| { |
| "case_id": "Case14", |
| "title": "Case14 — Nondipole Time Delay and Double-Slit Interference in Tunneling Ionization", |
| "atoms": [ |
| { |
| "criterion_id": "F1", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Instantiate both parities, both separations, orientation domain, total circular intensity and consistent light-front phase, p_minus, relative longitudinal coordinate, field and axes.", |
| "award_conditions": [ |
| "Both parities/separations and orientation cases use consistent total circular intensity, light-front phase, p_minus, relative longitudinal coordinate and axes." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.", |
| "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He, Hatsagortsyan and Keitel (2022), article pp.183201-2-3, Eqs.(1),(2),(5)-(7): light-front momentum, nondegenerate versus laser-dressed degenerate LCAO factors. The task retains the degenerate 1s even/odd branch, not the nondegenerate H2+ or Ne2 branches." |
| ], |
| "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "F2", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Derive parity-correct two-centre molecular factors from laser-dressed degenerate two-centre 1s LCAO states.", |
| "award_conditions": [ |
| "Laser-dressed degenerate two-centre 1s LCAO states yield the correct constructive/destructive parity factors." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: F1 (Instantiate both parities, both separations, orientation domain, total circular intensity and consistent light-front phase, p_minus, relative longitudinal coordinate, field and axes.)", |
| "Preserve independently valid work in O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He, Hatsagortsyan and Keitel (2022), article pp.183201-2-3, Eqs.(1),(2),(5)-(7): light-front momentum, nondegenerate versus laser-dressed degenerate LCAO factors. The task retains the degenerate 1s even/odd branch, not the nondegenerate H2+ or Ne2 branches." |
| ], |
| "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "F3", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Establish a reconstructible connection from two-centre structure to longitudinal momentum and effective-exit objects, preserving p_minus and common-translation identity.", |
| "award_conditions": [ |
| "The two-centre structure maps reconstructibly to longitudinal momentum and effective-exit objects while preserving light-front and common-translation identity." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: F2 (Derive parity-correct two-centre molecular factors from laser-dressed degenerate two-centre 1s LCAO states.)", |
| "Preserve independently valid work in O3, O4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article pp.183201-2-3, Eqs.(3),(4),(6),(7) and light-front exit-time/phase-difference paragraphs: longitudinal momentum and Wigner-derived exit identity; relative origin is q=p_minus-Ip/c." |
| ], |
| "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "O4", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Present the odd-branch phase-averaged orientation-dependent longitudinal diagnostic and relative yield, using mean shift, peak, asymmetry or a reconstructible equivalent without inventing absolute Ip or independently normalizing away relative relations.", |
| "award_conditions": [ |
| "The odd orientation longitudinal diagnostic and relative yield are reconstructible under common normalization without erasing relative relations.", |
| "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: F1 (Instantiate both parities, both separations, orientation domain, total circular intensity and consistent light-front phase, p_minus, relative longitudinal coordinate, field and axes.)", |
| "Preserve independently valid work in O3, O1, O2, I1, I2, I3, M1, M2, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article p.183201-4, Eq.(9), Fig.3(d), caption and destructive-interference/yield discussion: degenerate odd-branch orientation and observability; Fig.3(c) is nondegenerate and out of the retained branch." |
| ], |
| "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid." |
| }, |
| { |
| "criterion_id": "O1", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Present reconstructible compact-case even/odd effective-exit and relative-longitudinal-momentum object families with presentation sufficient to judge their separate structure/scale claims; local scale under-resolution does not invalidate the entire otherwise valid family.", |
| "award_conditions": [ |
| "The compact even/odd exit and longitudinal families are reconstructible and expose their separate topology/scale claims without invalidating independent structure for a local scale defect.", |
| "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: F3 (Establish a reconstructible connection from two-centre structure to longitudinal momentum and effective-exit objects, preserving p_minus and common-translation identity.)", |
| "Preserve independently valid work in O2, O3, O4, I3, I4, M7, M3, M4, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article p.183201-4, Fig.2(a,b,d,e), caption and first paragraph: compact R=5 even single structure versus odd node/two exits near +/-Rw and longitudinal maxima separated by about 2/Rw; article p.183201-3 light-front timing paragraph gives Delta t=Delta z/c." |
| ], |
| "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid." |
| }, |
| { |
| "criterion_id": "O2", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Present reconstructible separated-case even/odd exit and relative-longitudinal-momentum object families sufficient to judge exit separation and fringe claims separately; a local spacing/extraction defect does not invalidate the other feature path.", |
| "award_conditions": [ |
| "Separated even/odd families resolve exit separation and interference phase/fringe features, with local spacing defects confined to that feature path.", |
| "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: F3 (Establish a reconstructible connection from two-centre structure to longitudinal momentum and effective-exit objects, preserving p_minus and common-translation identity.)", |
| "Preserve independently valid work in O1, O3, O4, I1, I2, I4, M7, M1, M2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article pp.183201-3-4, Fig.2(c,f), caption and separation discussion: R=100 exit separation approaches R; opposite-parity fringes have 2pi/R spacing, distinct from compact odd peak splitting." |
| ], |
| "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid." |
| }, |
| { |
| "criterion_id": "O3", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Present the even-branch phase-averaged orientation-dependent longitudinal diagnostic and relative yield, using mean shift, peak, asymmetry or a reconstructible equivalent without inventing absolute Ip or independently normalizing away relative relations.", |
| "award_conditions": [ |
| "The even orientation longitudinal diagnostic and relative yield are reconstructible under common normalization without inventing absolute Ip.", |
| "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: F1 (Instantiate both parities, both separations, orientation domain, total circular intensity and consistent light-front phase, p_minus, relative longitudinal coordinate, field and axes.)", |
| "Preserve independently valid work in O4, O1, O2, I1, I2, I3, M1, M2, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article p.183201-4, Eq.(9), Fig.3(b) and caption: degenerate even-branch phase-averaged longitudinal shift and relative yield versus orientation. Fig.3(a) is the nondegenerate branch and is not the retained target." |
| ], |
| "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid." |
| }, |
| { |
| "criterion_id": "I1", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify from compact-case evidence the even constructive single large-scale structure and odd central node/two-exit structure.", |
| "award_conditions": [ |
| "The candidate identifies compact even constructive single structure and compact odd central-node/two-exit structure." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: O1 (Present reconstructible compact-case even/odd effective-exit and relative-longitudinal-momentum object families with presentation sufficient to judge their separate structure/scale claims; local scale under-resolution does not invalidate the entire otherwise valid family.)", |
| "Preserve independently valid work in I3, I4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article p.183201-4, Fig.2(a,b,d,e), caption and first paragraph: compact R=5 even single structure versus odd node/two exits near +/-Rw and longitudinal maxima separated by about 2/Rw; article p.183201-3 light-front timing paragraph gives Delta t=Delta z/c." |
| ], |
| "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "I2", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify the compact odd longitudinal splitting scale near 2/Rw, distinguishing it from an arbitrary common momentum translation.", |
| "award_conditions": [ |
| "The candidate identifies compact odd longitudinal two-peak splitting near 2/Rw, separately from an arbitrary common translation." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: O1 (Present reconstructible compact-case even/odd effective-exit and relative-longitudinal-momentum object families with presentation sufficient to judge their separate structure/scale claims; local scale under-resolution does not invalidate the entire otherwise valid family.)", |
| "Preserve independently valid work in I1, I3, I4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article p.183201-4, Fig.2(a,b,d,e), caption and first paragraph: compact R=5 even single structure versus odd node/two exits near +/-Rw and longitudinal maxima separated by about 2/Rw; article p.183201-3 light-front timing paragraph gives Delta t=Delta z/c." |
| ], |
| "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "I3", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify opposite even/odd interference phase and adjacent fringe scale near 2pi/R in the separated-case evidence, distinguishing it from common translation.", |
| "award_conditions": [ |
| "The candidate identifies opposite parity fringe phase and separated adjacent spacing near 2pi/R, separately from common translation." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.", |
| "Preserve independently valid work in I1, I2, I4, M7, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article pp.183201-3-4, Fig.2(c,f), caption and separation discussion: R=100 exit separation approaches R; opposite-parity fringes have 2pi/R spacing, distinct from compact odd peak splitting." |
| ], |
| "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "I4", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify in the even orientation branch a material longitudinal-signal/relative-yield relation, including endpoint disappearance or signal-yield tradeoff.", |
| "award_conditions": [ |
| "The candidate identifies the even orientation signal/yield tradeoff, including endpoint disappearance where applicable." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: O3 (Present the even-branch phase-averaged orientation-dependent longitudinal diagnostic and relative yield, using mean shift, peak, asymmetry or a reconstructible equivalent without inventing absolute Ip or independently normalizing away relative relations.)", |
| "Preserve independently valid work in M7, I1, I2, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article p.183201-4, Eq.(9), Fig.3(b) and caption: degenerate even-branch phase-averaged longitudinal shift and relative yield versus orientation. Fig.3(a) is the nondegenerate branch and is not the retained target." |
| ], |
| "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "M1", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Infer effective exit multiplicity and spatial organization from compact parity-resolved exit/momentum signals, explaining single-exit even and double-exit odd states.", |
| "award_conditions": [ |
| "Compact parity-resolved exit/momentum evidence explains even single-exit versus odd double-exit organization." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: all of: O1 (Present reconstructible compact-case even/odd effective-exit and relative-longitudinal-momentum object families with presentation sufficient to judge their separate structure/scale claims; local scale under-resolution does not invalidate the entire otherwise valid family.); I1 (Identify from compact-case evidence the even constructive single large-scale structure and odd central node/two-exit structure.)", |
| "Preserve independently valid work in M3, M4, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article p.183201-4, Fig.2(a,b,d,e), caption and first paragraph: compact R=5 even single structure versus odd node/two exits near +/-Rw and longitudinal maxima separated by about 2/Rw; article p.183201-3 light-front timing paragraph gives Delta t=Delta z/c." |
| ], |
| "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "M2", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Convert compact odd effective exit separation near 2Rw into a light-front birth-time delay near 2Rw/c rather than universally using R/c.", |
| "award_conditions": [ |
| "Compact odd effective separation near 2Rw is converted to light-front delay near 2Rw/c, not automatically R/c." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: all of: I2 (Identify the compact odd longitudinal splitting scale near 2/Rw, distinguishing it from an arbitrary common momentum translation.); M1 (Infer effective exit multiplicity and spatial organization from compact parity-resolved exit/momentum signals, explaining single-exit even and double-exit odd states.)", |
| "Preserve independently valid work in M3, M4, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article p.183201-4, Fig.2(a,b,d,e), caption and first paragraph: compact R=5 even single structure versus odd node/two exits near +/-Rw and longitudinal maxima separated by about 2/Rw; article p.183201-3 light-front timing paragraph gives Delta t=Delta z/c." |
| ], |
| "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "M3", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Infer from separated-case evidence effective exit separation approaching R and delay approaching R/c, distinguishing these from compact odd 2Rw/c.", |
| "award_conditions": [ |
| "Separated evidence supports effective separation approaching R and relative delay approaching R/c, distinguished from the compact odd limit." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: O2 (Present reconstructible separated-case even/odd exit and relative-longitudinal-momentum object families sufficient to judge exit separation and fringe claims separately; a local spacing/extraction defect does not invalidate the other feature path.)", |
| "Preserve independently valid work in I3, M1, M2, M4, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article pp.183201-3-4, Fig.2(c,f), caption and separation discussion: R=100 exit separation approaches R; opposite-parity fringes have 2pi/R spacing, distinct from compact odd peak splitting." |
| ], |
| "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "M4", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Explicitly distinguish compact two-peak splitting 2/Rw from separated periodic fringe spacing 2pi/R instead of treating them as the same scale.", |
| "award_conditions": [ |
| "The candidate explicitly distinguishes compact splitting 2/Rw from separated periodic spacing 2pi/R." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: all of: I2 (Identify the compact odd longitudinal splitting scale near 2/Rw, distinguishing it from an arbitrary common momentum translation.); I3 (Identify opposite even/odd interference phase and adjacent fringe scale near 2pi/R in the separated-case evidence, distinguishing it from common translation.)", |
| "Preserve independently valid work in M1, M2, M3, M5, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article pp.183201-3-4, Fig.2(c,f), caption and separation discussion: R=100 exit separation approaches R; opposite-parity fringes have 2pi/R spacing, distinct from compact odd peak splitting." |
| ], |
| "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "M5", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Explain laser-dressing/parity control of constructive/destructive two-centre interference using the submitted compact and separated structures.", |
| "award_conditions": [ |
| "Submitted compact/separated structures ground the laser-dressing/parity constructive-destructive interference explanation." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: all of: I1 (Identify from compact-case evidence the even constructive single large-scale structure and odd central node/two-exit structure.); I3 (Identify opposite even/odd interference phase and adjacent fringe scale near 2pi/R in the separated-case evidence, distinguishing it from common translation.)", |
| "Preserve independently valid work in M1, M2, M3, M4, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article pp.183201-3-4, Eq.(7), Fig.2 and Fig.3(b,d): parity/dressing sets exit interference, while orientation-dependent signal must be judged with relative yield, not independent per-angle normalization." |
| ], |
| "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "M6", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Use both parities' orientation-dependent longitudinal diagnostics and relative yields to judge when the nondipole signature is informative and observable, including strong-structure/suppressed-yield tradeoffs, consistently with compact/separated spatial-timing inference.", |
| "award_conditions": [ |
| "Both parity orientation diagnostics and relative yields support an observability assessment consistent with spatial/timing inference, including suppressed-yield tradeoffs." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: all of: I4 (Identify in the even orientation branch a material longitudinal-signal/relative-yield relation, including endpoint disappearance or signal-yield tradeoff.); M7 (Identify and explain from the odd orientation branch its longitudinal-signal/relative-yield relation and the observability implication of endpoint disappearance or signal-yield tradeoff.)", |
| "Preserve independently valid work in M1, M2, M3, M4, M5, V2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article pp.183201-3-4, Eq.(7), Fig.2 and Fig.3(b,d): parity/dressing sets exit interference, while orientation-dependent signal must be judged with relative yield, not independent per-angle normalization." |
| ], |
| "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "M7", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Identify and explain from the odd orientation branch its longitudinal-signal/relative-yield relation and the observability implication of endpoint disappearance or signal-yield tradeoff.", |
| "award_conditions": [ |
| "The candidate identifies and explains the odd orientation signal/yield relation and what it implies for observability." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: O4 (Present the odd-branch phase-averaged orientation-dependent longitudinal diagnostic and relative yield, using mean shift, peak, asymmetry or a reconstructible equivalent without inventing absolute Ip or independently normalizing away relative relations.)", |
| "Preserve independently valid work in I4, I1, I2, I3, M1, M2, M3, M4, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article p.183201-4, Eq.(9), Fig.3(d), caption and destructive-interference/yield discussion: degenerate odd-branch orientation and observability; Fig.3(c) is nondegenerate and out of the retained branch." |
| ], |
| "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "V1", |
| "dimension": "V", |
| "points": 0.5, |
| "scientific_requirement": "Only when the submitted method, data, anomaly or claim exposes a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.", |
| "award_conditions": [ |
| "Only a concrete triggered alternative threatening the actual inference requires capable evidence or narrowed claims; otherwise N/A." |
| ], |
| "applicability_and_na": [ |
| "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.", |
| "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.", |
| "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article pp.183201-2-4, leading nondipole PPT/SFA and degenerate-1s model. Relative-observable restriction and triggered validation are task duties; an absolute Ip translation, full Coulomb rerun or out-of-scope Ne2 panel is not compulsory." |
| ], |
| "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| }, |
| { |
| "criterion_id": "V2", |
| "dimension": "V", |
| "points": 0.5, |
| "scientific_requirement": "Positively identify the actual leading-order nondipole PPT/SFA, degenerate two-centre 1s LCAO, relative-longitudinal-observable and calculated-case domain.", |
| "award_conditions": [ |
| "The candidate positively states the leading-order nondipole PPT/SFA, degenerate two-centre 1s LCAO, relative-observable and computed-case domain." |
| ], |
| "applicability_and_na": [ |
| "This positive scientific scope/evidence duty is unconditional; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.", |
| "Preserve all other independently valid work; no additional unlisted hard dependency or duplicate deduction is implied." |
| ], |
| "equivalent_evidence": [ |
| "Declared common momentum translations, axis reversals, phase origins, units and common multiplicative scales are accepted. Translated q, light-front p_minus with a common offset, and equivalent marginals/lineouts are accepted when they preserve structure and case relations.", |
| "Independent shape normalization may support peak/support analysis but cannot establish relative yield or erase parity/orientation yield information.", |
| "The restricted analytic exit/momentum representatives and direct standard nondipole PPT/SFA plus Wigner constructions are equivalent when they yield the same physical objects under declared conventions.", |
| "Mean shift, peak, asymmetry or another longitudinal diagnostic is accepted under its own derived physical structure; canonical mean-shift signs/extrema must not be imposed on a mathematically different observable." |
| ], |
| "source_support": [ |
| "He et al. (2022), article pp.183201-2-4, leading nondipole PPT/SFA and degenerate-1s model. Relative-observable restriction and triggered validation are task duties; an absolute Ip translation, full Coulomb rerun or out-of-scope Ne2 panel is not compulsory." |
| ], |
| "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure." |
| } |
| ], |
| "case_scientific_rules": [ |
| "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.", |
| "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.", |
| "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.", |
| "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.", |
| "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.", |
| "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.", |
| "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.", |
| "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.", |
| "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.", |
| "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.", |
| "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.", |
| "This restricted He2 case excludes absolute-Ip displacement and the Ne2 phase-map/exit branch. Do not require an atomic overlay, full CC-SFA, finite pulse or source-specific grid/range.", |
| "For aligned R=5 a.u., the even exit/momentum structure is constructive and compact with one longitudinal maximum; the odd state has a central node, effective exit maxima near +/-Rw and momentum maxima near +/-1/Rw.", |
| "For aligned R=100 a.u., exit maxima approach +/-R/2 and opposite-parity fringes have scale 2pi/R, approximately 0.0628 a.u.; compact odd splitting is about 2/Rw, approximately 0.267 a.u. These are physical scales, not pointwise tolerances.", |
| "At common light-front exit time, Delta t_e=Delta z_e/c. Compact odd timing therefore follows 2Rw/c, compact even single-exit structure does not support the same split-delay inference, and the separated limit approaches R/c.", |
| "For the canonical mean shift at compact separation, the even branch starts positive, develops an intermediate negative minimum and vanishes toward perpendicular alignment; the odd branch begins strongly negative, rises toward zero/slightly positive and also vanishes. Corresponding yield suppression/enhancement must inform observability.", |
| "A true even/odd physics reversal is not a harmless label change. An invented absolute Ip used only for a common translation does not erase correct relative shape, but cannot support an absolute-translation conclusion.", |
| "Local scale or spacing extraction defects do not erase a distinct valid structural feature of the same family. Assess exit and fringe paths through their actual necessary evidence.", |
| "For the circular field and geometry visible in task, use", |
| "$$\nR_z=R\\cos\\theta_m,\n\\qquad\nR_\\perp=R\\sin\\theta_m,\n\\qquad\nq=p_- - I_p/c.\n$$", |
| "The degenerate two-centre $1s$ states are dressed by opposite laser phases at the two sites. Up to normalization and an overlap factor that cancels from the graded normalized structures,", |
| "$$\n\\Psi_{g/u}\\sim\ne^{+i\\mathbf A\\cdot\\mathbf R/2}e^{-\\kappa r_a}\n\\pm\ne^{-i\\mathbf A\\cdot\\mathbf R/2}e^{-\\kappa r_b}.\n$$", |
| "Consequently, the parity-resolved molecular factors have the two-centre form", |
| "$$\nF_g\\propto 1+\\cos(\\mathbf R\\cdot\\widetilde{\\mathbf p}),\n\\qquad\nF_u\\propto 1-\\cos(\\mathbf R\\cdot\\widetilde{\\mathbf p}).\n$$", |
| "The exact common prefactors, LCAO normalization and absolute yield are not graded when the student uses relative distributions and retains the correct parity and case relations.", |
| "For the aligned restricted analytical route, physically equivalent normalized representatives are", |
| "$$\nG_{g/u}(z;R)\\propto\n\\left[\ne^{-(z-R/2)^2/(2R_w^2)}\n\\pm\ne^{-(z+R/2)^2/(2R_w^2)}\n\\right]^2,\n$$", |
| "$$\nP_{g/u}(q;R)\\propto\ne^{-(R_wq)^2}\\left[1\\pm\\cos(Rq)\\right].\n$$", |
| "These representatives are an accepted solution route, not mandatory task formulas. A direct evaluation of a standard nondipole PPT/SFA rate and Wigner construction is equivalent if it yields the same physical objects within its declared convention.", |
| "For $R=5$ a.u. and $\\theta_m=0$:", |
| "the even state has a constructive compact exit structure and a single large-scale longitudinal maximum about the translated origin;", |
| "the odd state has a node at the centre, two effective exit maxima near $z=\\pm R_w$, and a split longitudinal distribution with maxima near $q=\\pm1/R_w$;", |
| "For $R=100$ a.u. at the same alignment, the centres are well separated relative to $R_w$. The exit maxima approach $z=\\pm R/2$, both parities show two-centre momentum fringes with opposite interference phase, and the robust fringe spacing approaches", |
| "$$\n\\Delta q\\simeq\\frac{2\\pi}{R}\\simeq0.0628\\ \\mathrm{a.u.}\n$$", |
| "After subtracting the atomic $I_p/(3c)$ contribution, main-text Eq. (9) gives the canonical dimensionless molecular shift", |
| "$$\n\\frac{\\delta\\langle p_-\\rangle}{I_p/c}\n=\n\\frac{(R_z^2/R_w^2)J_0(A_0R_\\perp)}\n{3\\left[J_0(A_0R_\\perp)\\pm\n\\exp\\!\\left(R_z^2/(4R_w^2)\\right)\\right]},\n$$", |
| "where the upper/lower branches correspond to $\\sigma_g/\\sigma_u$. A globally equivalent field-amplitude convention is accepted only after the quoted total circular intensity and two quadratures are mapped consistently.", |
| "For $R=5$ a.u. the source-supported large-scale orientation anchors are:", |
| "the even branch begins with a positive molecular contribution, develops a negative local minimum at an intermediate orientation near $0.15\\pi$, and returns toward zero as $R_z$ vanishes;", |
| "the odd branch has a large negative contribution near parallel alignment, rises toward zero or a small positive local maximum near the same intermediate-orientation region, and also vanishes at perpendicular alignment;", |
| "the even-branch negative shift feature is associated with a suppression of the relative yield, while the odd branch changes from a strongly suppressed parallel yield toward a pronounced intermediate-orientation yield maximum;", |
| "the source/restricted benchmark values near $-0.067$ for the even local minimum and about $-1.26$ for the odd parallel shift are useful branch diagnostics, not mandatory pointwise targets.", |
| "These orientation anchors describe the canonical mean-shift route. If a student uses another reconstructible longitudinal diagnostic, grade the physical structure expected for that diagnostic and whether it discriminates the same exit/interference and observability claims. Do not impose the canonical mean-shift sign, extrema or numerical values on a non-equivalent mathematical observable.", |
| "At a common light-front exit time $\\eta_e$, two exit positions satisfy $t_{e,2}-t_{e,1}=\\Delta z_e/c$. The compact odd branch therefore supports an effective separation near $2R_w$ and a delay near $2R_w/c$, rather than $R/c$. The compact even branch is single-exit at this alignment and does not support the same split-delay inference. In the $R\\gg R_w$ regime, the effective separation approaches $R$ and the delay approaches $R/c$.", |
| "The momentum structures are evidence for these claims, not time values read off from a plotting translation. The two-peak $2/R_w$ scale of the compact odd case and the periodic $2\\pi/R$ fringe scale of the separated case must not be conflated.", |
| "The parity-resolved exit, momentum and orientation formulas refer to article pp.183201-2-4, Eqs.(2)-(7),(9), Fig.2 and Fig.3(b,d). The transverse/longitudinal molecular geometry is $R_z=R\\cos\\theta_m$, $R_\\perp=R\\sin\\theta_m$ and $R_w=\\sqrt{\\kappa/|E|}$. At a common $\\eta_e=t_e-z_e/c$, $\\Delta t_e=\\Delta z_e/c$. The compact odd $2/R_w$ peak separation is not a periodic fringe spacing $2\\pi/R$; the compact even single-exit object does not support the same two-exit delay. The source absolute common translation $I_p/c$ cannot be manufactured when the retained task gives only relative longitudinal objects. Canonical mean-shift signs in Fig.3(b,d) must not be imposed on a different mathematical diagnostic without deriving its mapping." |
| ], |
| "closure_requirements": { |
| "RC0": [ |
| "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.", |
| "Required indispensable claim CL0, central physical object: all of: F1 (Instantiate both parities, both separations, orientation domain, total circular intensity and consistent light-front phase, p_minus, relative longitudinal coordinate, field and axes.); F2 (Derive parity-correct two-centre molecular factors from laser-dressed degenerate two-centre 1s LCAO states.); F3 (Establish a reconstructible connection from two-centre structure to longitudinal momentum and effective-exit objects, preserving p_minus and common-translation identity.). Judge the role-specific failure facts, not the corresponding atom scores." |
| ], |
| "RC1": [ |
| "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.", |
| "Required co primary claim CL1, indispensable material component: O1 (Present reconstructible compact-case even/odd effective-exit and relative-longitudinal-momentum object families with presentation sufficient to judge their separate structure/scale claims; local scale under-resolution does not invalidate the entire otherwise valid family.). Judge the role-specific failure facts, not the corresponding atom scores.", |
| "Required co primary claim CL2, indispensable material component: O2 (Present reconstructible separated-case even/odd exit and relative-longitudinal-momentum object families sufficient to judge exit separation and fringe claims separately; a local spacing/extraction defect does not invalidate the other feature path.). Judge the role-specific failure facts, not the corresponding atom scores.", |
| "Required co primary claim CL3, indispensable material component: all of: O3 (Present the even-branch phase-averaged orientation-dependent longitudinal diagnostic and relative yield, using mean shift, peak, asymmetry or a reconstructible equivalent without inventing absolute Ip or independently normalizing away relative relations.); O4 (Present the odd-branch phase-averaged orientation-dependent longitudinal diagnostic and relative yield, using mean shift, peak, asymmetry or a reconstructible equivalent without inventing absolute Ip or independently normalizing away relative relations.). Judge the role-specific failure facts, not the corresponding atom scores." |
| ], |
| "RC2": [ |
| "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.", |
| "Required co primary claim CL1, principal mechanism or commissioned conclusion: all of: M1 (Infer effective exit multiplicity and spatial organization from compact parity-resolved exit/momentum signals, explaining single-exit even and double-exit odd states.); M2 (Convert compact odd effective exit separation near 2Rw into a light-front birth-time delay near 2Rw/c rather than universally using R/c.). Judge the role-specific failure facts, not the corresponding atom scores.", |
| "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M3 (Infer from separated-case evidence effective exit separation approaching R and delay approaching R/c, distinguishing these from compact odd 2Rw/c.); M4 (Explicitly distinguish compact two-peak splitting 2/Rw from separated periodic fringe spacing 2pi/R instead of treating them as the same scale.). Judge the role-specific failure facts, not the corresponding atom scores.", |
| "Required co primary claim CL3, principal mechanism or commissioned conclusion: M6 (Use both parities' orientation-dependent longitudinal diagnostics and relative yields to judge when the nondipole signature is informative and observable, including strong-structure/suppressed-yield tradeoffs, consistently with compact/separated spatial-timing inference.). Judge the role-specific failure facts, not the corresponding atom scores.", |
| "Required co primary claim CL4, principal mechanism or commissioned conclusion: M5 (Explain laser-dressing/parity control of constructive/destructive two-centre interference using the submitted compact and separated structures.). Judge the role-specific failure facts, not the corresponding atom scores." |
| ], |
| "RC3": [ |
| "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.", |
| "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.", |
| "Required co primary claim CL3, material validation/scope: V1 (Only when the submitted method, data, anomaly or claim exposes a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.). Judge the role-specific failure facts, not the corresponding atom scores." |
| ], |
| "RC4": [ |
| "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.", |
| "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.", |
| "Close CL0 central physical object: all of: F1 (Instantiate both parities, both separations, orientation domain, total circular intensity and consistent light-front phase, p_minus, relative longitudinal coordinate, field and axes.); F2 (Derive parity-correct two-centre molecular factors from laser-dressed degenerate two-centre 1s LCAO states.); F3 (Establish a reconstructible connection from two-centre structure to longitudinal momentum and effective-exit objects, preserving p_minus and common-translation identity.).", |
| "Close CL1 indispensable material component: O1 (Present reconstructible compact-case even/odd effective-exit and relative-longitudinal-momentum object families with presentation sufficient to judge their separate structure/scale claims; local scale under-resolution does not invalidate the entire otherwise valid family.).", |
| "Close CL1 principal mechanism or commissioned conclusion: all of: M1 (Infer effective exit multiplicity and spatial organization from compact parity-resolved exit/momentum signals, explaining single-exit even and double-exit odd states.); M2 (Convert compact odd effective exit separation near 2Rw into a light-front birth-time delay near 2Rw/c rather than universally using R/c.).", |
| "Close CL2 indispensable material component: O2 (Present reconstructible separated-case even/odd exit and relative-longitudinal-momentum object families sufficient to judge exit separation and fringe claims separately; a local spacing/extraction defect does not invalidate the other feature path.).", |
| "Close CL2 principal mechanism or commissioned conclusion: all of: M3 (Infer from separated-case evidence effective exit separation approaching R and delay approaching R/c, distinguishing these from compact odd 2Rw/c.); M4 (Explicitly distinguish compact two-peak splitting 2/Rw from separated periodic fringe spacing 2pi/R instead of treating them as the same scale.).", |
| "Close CL3 indispensable material component: all of: O3 (Present the even-branch phase-averaged orientation-dependent longitudinal diagnostic and relative yield, using mean shift, peak, asymmetry or a reconstructible equivalent without inventing absolute Ip or independently normalizing away relative relations.); O4 (Present the odd-branch phase-averaged orientation-dependent longitudinal diagnostic and relative yield, using mean shift, peak, asymmetry or a reconstructible equivalent without inventing absolute Ip or independently normalizing away relative relations.).", |
| "Close CL3 principal mechanism or commissioned conclusion: M6 (Use both parities' orientation-dependent longitudinal diagnostics and relative yields to judge when the nondipole signature is informative and observable, including strong-structure/suppressed-yield tradeoffs, consistently with compact/separated spatial-timing inference.).", |
| "Close CL3 material validation/scope: V1 (Only when the submitted method, data, anomaly or claim exposes a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.).", |
| "Close CL4 principal mechanism or commissioned conclusion: M5 (Explain laser-dressing/parity control of constructive/destructive two-centre interference using the submitted compact and separated structures.)." |
| ] |
| }, |
| "references": [ |
| { |
| "citation": "Pei-Lun He, Karen Z. Hatsagortsyan, and Christoph H. Keitel. 2022a. *Nondipole Time Delay and Double-Slit Interference in Tunneling Ionization*. *Physical Review Letters*, 128, 183201.", |
| "url": "https://doi.org/10.1103/PhysRevLett.128.183201", |
| "scientific_scope": "Nondipole Time Delay and Double-Slit Interference in Tunneling Ionization", |
| "anchors": [ |
| "He, Hatsagortsyan and Keitel (2022), article pp.183201-2-3, Eqs.(1),(2),(5)-(7): light-front momentum, nondegenerate versus laser-dressed degenerate LCAO factors. The task retains the degenerate 1s even/odd branch, not the nondegenerate H2+ or Ne2 branches.", |
| "He et al. (2022), article pp.183201-2-3, Eqs.(3),(4),(6),(7) and light-front exit-time/phase-difference paragraphs: longitudinal momentum and Wigner-derived exit identity; relative origin is q=p_minus-Ip/c.", |
| "He et al. (2022), article p.183201-4, Fig.2(a,b,d,e), caption and first paragraph: compact R=5 even single structure versus odd node/two exits near +/-Rw and longitudinal maxima separated by about 2/Rw; article p.183201-3 light-front timing paragraph gives Delta t=Delta z/c.", |
| "He et al. (2022), article pp.183201-3-4, Fig.2(c,f), caption and separation discussion: R=100 exit separation approaches R; opposite-parity fringes have 2pi/R spacing, distinct from compact odd peak splitting.", |
| "He et al. (2022), article p.183201-4, Eq.(9), Fig.3(b) and caption: degenerate even-branch phase-averaged longitudinal shift and relative yield versus orientation. Fig.3(a) is the nondegenerate branch and is not the retained target.", |
| "He et al. (2022), article p.183201-4, Eq.(9), Fig.3(d), caption and destructive-interference/yield discussion: degenerate odd-branch orientation and observability; Fig.3(c) is nondegenerate and out of the retained branch.", |
| "He et al. (2022), article pp.183201-3-4, Eq.(7), Fig.2 and Fig.3(b,d): parity/dressing sets exit interference, while orientation-dependent signal must be judged with relative yield, not independent per-angle normalization.", |
| "He et al. (2022), article pp.183201-2-4, leading nondipole PPT/SFA and degenerate-1s model. Relative-observable restriction and triggered validation are task duties; an absolute Ip translation, full Coulomb rerun or out-of-scope Ne2 panel is not compulsory." |
| ] |
| } |
| ] |
| } |
|
|
