, timing, control or equivalent causal signature to explain electron-mediated cavity exchange and reject direct cavity driving or a DSE-omitted model as the same mechanism.",
      "M7: Integrate the case-resolved HHG relation, DSE-inclusive electron/cavity dynamics, electron-mediated exchange, causal discrimination and computed-case boundary into the strongest physically consistent conclusion supported by the evidence."
    ],
    "RC3": [
      "Required objects and principal mechanisms are established, but a concrete material validation or scope threat to a central conclusion remains unresolved.",
      "V2: When the candidate's actual method, data, anomaly or claim raises a concrete material failure mode capable of changing the central conclusion, provide evidence that can expose it or proportionately narrow the claim; otherwise record N/A without claiming validation evidence.",
      "Before assigning RC3, establish all six elements: the concrete failure mode; its origin in the submitted method/data/conclusion; a fair recognizable scientific risk; the affected central conclusion; why the submitted evidence cannot discriminate or exclude it; and functionally equivalent remedies. Evidence-based restriction may remove unsupported breadth, but cannot repair an incorrect signal, absent component or missing mechanism."
    ],
    "RC4": [
      "Every indispensable and co-primary claim has all its nonempty required role slots closed; supporting claims do not independently determine overall RC. Preserve AND/OR branch logic shown above and use scientific gate outcomes, not atomic scores.",
      "No triggered material risk remains unresolved. Untriggered risk criteria recorded N/A do not block RC4 and do not establish validation evidence.",
      "Classify descriptively by the most severe applicable failed required role (lowest RC), without score ceilings or target distributions. A score/RC tension prompts scientific review, not forced adjustment."
    ]
  },
  "references": [
    {
      "citation": "Paul A. Albrecht, Eric W. Fischer, Tillmann Klamroth, and Peter Saalfrank. 2025. *High-harmonic generation under electronic strong coupling: A time-dependent combined quantum electrodynamics/quantum chemistry study*. *arXiv*, 2507.21687.  Version 1.",
      "url": "https://arxiv.org/abs/2507.21687v1",
      "scientific_scope": "Atomic DSE-inclusive cavity-HHG branch only, with coupled ground states, norm-loss-aware spectra and electron-mediated cavity response. The disputed photon transient and conflicting Fig. 3(b) parameter annotations are excluded as quantitative targets; molecular results are context only.",
      "anchors": [
        "Albrecht et al. (2025), article pp. 4–7, Eqs. (1)–(7), (11)–(16).",
        "Article pp. 7–8, Sec. III A; p. 12, Sec. IV A opening paragraph.",
        "Article p. 6, Eqs. (8)–(9) and no-renormalization paragraph.",
        "Article p. 6, Eq. (10); pp. 12–16, Sec. IV A, Figs. 2(a,b), 3(a,b).",
        "Article pp. 12–14, Sec. IV A, Fig. 1(a,b) and discussion of the 5th–9th harmonics.",
        "Article pp. 13–16, Fig. 2(a,b), Fig. 3(a) and adjacent persistent/transient discussion.",
        "Article pp. 14–16, Fig. 3(b), energy-decomposition paragraphs; Eqs. (1), (3), (5), (6), (14)–(16).",
        "Article pp. 12–16, Figs. 1(a,b), 2(a,b), 3(a,b), Sec. IV A.",
        "Article pp. 4–7, Eqs. (1), (3), (5), (6), (14)–(16); pp. 13–16, Sec. IV A.",
        "Article p. 6, Eq. (8), window and norm-loss paragraphs; pp. 7–8, grid-model boundary treatment.",
        "Article pp. 5, 7–8, coupling-parameter qualification and Sec. III A; pp. 9–12, Sec. III B as contrast."
      ]
    }
  ]
}