| { |
| "case_id": "Case43", |
| "title": "Photon-traced and photon-conditioned quantum radiation pressure", |
| "atoms": [ |
| { |
| "criterion_id": "F1", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Bind H/Na, BSV/coherent states, the common mean-intensity convention, circular leading-order light-front nondipole direct-SFA model, photon-traced phase-space probability and target-dependent longitudinal-momentum offset.", |
| "award_conditions": [ |
| "Bind H/Na, BSV/coherent states, the common mean-intensity convention, circular leading-order light-front nondipole direct-SFA model, photon-traced phase-space probability and target-dependent longitudinal-momentum offset." |
| ], |
| "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, O2, O3, O4, I2, I3, I4, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Mao, He and He (2026), main pp. 1–3, Eqs. (1)–(7). Photon-traced phase-space probability, direct light-front amplitude, common intensity convention and target-dependent offset." |
| ], |
| "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": "Bind the Na low-field neighboring final-number pair to one common-radius pair of opposite-phase field points, exact squeezed-vacuum/Fock overlaps and the complete finite-pulse coherent amplitude sum before the modulus square.", |
| "award_conditions": [ |
| "Bind the Na low-field neighboring final-number pair to one common-radius pair of opposite-phase field points, exact squeezed-vacuum/Fock overlaps and the complete finite-pulse coherent amplitude sum before the modulus square." |
| ], |
| "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, O1, I1, M1, M2, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 3–4, Eqs. (8)–(10); SI pp. 9–11, Eqs. (S59)–(S82). Fixed-number amplitude projection and opposite same-radius field paths; finite-pulse two-point production is the visible bounded task approximation, not the full phase-space integral." |
| ], |
| "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 its longitudinal moment, units, normalization and data binding, and submit reconstructible H/Na and BSV/coherent photon-traced intensity-response evidence resolving the two state laws, target dependence, offset and credible scale without requiring pointwise source equality.", |
| "award_conditions": [ |
| "Define its longitudinal moment, units, normalization and data binding, and submit reconstructible H/Na and BSV/coherent photon-traced intensity-response evidence resolving the two state laws, target dependence, offset and credible scale without requiring pointwise source equality.", |
| "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. This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for O2, O3, O4, I2, I3, I4, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 2–3, Fig. 1(a,b), Eqs. (5)–(7); SI pp. 7–8, Eqs. (S46)–(S58). Coherent linear versus BSV two-thirds field law, nonlinear amplitude selection, target prefactor and offset. Leading-order curves are not pointwise source-data gold." |
| ], |
| "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 the consistently normalized relative yield and its data binding, and submit reconstructible yield evidence for both correctly bound neighboring conditioned channels on the retained low-field domain.", |
| "award_conditions": [ |
| "Define the consistently normalized relative yield and its data binding, and submit reconstructible yield evidence for both correctly bound neighboring conditioned channels on the retained low-field domain.", |
| "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: F2. This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for O1, O3, O4, I1, I3, I4, M1, M2, M3, M4, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main p. 4, Fig. 3(b), low-effective-intensity paragraph. Neighboring conditioned-channel relative-yield ordering at low field, not the excluded full-channel/high-field reversal." |
| ], |
| "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 the longitudinal-moment measure, units and data binding, and submit reconstructible mean-pz evidence for both correctly bound neighboring conditioned channels with sufficient momentum support.", |
| "award_conditions": [ |
| "Define the longitudinal-moment measure, units and data binding, and submit reconstructible mean-pz evidence for both correctly bound neighboring conditioned channels with sufficient momentum support.", |
| "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: F2. This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for O1, O2, O4, I1, I2, I4, M1, M2, M3, M4, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main p. 4, Fig. 3(a), low-effective-intensity paragraph. Positive mean-longitudinal-momentum ordering for the same channel pair; adequate tails and common measure remain necessary." |
| ], |
| "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": "O4", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Define the spectral or functionally equivalent quantity with its measure, normalization and data binding, and submit reconstructible same-object evidence with enough discriminating force to isolate the amplitude-level cross-term-sensitive channel-complementary structure.", |
| "award_conditions": [ |
| "Define the spectral or functionally equivalent quantity with its measure, normalization and data binding, and submit reconstructible same-object evidence with enough discriminating force to isolate the amplitude-level cross-term-sensitive channel-complementary structure.", |
| "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: F2. This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for O1, O2, O3, I1, I2, I3, M1, M2, M3, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 4–5, Fig. 4(b1,b2), Eqs. (10)–(12); SI pp. 11–14, Eqs. (S82)–(S101). Low-field complementary spectral redistribution and sign-sensitive cross term. Fig. 4(a1,a2) is the unrequired high-field contrast; exact peak widths/heights are not targets." |
| ], |
| "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 candidate-presented photon-traced evidence, identify the coherent linear and BSV two-thirds intensity-law families while separating target-dependent prefactor and nearly constant offset.", |
| "award_conditions": [ |
| "From candidate-presented photon-traced evidence, identify the coherent linear and BSV two-thirds intensity-law families while separating target-dependent prefactor and nearly constant offset." |
| ], |
| "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, I4, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 2–3, Fig. 1(a,b), Eqs. (5)–(7); SI pp. 7–8, Eqs. (S46)–(S58). Coherent linear versus BSV two-thirds field law, nonlinear amplitude selection, target prefactor and offset. Leading-order curves are not pointwise source-data gold." |
| ], |
| "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 candidate-presented conditioned data, identify the material neighboring-channel relative-yield ordering without requiring additional numerical scale checks not specified in the task.", |
| "award_conditions": [ |
| "From candidate-presented conditioned data, identify the material neighboring-channel relative-yield ordering without requiring additional numerical scale checks not specified in the task." |
| ], |
| "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, I4, M1, M2, M3, M4, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main p. 4, Fig. 3(b), low-effective-intensity paragraph. Neighboring conditioned-channel relative-yield ordering at low field, not the excluded full-channel/high-field reversal." |
| ], |
| "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 candidate-presented conditioned data, identify the material neighboring-channel positive mean-pz ordering with adequate tail support.", |
| "award_conditions": [ |
| "From candidate-presented conditioned data, identify the material neighboring-channel positive mean-pz ordering with adequate tail support." |
| ], |
| "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, I4, M1, M2, M3, M4, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main p. 4, Fig. 3(a), low-effective-intensity paragraph. Positive mean-longitudinal-momentum ordering for the same channel pair; adequate tails and common measure remain necessary." |
| ], |
| "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim." |
| }, |
| { |
| "criterion_id": "I4", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "From candidate-presented cross-term-sensitive evidence, identify the channel-complementary spectral redistribution or equivalent sign-changing cross-term structure.", |
| "award_conditions": [ |
| "From candidate-presented cross-term-sensitive evidence, identify the channel-complementary spectral redistribution or equivalent sign-changing cross-term structure." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: O4. This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for I1, I2, I3, M1, M2, M3, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 4–5, Fig. 4(b1,b2), Eqs. (10)–(12); SI pp. 11–14, Eqs. (S82)–(S101). Low-field complementary spectral redistribution and sign-sensitive cross term. Fig. 4(a1,a2) is the unrequired high-field contrast; exact peak widths/heights are not targets." |
| ], |
| "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 from the traced signal how nonlinear amplitude selection under BSV phase-space averaging changes the field-dependent law from the coherent linear response to the two-thirds family.", |
| "award_conditions": [ |
| "Explain from the traced signal how nonlinear amplitude selection under BSV phase-space averaging changes the field-dependent law from the coherent linear response to the two-thirds family." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: (F1 AND I1). This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 2–3, Fig. 1(a,b), Eqs. (5)–(7); SI pp. 7–8, Eqs. (S46)–(S58). Coherent linear versus BSV two-thirds field law, nonlinear amplitude selection, target prefactor and offset. Leading-order curves are not pointwise source-data gold." |
| ], |
| "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": "Separate the field-dependent traced scaling from the target-dependent BSV prefactor and the nearly field-independent ionization-potential offset.", |
| "award_conditions": [ |
| "Separate the field-dependent traced scaling from the target-dependent BSV prefactor and the nearly field-independent ionization-potential offset." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: (F1 AND I1). This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M1, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 2–3, Fig. 1(a,b), Eqs. (5)–(7); SI pp. 7–8, Eqs. (S46)–(S58). Coherent linear versus BSV two-thirds field law, nonlinear amplitude selection, target prefactor and offset. Leading-order curves are not pointwise source-data gold." |
| ], |
| "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 the independent projection-phase distinction: fixed-final-number amplitude projection retains branch-relative phase and therefore an amplitude-level cross term whose sign or role may differ between neighboring channels, whereas photon tracing or a probability-level sum is a different object. This conceptual credit does not validate a quantitatively wrong action/phase or supply unshown channel-resolved spectral redistribution, which remain scored in their own atoms.", |
| "award_conditions": [ |
| "The candidate correctly explains why fixed-final-number projection retains branch-relative phase and an amplitude-level cross term, unlike photon tracing/probability addition.", |
| "This conceptual distinction is independently judgeable but supplies neither correct numerical action/phase nor unshown complementary redistribution." |
| ], |
| "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 M1, M2, I2, I3, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main p. 3, Eq. (8), completeness paragraph; p. 4, Eq. (10); SI p. 11, Eqs. (S82)–(S85). Independent conceptual distinction between photon tracing and fixed-number phase retention. It does not backfill correct numerical action, phase or candidate-identified redistribution." |
| ], |
| "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": "Using the same conditioned amplitude arrays and candidate-identified cross-term-sensitive redistribution, connect the cross-term mechanism to the neighboring-channel relative-yield ordering.", |
| "award_conditions": [ |
| "Using the same conditioned amplitude arrays and candidate-identified cross-term-sensitive redistribution, connect the cross-term mechanism to the neighboring-channel relative-yield ordering." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: (M3 AND I4 AND I2). This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M1, M2, I3, M5, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 4–5, Eq. (10), Fig. 4(b1,b2) and low-energy-weight interpretation paragraph. Connect the same conditioned redistribution to both integrated yield and mean momentum; theoretical parity alone is not candidate-computed quantitative evidence." |
| ], |
| "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": "Using the same conditioned amplitude arrays and candidate-identified cross-term-sensitive redistribution, connect the cross-term mechanism to the neighboring-channel mean longitudinal-momentum ordering.", |
| "award_conditions": [ |
| "Using the same conditioned amplitude arrays and candidate-identified cross-term-sensitive redistribution, connect the cross-term mechanism to the neighboring-channel mean longitudinal-momentum ordering." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: (M3 AND I4 AND I3). This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M1, M2, I2, M4, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 4–5, Eq. (10), Fig. 4(b1,b2) and low-energy-weight interpretation paragraph. Connect the same conditioned redistribution to both integrated yield and mean momentum; theoretical parity alone is not candidate-computed quantitative evidence." |
| ], |
| "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": "Explain the two-regime information mechanism: final-state tracing removes the off-diagonal coherent-state phase relation, whereas fixed-number amplitude projection retains branch-relative phase and can in principle redistribute channel-resolved weight. Award this distinction independently; it does not restore an invalid traced law, wrong conditioned action/phase, or missing candidate-grounded redistribution evidence.", |
| "award_conditions": [ |
| "The candidate correctly contrasts phase-insensitive tracing with phase-retaining fixed-number projection as two measurement regimes.", |
| "Conceptual information credit does not repair invalid traced scaling, a wrong conditioned phase or missing candidate-grounded cross-term evidence." |
| ], |
| "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 M2, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main p. 3, Eq. (8), completeness paragraph; p. 4, Eq. (10); SI p. 11, Eqs. (S82)–(S85). Independent conceptual distinction between photon tracing and fixed-number phase retention. It does not backfill correct numerical action, phase or candidate-identified redistribution." |
| ], |
| "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": "Determine what the bounded low-field neighboring-channel evidence supports about alternative field pathways and the relation between traced and conditioned radiation-pressure transfer, without claiming an uncomputed full-channel or high-field survey.", |
| "award_conditions": [ |
| "Determine what the bounded low-field neighboring-channel evidence supports about alternative field pathways and the relation between traced and conditioned radiation-pressure transfer, without claiming an uncomputed full-channel or high-field survey." |
| ], |
| "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 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 3–5, Eqs. (8)–(12), Figs. 3–4 and conclusion. Task-defined bounded relation between regimes; the one low-field pair cannot establish a complete channel or high-field survey." |
| ], |
| "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": "Justify that the submitted matched or alternative diagnostic preserves the field points, overlaps, radius, parameters, domain, normalization and final observable while isolating the amplitude-level cross term strongly enough to distinguish coherent from incoherent explanations.", |
| "award_conditions": [ |
| "The chosen diagnostic preserves the conditioned field points, exact overlaps, radius, parameters, domain, normalization relation and final observable.", |
| "It actually isolates the claim-bearing amplitude cross term; matched deletion, explicit reconstruction and controlled relative-phase intervention are nonexclusive alternatives." |
| ], |
| "applicability_and_na": [ |
| "Applies to every assessable submission; absence or failure is scored 0, not N/A." |
| ], |
| "dependencies": [ |
| "Necessary scientific premises: O4. This identifies facts, not prerequisite half-point awards.", |
| "Preserve independently valid evidence for M1, M2, M3, M4, M5, M6, M7, I2, I3, 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main p. 4, Eq. (10), Fig. 4(b1,b2); SI pp. 11–14, Eqs. (S82)–(S101). Matched incoherent deletion is one cross-term discriminator, not an exclusive control. A phase intervention or explicit term reconstruction must preserve field points, overlaps, radius, parameters, domain, normalization and observable." |
| ], |
| "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 extrapolation risk emerges that could change a material scaling, channel, cross-term or information conclusion, validate, exclude or explicitly retract the affected claim.", |
| "award_conditions": [ |
| "When a concrete numerical, identity, representation or extrapolation risk emerges that could change a material scaling, channel, cross-term or information 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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 2–5, Eqs. (3)–(4), (7)–(12); SI pp. 9–14, conditioned construction. Task-defined conditional threats from wrong phase/action, mean tails, offset fits, channel/radius or normalization, without a prescribed validation recipe." |
| ], |
| "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 direct ionization, leading-order nondipole dynamics, the stated targets/fields and one low-field neighboring pair; distinguish established results from an uncomputed full-channel or high-field survey.", |
| "award_conditions": [ |
| "Limit conclusions to direct ionization, leading-order nondipole dynamics, the stated targets/fields and one low-field neighboring pair; distinguish established results from an uncomputed full-channel or high-field survey." |
| ], |
| "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": [ |
| "A matched incoherent control is optional. Direct reconstruction of 2Re[(C+M+)(C−M−)*], controlled relative-phase intervention or an equally discriminating same-object diagnostic is accepted only if field points, exact overlaps, radius, parameters, domain, normalization relation and final observable remain unchanged.", |
| "Accept consistent handedness, axes, units, common normalization, projections and smooth-envelope mappings preserving the bounded physical conclusions. No fixed pixels, source grids/bins, smoothing, exact lineshapes, absolute arbitrary yield, full 30-channel scan or high-field reversal." |
| ], |
| "source_support": [ |
| "Main pp. 2–5, leading-order direct-ionization qualification, Fig. 3 and Fig. 4 captions. Direct-model low-field neighboring-pair scope; full scan, reversal, width study and continuum/over-barrier extensions are not commissioned calculations." |
| ], |
| "rc_relation": "Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim." |
| } |
| ], |
| "case_scientific_rules": [ |
| "The traced BSV object is P(p)=integral dA/[sqrt(2pi)A_rms] exp[−A²/(2A_rms²)] |M_A(p)|², a probability average rather than a conditioned coherent amplitude.", |
| "Adiabatic circular stationary amplitudes satisfy A_s≈±sqrt(2Ip)[4A_rms²/(3omega)]^(1/3), hence A_s² proportional to I^(2/3). The leading means are <pz>_coh≈I/(4omega²c)+Ip/(3c) and <pz>_BSV≈[Ip/(omega²c)] · (2/3)^(2/3) I^(2/3)+Ip/(3c). Separate the near-constant offset before assigning slopes 1 and 2/3; BSV prefactor and offset retain target dependence.", |
| "The fixed-number projection is P_n(p)=|integral d²alpha/pi <n|alpha><alpha|xi>M_alpha(p)|². The bounded two-point production is |C+M++C−M−|² with exact squeezed-vacuum/Fock overlaps, a common radius and complete finite-pulse direct-time amplitudes, not a probability-level sum.", |
| "The matched cross-term-removed comparison |C+M+|²+|C−M−|² removes only interference. The source phase includes Fock parity and half-cycle light-front quasienergy, yielding a contribution proportional to (−1)^n cos Delta S_n and complementary adjacent-channel enhancement families.", |
| "At the retained low-field pair the even channel has larger relative yield but smaller positive mean pz; the odd channel has smaller yield but larger positive mean. The same amplitude arrays must support yields, moments and cross-term-sensitive redistribution. Exact peak heights/widths and source numerical readbacks are not fixed targets.", |
| "Photon tracing uses final-state completeness and removes off-diagonal coherent-state phase relations; fixed-n projection retains relative phase and can redistribute weight. The conditional pair alone does not establish the traced anomalous scaling or an uncomputed high-field/full-channel survey.", |
| "Projection/information distinctions in M3/M6 are independently awardable conceptual facts; a wrong action/phase still fails the affected quantitative object and spectral-redistribution criteria. Conceptual credit cannot backfill absent candidate evidence.", |
| "The visible reduced production identity uses two phase-space points and a ten-cycle cos^4 envelope. The source's Gaussian-envelope prose and pointwise traced BSV curves are not unique numerical gold; compare state laws, target/offset logic, sign/order and credible scale.", |
| "Risks include phase-space/state/radius misbinding, probability-before-amplitude mixing, mismatched diagnostic objects, insufficient longitudinal tails, offset-dominated slope fits, normalization, under-resolved interference, envelope sensitivity and unsupported extrapolation. Resolve only actual material threats.", |
| "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.", |
| "Photon tracing uses $P(\\mathbf p)=\\int dA\\,e^{-A^2/(2A_{\\rm rms}^2)}|M_A(\\mathbf p)|^2/(\\sqrt{2\\pi}A_{\\rm rms})$, $I=2\\omega^2A_{\\rm rms}^2$ (Eqs. (1)–(2)). The leading adiabatic circular saddle is $A_s\\simeq\\pm\\sqrt{2I_p}[4A_{\\rm rms}^2/(3\\omega)]^{1/3}$, so $A_s^2\\propto I^{2/3}$, not a linear law.", |
| "The leading mean shifts are $\\langle p_z\\rangle_{\\rm coh}\\simeq I/(4\\omega^2c)+I_p/(3c)$ and $\\langle p_z\\rangle_{\\rm BSV}\\simeq\\frac{I_p}{\\omega^2c}\\left(\\frac{2}{3}\\right)^{2/3}I^{2/3}+I_p/(3c)$ (Eq. (7)). $I_p$ is target binding energy; $\\omega$ carrier frequency, $c$ light speed and $I$ the declared atomic-unit mean intensity. Exponents concern the field-dependent part after offset handling; these are leading-order adiabatic relations, not exact pointwise spectra.", |
| "For fixed final photon number $n$, $P_n(\\mathbf p)=|\\int d^2\\alpha\\,\\langle n|\\alpha\\rangle\\langle\\alpha|\\xi\\rangle M_\\alpha(\\mathbf p)/\\pi|^2$. In the bounded two-point task approximation, write $a_\\pm=C_\\pm M_\\pm$, $P_n=|a_++a_-|^2$, $P_n^{\\rm inc}=|a_+|^2+|a_-|^2$ and $P_n-P_n^{\\rm inc}=2\\operatorname{Re}(a_+a_-^*)$. Here $C_\\pm$ contain the exact Fock/squeezed-vacuum overlaps at the common-radius opposite points. Computing the cross term requires the full finite-pulse complex phases, not probability addition.", |
| "With $\\widetilde p_z=p_z-(p^2/2+I_p)/c$, $\\Lambda=1-\\widetilde p_z/c$, $\\kappa=\\sqrt{2I_p}$, the source leading branch phase is $\\Delta\\phi_n=\\pi(\\widetilde p^2+\\kappa^2+A_n^2)/(2\\omega\\Lambda)$, $A_n=2\\epsilon_V\\sqrt n$ (Eqs. (9)–(12)). The term $(-1)^n\\cos\\Delta\\phi_n$ distinguishes neighboring parity channels; this analytic phase is mechanism support, not a substitute for the task full-pulse amplitudes. $Y_n=\\int P_n d^3p$ and $\\langle p_z\\rangle_n=\\int p_zP_n d^3p/Y_n$ must come from the same arrays and measure." |
| ], |
| "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: Bind H/Na, BSV/coherent states, the common mean-intensity convention, circular leading-order light-front nondipole direct-SFA model, photon-traced phase-space probability and target-dependent longitudinal-momentum offset.", |
| "F2: Bind the Na low-field neighboring final-number pair to one common-radius pair of opposite-phase field points, exact squeezed-vacuum/Fock overlaps and the complete finite-pulse coherent amplitude sum before the modulus square." |
| ], |
| "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 its longitudinal moment, units, normalization and data binding, and submit reconstructible H/Na and BSV/coherent photon-traced intensity-response evidence resolving the two state laws, target dependence, offset and credible scale without requiring pointwise source equality.", |
| "(O2 AND O3 AND O4): Define the consistently normalized relative yield and its data binding, and submit reconstructible yield evidence for both correctly bound neighboring conditioned channels on the retained low-field domain. Define the longitudinal-moment measure, units and data binding, and submit reconstructible mean-pz evidence for both correctly bound neighboring conditioned channels with sufficient momentum support. Define the spectral or functionally equivalent quantity with its measure, normalization and data binding, and submit reconstructible same-object evidence with enough discriminating force to isolate the amplitude-level cross-term-sensitive channel-complementary structure." |
| ], |
| "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 M3 AND (M4 AND M5) AND M6 AND M7): Explain from the traced signal how nonlinear amplitude selection under BSV phase-space averaging changes the field-dependent law from the coherent linear response to the two-thirds family. Explain the independent projection-phase distinction: fixed-final-number amplitude projection retains branch-relative phase and therefore an amplitude-level cross term whose sign or role may differ between neighboring channels, whereas photon tracing or a probability-level sum is a different object. This conceptual credit does not validate a quantitatively wrong action/phase or supply unshown channel-resolved spectral redistribution, which remain scored in their own atoms. Using the same conditioned amplitude arrays and candidate-identified cross-term-sensitive redistribution, connect the cross-term mechanism to the neighboring-channel relative-yield ordering. Using the same conditioned amplitude arrays and candidate-identified cross-term-sensitive redistribution, connect the cross-term mechanism to the neighboring-channel mean longitudinal-momentum ordering. Explain the two-regime information mechanism: final-state tracing removes the off-diagonal coherent-state phase relation, whereas fixed-number amplitude projection retains branch-relative phase and can in principle redistribute channel-resolved weight. Award this distinction independently; it does not restore an invalid traced law, wrong conditioned action/phase, or missing candidate-grounded redistribution evidence. Determine what the bounded low-field neighboring-channel evidence supports about alternative field pathways and the relation between traced and conditioned radiation-pressure transfer, without claiming an uncomputed full-channel or high-field survey." |
| ], |
| "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 extrapolation risk emerges that could change a material scaling, channel, cross-term or information 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": "Xiaodan Mao, Feng He, and Pei-Lun He. 2026. *Anomalous radiation pressure in strong-field ionization driven by quantum light*. *arXiv*, 2608.15859. Version 1.", |
| "url": "https://arxiv.org/abs/2608.15859v1", |
| "scientific_scope": "Photon-traced H/Na coherent/BSV scaling plus one reduced low-field Na neighboring conditioned pair. Full channel scans, high-field reversal and exact source line shapes are excluded; common-object cross-term alternatives remain accepted.", |
| "anchors": [ |
| "Mao, He and He (2026), main pp. 1–3, Eqs. (1)–(7).", |
| "Main pp. 3–4, Eqs. (8)–(10); SI pp. 9–11, Eqs. (S59)–(S82).", |
| "Main pp. 2–3, Fig. 1(a,b), Eqs. (5)–(7); SI pp. 7–8, Eqs. (S46)–(S58).", |
| "Main p. 4, Fig. 3(b), low-effective-intensity paragraph.", |
| "Main p. 4, Fig. 3(a), low-effective-intensity paragraph.", |
| "Main pp. 4–5, Fig. 4(b1,b2), Eqs. (10)–(12); SI pp. 11–14, Eqs. (S82)–(S101).", |
| "Main p. 3, Eq. (8), completeness paragraph; p. 4, Eq. (10); SI p. 11, Eqs. (S82)–(S85).", |
| "Main pp. 4–5, Eq. (10), Fig. 4(b1,b2) and low-energy-weight interpretation paragraph.", |
| "Main pp. 3–5, Eqs. (8)–(12), Figs. 3–4 and conclusion.", |
| "Main p. 4, Eq. (10), Fig. 4(b1,b2); SI pp. 11–14, Eqs. (S82)–(S101).", |
| "Main pp. 2–5, Eqs. (3)–(4), (7)–(12); SI pp. 9–14, conditioned construction.", |
| "Main pp. 2–5, leading-order direct-ionization qualification, Fig. 3 and Fig. 4 captions." |
| ] |
| } |
| ] |
| } |
|
|
