| { |
| "case_id": "Case41", |
| "title": "State-resolved light-front momentum transfer from tunnelling to asymptotia", |
| "atoms": [ |
| { |
| "criterion_id": "F1", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Bind all three target-state channels to the visible leading-order light-front launch probability, including Ip/Z, p_minus, the Coulomb/PPT momentum factor and the state-resolving spherical-harmonic factor.", |
| "award_conditions": [ |
| "Bind all three target-state channels to the visible leading-order light-front launch probability, including Ip/Z, p_minus, the Coulomb/PPT momentum factor and the state-resolving spherical-harmonic factor." |
| ], |
| "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 F3, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "He et al. (2022), article p. L031102-2, Eqs. (2)–(4); SI p. 3, Eqs. (S21)–(S25). State-resolved Coulomb/PPT launch measure and spherical-harmonic weights; statewise constants may cancel in normalized moments but momentum-dependent factors may not." |
| ], |
| "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": "Derive the saddle exit and initial p_minus map, carry the differential launch probability as the trajectory weight, and distinguish the Coulomb-corrected launch from the short-range/no-sub-barrier-Coulomb launch policy.", |
| "award_conditions": [ |
| "Derive the saddle exit and initial p_minus map, carry the differential launch probability as the trajectory weight, and distinguish the Coulomb-corrected launch from the short-range/no-sub-barrier-Coulomb launch policy." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: F1. This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for F3, M1, M2, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article p. L031102-2, exit statement after Eq. (6); SI pp. 1–5, Eqs. (S7), (S9), (S15), (S24)–(S25), (S37)–(S39). Saddle exit, launch momentum and probability weights; short-range launch removes sub-barrier Coulomb contributions, not the angular-state identity." |
| ], |
| "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": "Establish the full and sub-barrier-only asymptotic branches with the same Coulomb-corrected launch identity, the correct longitudinal Hamiltonian sign, field-off evolution and asymptotic momentum map.", |
| "award_conditions": [ |
| "Full and sub-barrier-only propagation share the same Coulomb-corrected launch ensemble, exit and trajectory weights.", |
| "The longitudinal equation has the correct negative quadratic term and the final observable uses field-off asymptotic mapping; the short-range-launch control is not a substitute." |
| ], |
| "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, I1, M1, M2, M3, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article p. L031102-2, Eqs. (5)–(6); SI pp. 6–7, Eqs. (S54)–(S60) and Kepler-projection paragraph. Common launch for full/sub-barrier-only propagation, correct negative longitudinal quadratic term, field-off Kepler map and asymptotic momentum." |
| ], |
| "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": "Define units, normalization, state/policy metadata and reconstructible data, and submit field-dependent birth-stage evidence for all three states under both Coulomb-corrected and short-range launch policies.", |
| "award_conditions": [ |
| "Define units, normalization, state/policy metadata and reconstructible data, and submit field-dependent birth-stage evidence for all three states under both Coulomb-corrected and short-range launch policies.", |
| "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": [ |
| "Necessary scientific premises: (F1 AND F2). This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for O2, O3, I2, I3, M4, M5, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article pp. L031102-2–3, Fig. 1(a–f), Eqs. (7)–(8); SI p. 3, Eq. (S25). Three-state launch-policy response and angular-weighting signatures. Canonical one-/two-lobe marginals are not the only valid representation." |
| ], |
| "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": "Define units, normalization and branch metadata, and submit reconstructible field-dependent full versus sub-barrier-only asymptotic evidence for Ar(3p,m=1).", |
| "award_conditions": [ |
| "Define units, normalization and branch metadata, and submit reconstructible field-dependent full versus sub-barrier-only asymptotic evidence for Ar(3p,m=1).", |
| "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": [ |
| "Necessary scientific premises: F3. This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for O1, O3, I1, I3, M1, M2, M3, M5, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article pp. L031102-3–4, Fig. 3(a), caption and continuum discussion; SI p. 7, Eqs. (S58)–(S65). Ar(3p,m=1) full/sub-barrier-only field response and retained/reshaped birth information; nonadiabatic additional curves are not compulsory." |
| ], |
| "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": "Define units, normalization and branch metadata, and submit reconstructible field-dependent full versus sub-barrier-only asymptotic evidence for Ar(3p,m=0).", |
| "award_conditions": [ |
| "Define units, normalization and branch metadata, and submit reconstructible field-dependent full versus sub-barrier-only asymptotic evidence for Ar(3p,m=0).", |
| "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": [ |
| "Necessary scientific premises: F3. This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for O1, O2, I1, I2, M1, M2, M3, M4, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article pp. L031102-3–4, Fig. 3(b), caption and continuum discussion; SI p. 7, Eqs. (S58)–(S65). Distinct Ar(3p,m=0) channel and nonmonotonic structure; do not exchange the two magnetic channels or impose a capture-sensitive exact endpoint." |
| ], |
| "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": "I1", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "From the candidate-presented launch evidence, identify the material three-state topology or functional equivalent state/angular-weight signature and the distinct launch-policy field response.", |
| "award_conditions": [ |
| "From the candidate-presented launch evidence, identify the material three-state topology or functional equivalent state/angular-weight signature and the distinct launch-policy field response." |
| ], |
| "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, M1, M2, M4, M5, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article pp. L031102-2–3, Fig. 1(a–f), Eqs. (7)–(8); SI p. 3, Eq. (S25). Three-state launch-policy response and angular-weighting signatures. Canonical one-/two-lobe marginals are not the only valid representation." |
| ], |
| "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-presented Ar(3p,m=1) asymptotic evidence, identify the material full/sub-barrier-only separation and its field-dependent structure.", |
| "award_conditions": [ |
| "From the candidate-presented Ar(3p,m=1) asymptotic evidence, identify the material full/sub-barrier-only separation and its field-dependent structure." |
| ], |
| "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, M2, M3, M5, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article pp. L031102-3–4, Fig. 3(a), caption and continuum discussion; SI p. 7, Eqs. (S58)–(S65). Ar(3p,m=1) full/sub-barrier-only field response and retained/reshaped birth information; nonadiabatic additional curves are not compulsory." |
| ], |
| "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-presented Ar(3p,m=0) asymptotic evidence, identify its material nonmonotonic or otherwise channel-specific full/sub-barrier-only structure without exchanging the two magnetic sublevels.", |
| "award_conditions": [ |
| "From the candidate-presented Ar(3p,m=0) asymptotic evidence, identify its material nonmonotonic or otherwise channel-specific full/sub-barrier-only structure without exchanging the two magnetic sublevels." |
| ], |
| "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, M4, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article pp. L031102-3–4, Fig. 3(b), caption and continuum discussion; SI p. 7, Eqs. (S58)–(S65). Distinct Ar(3p,m=0) channel and nonmonotonic structure; do not exchange the two magnetic channels or impose a capture-sensitive exact endpoint." |
| ], |
| "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": "Explain how the nondipole ionization window and sub-barrier Coulomb action set and reweight the launch-momentum window rather than acting as a state-independent classical offset.", |
| "award_conditions": [ |
| "Explain how the nondipole ionization window and sub-barrier Coulomb action set and reweight the launch-momentum window rather than acting as a state-independent classical offset." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: F1. This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M2, M4, M5, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article p. L031102-3, Fig. 2(a–c), ionization-window and bound-state-matching paragraphs; SI pp. 3–5, Eq. (S25), Sec. I A 7, Fig. S1. Nondipole window, Coulomb action and angular prefactor jointly reweight the launch ensemble. An attraction slogan or one mean without claim-relevant weighting evidence is insufficient." |
| ], |
| "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": "M2", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Explain how the Coulomb bound-state and angular momentum factor changes the sampled weight, including why the m=0 multi-lobed family and mean response cannot be inferred from a single attraction slogan.", |
| "award_conditions": [ |
| "Explain how the Coulomb bound-state and angular momentum factor changes the sampled weight, including why the m=0 multi-lobed family and mean response cannot be inferred from a single attraction slogan." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: F1. This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M1, M4, M5, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article p. L031102-3, Fig. 2(a–c), ionization-window and bound-state-matching paragraphs; SI pp. 3–5, Eq. (S25), Sec. I A 7, Fig. S1. Nondipole window, Coulomb action and angular prefactor jointly reweight the launch ensemble. An attraction slogan or one mean without claim-relevant weighting evidence is insufficient." |
| ], |
| "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": "M3", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Use the candidate-identified launch evidence to connect the window/action and angular weighting to the observed state- and launch-policy-dependent response.", |
| "award_conditions": [ |
| "Use the candidate-identified launch evidence to connect the window/action and angular weighting to the observed state- and launch-policy-dependent response." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: (M1 AND M2 AND I1). This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M4, M5, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article p. L031102-3, Fig. 2(a–c), ionization-window and bound-state-matching paragraphs; SI pp. 3–5, Eq. (S25), Sec. I A 7, Fig. S1. Nondipole window, Coulomb action and angular prefactor jointly reweight the launch ensemble. An attraction slogan or one mean without claim-relevant weighting evidence is insufficient." |
| ], |
| "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": "M4", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Determine from the m=1 paired branch signal which launch-stage features are retained or reshaped by continuum Coulomb dynamics.", |
| "award_conditions": [ |
| "Determine from the m=1 paired branch signal which launch-stage features are retained or reshaped by continuum Coulomb dynamics." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: (F3 AND I2). This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M1, M2, M3, M5, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article pp. L031102-3–4, Fig. 3(a), caption and continuum discussion; SI p. 7, Eqs. (S58)–(S65). Ar(3p,m=1) full/sub-barrier-only field response and retained/reshaped birth information; nonadiabatic additional curves are not compulsory." |
| ], |
| "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": "Determine from the m=0 paired branch signal which launch-stage features are retained or reshaped by continuum Coulomb dynamics.", |
| "award_conditions": [ |
| "Determine from the m=0 paired branch signal which launch-stage features are retained or reshaped by continuum Coulomb dynamics." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: (F3 AND I3). This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M1, M2, M3, M4, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article pp. L031102-3–4, Fig. 3(b), caption and continuum discussion; SI p. 7, Eqs. (S58)–(S65). Distinct Ar(3p,m=0) channel and nonmonotonic structure; do not exchange the two magnetic channels or impose a capture-sensitive exact endpoint." |
| ], |
| "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": "M6", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Distinguish the causal role of changing the under-barrier launch ensemble from changing only post-exit continuum propagation; do not treat short-range launch and sub-barrier-only asymptotic branches as the same toggle.", |
| "award_conditions": [ |
| "The candidate distinguishes changing the sub-barrier launch weighting from changing post-exit Coulomb propagation.", |
| "This causal distinction does not depend on reproducing a preferred topology plot or using one fixed wavelength." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: (F2 AND F3). This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M1, M2, M3, M4, M5, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article pp. L031102-2–4, Figs. 1(a–f), 3(a,b), Eq. (6); SI p. 7, Eqs. (S58)–(S60). Task-defined causal synthesis distinguishes changing launch policy from changing post-exit propagation and establishes state-dependent continuum reshaping." |
| ], |
| "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": "M7", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Integrate the two Ar channel results to explain why continuum Coulomb dynamics produces state-dependent preservation or reshaping rather than a common offset or scale change.", |
| "award_conditions": [ |
| "Integrate the two Ar channel results to explain why continuum Coulomb dynamics produces state-dependent preservation or reshaping rather than a common offset or scale change." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: (M4 AND M5 AND M6). This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M1, M2, M3, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article pp. L031102-2–4, Figs. 1(a–f), 3(a,b), Eq. (6); SI p. 7, Eqs. (S58)–(S60). Task-defined causal synthesis distinguishes changing launch policy from changing post-exit propagation and establishes state-dependent continuum reshaping." |
| ], |
| "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": "M8", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "State the evidence-supported extent to which birth-stage state/weighting information remains inferable from asymptotic momentum in the specified model and field domain.", |
| "award_conditions": [ |
| "State the evidence-supported extent to which birth-stage state/weighting information remains inferable from asymptotic momentum in the specified model and field domain." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: (M3 AND M7). This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M1, M2, M4, M5, M6, V1, 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article pp. L031102-2–4, Figs. 1(a–f), 3(a,b), Eq. (6); SI p. 7, Eqs. (S58)–(S60). Task-defined causal synthesis distinguishes changing launch policy from changing post-exit propagation and establishes state-dependent continuum reshaping." |
| ], |
| "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": "Address one claim-changing alternative or failure mode arising from the chosen method, data or conclusion, using a relevant check or honestly narrowing the affected claim.", |
| "award_conditions": [ |
| "Address one claim-changing alternative or failure mode arising from the chosen method, data or conclusion, using a relevant check or honestly narrowing the affected claim." |
| ], |
| "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, M1, M2, M3, M4, M5, M6, M7, M8; 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "SI p. 3, Eq. (S24); p. 7, Eq. (S58), field-off Kepler statement; article Fig. 3(a,b), p. L031102-4. Same-weight branch/sign/normalization and asymptotic-identity alternatives. V1 positive claim-relevant discrimination and V2 triggered risks remain distinct task roles; no unique check is prescribed." |
| ], |
| "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 a concrete numerical, identity, representation or scope risk emerges that could change a material state/branch/sign conclusion, validate, exclude or explicitly retract the affected claim.", |
| "award_conditions": [ |
| "When a concrete numerical, identity, representation or scope risk emerges that could change a material state/branch/sign conclusion, validate, exclude or explicitly retract the affected claim.", |
| "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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "SI p. 3, Eq. (S24); p. 7, Eq. (S58), field-off Kepler statement; article Fig. 3(a,b), p. L031102-4. Same-weight branch/sign/normalization and asymptotic-identity alternatives. V1 positive claim-relevant discrimination and V2 triggered risks remain distinct task roles; no unique check is prescribed." |
| ], |
| "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": "Identify the leading-order light-front, single-active-electron, direct-tunnelling and selected field/data limits, and avoid claims of universal relativistic, multielectron, experimental or excluded slope closure.", |
| "award_conditions": [ |
| "Identify the leading-order light-front, single-active-electron, direct-tunnelling and selected field/data limits, and avoid claims of universal relativistic, multielectron, experimental or excluded slope closure." |
| ], |
| "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 V1, V2; 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 physical gauge/coordinate/unit transformations, common normalization, deterministic quadrature or statistical sampling, ODE solvers, field-off/Kepler implementations, scan density and pulse realizations preserving p_minus, state, launch policy, trajectory weight and asymptotic branch.", |
| "Full normalized p_minus marginals are canonical but not uniquely required: weighted components, state analyses, moment families, interventions or reconstructible equivalent evidence may establish the same state/angular weighting and any claim-material multi-lobed structure. A mean alone cannot support a mechanism depending on unestablished hidden topology." |
| ], |
| "source_support": [ |
| "Article p. L031102-2, leading-1/c validity paragraph; p. L031102-4, Fig. 3(c), Fig. 4 and conclusion. Leading-order direct-tunnelling scope. Fig. 4 slope/TDSE comparison is excluded as a quantitative endpoint; it cannot supply required closure." |
| ], |
| "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim." |
| } |
| ], |
| "case_scientific_rules": [ |
| "Channels are H(1s), Ar(3p,m=1), Ar(3p,m=0), with quantization axis along propagation; swapping the Ar magnetic sublevels changes physical weighting, not just labels.", |
| "Use dmu_nlm=Gamma_nlm d eta dv_perp d pz_tilde; kappa=sqrt(2Ip), nu=Z/kappa and kappa_tilde²=kappa²+v_perp²+pz_tilde². Gamma is proportional to (kappa/kappa_tilde) 2^(2nu+2) C_(kappa l)² kappa^(6nu) |Y_lm(p_tilde(eta_s))|² /[(1−pz_tilde/c)^(2nu)E(eta)^(2nu)] times exp{−2 kappa_tilde³/[3E(eta)(1−pz_tilde/c)]}. Statewise constants may cancel in normalized observables, but angular, Coulomb/PPT momentum and light-front factors cannot be dropped.", |
| "The exit is x_e=−kappa_tilde² E/[2(1−pz_tilde/c)E²], p_perp^e=v_perp−A_perp(eta), p_minus^e=pz_tilde+Ip/c. Carry the differential launch measure as each trajectory's weight into final normalized marginals/moments.", |
| "The short-range launch control removes under-barrier Coulomb action and asymptotic enhancement while retaining the nondipole kinetic window, state/angular identity, launch variables and exit p_minus. It is not the sub-barrier-only asymptotic toggle.", |
| "Full and sub-barrier-only asymptotic branches use the identical Coulomb-corrected launch ensemble, exit and weights. Full propagation retains V=−Z/r and uses the outgoing field-off Kepler map; sub-barrier-only sets V=0 after exit and retains field-only evolution and the same final p_minus.", |
| "The longitudinal-velocity numerator contains p_minus+V/c+{−(p_minus+V/c)²+|p_perp+A_perp|²}/(2c). A positive sign on that longitudinal square is not an equivalent convention.", |
| "H(1s) and Ar m=1 have single-main-lobe launch families; Ar m=0 has a two-main-lobe angular-weight family. Equivalent evidence is acceptable, not a compulsory topology plot. Leading checks include <p_minus>_H=(Ip/c)[1/3+(2nu−1)E0/kappa³] and <p_minus>_Ar,m0=(Ip/c)[−1+(6nu−5)E0/kappa³]; these do not replace full weighted evidence.", |
| "The ionization exponent sets a shared kinetic window, sub-barrier action reweights momentum, and bound-state/angular factors alter the sampled signal. Continuum Coulomb action reshapes the two Ar channels differently: m=1 full/sub-only separation and saturation/slight return differs from m=0's pronounced nonmonotonic full family. A common offset or scale cannot explain both.", |
| "No hidden fixed wavelength, field mesh or exact capture-sensitive endpoint is mandatory. Average-slope/TDSE endpoint comparisons are excluded as gold; do not claim they are closed or use printed slopes to penalize an otherwise valid calculation. Scope is leading-1/c direct single-active-electron tunnelling, not exact relativity, real multielectron Ar or experiment.", |
| "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.", |
| "$p_-=p_z-p^2/(2c)$, $\\kappa=\\sqrt{2I_p}$, $\\nu=Z/\\kappa$, $\\widetilde\\kappa^2=\\kappa^2+v_\\perp^2+\\widetilde p_z^2$. The weighted launch measure is $d\\mu=\\Gamma_{nlm}d\\eta\\,dv_\\perp\\,d\\widetilde p_z$ with $\\Gamma_{nlm}=(\\kappa/\\widetilde\\kappa)2^{2\\nu+2}C_{\\kappa l}^2\\kappa^{6\\nu}|Y_{lm}(\\widetilde{\\mathbf p}_s)|^2[(1-\\widetilde p_z/c)^{2\\nu}E^{2\\nu}]^{-1}\\exp[-2\\widetilde\\kappa^3/\\{3E(1-\\widetilde p_z/c)\\}]$ (SI Eq. (S24)). $E=|\\mathbf E(\\eta)|$ and $C_{\\kappa l}$ is the statewise asymptotic normalization. Constants cancel only within a state/policy normalization; angular and momentum weights do not.", |
| "The task saddle map is $\\mathbf x_e=-\\widetilde\\kappa^2\\mathbf E/[2(1-\\widetilde p_z/c)E^2]$, $\\mathbf p_\\perp^e=\\mathbf v_\\perp-\\mathbf A_\\perp$, $p_-^e=\\widetilde p_z+I_p/c$. Weighted final means use the same launch weights. Full and sub-barrier-only branches share this Coulomb-corrected ensemble; only the post-exit potential is changed to $V=0$ for sub-barrier-only. That branch is not the short-range-launch control.", |
| "Writing $q=p_-+V/c$ and $\\boldsymbol\\pi_\\perp=\\mathbf p_\\perp+\\mathbf A_\\perp$, SI Eq. (S58) gives $dz/d\\eta=[q+(-q^2+|\\boldsymbol\\pi_\\perp|^2)/(2c)]/(1-q/c)^2$. The minus sign on $q^2$ is essential. After field-off, outgoing Coulomb trajectories require the asymptotic Kepler map; the instantaneous canonical momentum is not automatically the asymptotic mechanical momentum.", |
| "As leading quasistatic checks only, $\\langle p_-\\rangle_s=(I_p/c)[1/3+(2\\nu-1)E_0/E_a]$ and $\\langle p_-\\rangle_{p,m=0}=(I_p/c)[-1+(6\\nu-5)E_0/E_a]$, $E_a=\\kappa^3$ (Eqs. (7)–(8)). They do not replace complete state/policy weighted evidence and do not prove exact relativistic or multielectron dynamics." |
| ], |
| "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): Bind all three target-state channels to the visible leading-order light-front launch probability, including Ip/Z, p_minus, the Coulomb/PPT momentum factor and the state-resolving spherical-harmonic factor. Derive the saddle exit and initial p_minus map, carry the differential launch probability as the trajectory weight, and distinguish the Coulomb-corrected launch from the short-range/no-sub-barrier-Coulomb launch policy.", |
| "F3: Establish the full and sub-barrier-only asymptotic branches with the same Coulomb-corrected launch identity, the correct longitudinal Hamiltonian sign, field-off evolution and asymptotic momentum map." |
| ], |
| "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: Define units, normalization, state/policy metadata and reconstructible data, and submit field-dependent birth-stage evidence for all three states under both Coulomb-corrected and short-range launch policies.", |
| "(O2 AND O3): Define units, normalization and branch metadata, and submit reconstructible field-dependent full versus sub-barrier-only asymptotic evidence for Ar(3p,m=1). Define units, normalization and branch metadata, and submit reconstructible field-dependent full versus sub-barrier-only asymptotic evidence for Ar(3p,m=0)." |
| ], |
| "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.", |
| "(M1 AND M2 AND M3): Explain how the nondipole ionization window and sub-barrier Coulomb action set and reweight the launch-momentum window rather than acting as a state-independent classical offset. Explain how the Coulomb bound-state and angular momentum factor changes the sampled weight, including why the m=0 multi-lobed family and mean response cannot be inferred from a single attraction slogan. Use the candidate-identified launch evidence to connect the window/action and angular weighting to the observed state- and launch-policy-dependent response.", |
| "(M4 AND M5 AND M6 AND M7 AND M8): Determine from the m=1 paired branch signal which launch-stage features are retained or reshaped by continuum Coulomb dynamics. Determine from the m=0 paired branch signal which launch-stage features are retained or reshaped by continuum Coulomb dynamics. Distinguish the causal role of changing the under-barrier launch ensemble from changing only post-exit continuum propagation; do not treat short-range launch and sub-barrier-only asymptotic branches as the same toggle. Integrate the two Ar channel results to explain why continuum Coulomb dynamics produces state-dependent preservation or reshaping rather than a common offset or scale change. State the evidence-supported extent to which birth-stage state/weighting information remains inferable from asymptotic momentum in the specified model and field domain." |
| ], |
| "RC3": [ |
| "Required objects and principal mechanisms are established, but a concrete material validation or scope threat to a central conclusion remains unresolved.", |
| "V2: When a concrete numerical, identity, representation or scope risk emerges that could change a material state/branch/sign conclusion, validate, exclude or explicitly retract the affected claim.", |
| "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": "Pei-Lun He, Michael Klaiber, Karen Z. Hatsagortsyan, and Christoph H. Keitel. 2022b. *Nondipole Coulomb sub-barrier ionization dynamics and photon momentum sharing*. *Physical Review A*, 105, L031102.", |
| "url": "https://doi.org/10.1103/PhysRevA.105.L031102", |
| "scientific_scope": "Three-state launch weighting and two Ar-channel asymptotic comparison under the leading-order light-front model. Canonical topology plots are optional equivalents; source Fig. 4/TDSE average-slope claims are outside the quantitative grading scope.", |
| "anchors": [ |
| "He et al. (2022), article p. L031102-2, Eqs. (2)–(4); SI p. 3, Eqs. (S21)–(S25).", |
| "Article p. L031102-2, exit statement after Eq. (6); SI pp. 1–5, Eqs. (S7), (S9), (S15), (S24)–(S25), (S37)–(S39).", |
| "Article p. L031102-2, Eqs. (5)–(6); SI pp. 6–7, Eqs. (S54)–(S60) and Kepler-projection paragraph.", |
| "Article pp. L031102-2–3, Fig. 1(a–f), Eqs. (7)–(8); SI p. 3, Eq. (S25).", |
| "Article pp. L031102-3–4, Fig. 3(a), caption and continuum discussion; SI p. 7, Eqs. (S58)–(S65).", |
| "Article pp. L031102-3–4, Fig. 3(b), caption and continuum discussion; SI p. 7, Eqs. (S58)–(S65).", |
| "Article p. L031102-3, Fig. 2(a–c), ionization-window and bound-state-matching paragraphs; SI pp. 3–5, Eq. (S25), Sec. I A 7, Fig. S1.", |
| "Article pp. L031102-2–4, Figs. 1(a–f), 3(a,b), Eq. (6); SI p. 7, Eqs. (S58)–(S60).", |
| "SI p. 3, Eq. (S24); p. 7, Eq. (S58), field-off Kepler statement; article Fig. 3(a,b), p. L031102-4.", |
| "Article p. L031102-2, leading-1/c validity paragraph; p. L031102-4, Fig. 3(c), Fig. 4 and conclusion." |
| ] |
| } |
| ] |
| } |
|
|
