| { |
| "case_id": "Case20", |
| "title": "Dark and bright autoionizing states in resonant high-order harmonic generation: Simulation via a one-dimensional helium model", |
| "atoms": [ |
| { |
| "criterion_id": "F1", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Establish the shared physical object of the supplied correlated one-dimensional two-electron Hamiltonian, exchange-symmetric ground state and specified strong-field pulse.", |
| "award_conditions": [ |
| "The production state uses the correlated exchange-symmetric two-electron Hamiltonian and specified strong-field pulse, not a single-electron substitute." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article p. 053506-2, Eqs. (1)-(2), Fig. 1 and Sec. III parity discussion; p. 053506-4, Sec. V pulse paragraph: The correlated exchange-symmetric two-electron target distinguishes even dark (1,1) from odd bright (1,2) and their 14-/17-photon resonance neighborhoods." |
| ], |
| "rc_relation": "RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "F2", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Bind the even-parity dark (1,1), 14-photon neighborhood and odd-parity bright (1,2), 17-photon neighborhood to their correct resonance branches.", |
| "award_conditions": [ |
| "Parity and photon-neighborhood binding distinguish dark even (1,1)/14-photon from bright odd (1,2)/17-photon response." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "F1: Establish the shared physical object of the supplied correlated one-dimensional two-electron Hamiltonian, exchange-symmetric ground state and specified strong-field pulse. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in O1, O2, I1, I2, I3, I4, M2, M3, M5, M6 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "A local resonance misbinding does not erase the other correctly bound branch; each branch output, identification and inference is judged by its own identity and evidence." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article p. 053506-2, Eqs. (1)-(2), Fig. 1 and Sec. III parity discussion; p. 053506-4, Sec. V pulse paragraph: The correlated exchange-symmetric two-electron target distinguishes even dark (1,1) from odd bright (1,2) and their 14-/17-photon resonance neighborhoods." |
| ], |
| "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "F3", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Construct a reconstructible complex HHG response from the propagated state, consistently binding amplitude, harmonic order, detuning, phase origin and normalization.", |
| "award_conditions": [ |
| "The complex harmonic extraction fixes amplitude, phase origin, harmonic order, detuning and relative normalization consistently from the propagated state." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "F1: Establish the shared physical object of the supplied correlated one-dimensional two-electron Hamiltonian, exchange-symmetric ground state and specified strong-field pulse. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in F2 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-4-6, Figs. 4(a,b), 6(a,b) and Sec. V: A common complex-response and relative-scale convention is needed to compare resonance classes. Reconstruction and absolute-scale restrictions are task obligations, not source file requirements." |
| ], |
| "rc_relation": "RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "F4", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Define the dark H13/H15 inter-harmonic emission-phase difference and distinguish it from the resonant-minus-nonresonant phase difference.", |
| "award_conditions": [ |
| "The defined dark H15-H13 phase difference is distinguished from the resonant-minus-background phase of one harmonic." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "F3: Construct a reconstructible complex HHG response from the propagated state, consistently binding amplitude, harmonic order, detuning, phase origin and normalization. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in O1, I1, I2, I4, M2 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "A local phase/timing-definition omission does not erase an independently identified dark phase signal in I4 and does not itself establish RC1. Only absence/material invalidity of the dark temporal observable triggers its component gate." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article p. 053506-6, Eq. (4), unnumbered emission-time relation and Eqs. (5)-(6): The H15-H13 phase difference determines relative emission timing and is not the resonant-minus-background phase of one harmonic." |
| ], |
| "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "O1", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Provide a locally correctly bound odd-parity bright (1,2), 17-photon complex HHG output family, physically valid, reconstructible and adequately presented to audit its material amplitude and phase structure.", |
| "award_conditions": [ |
| "The correctly bound bright family provides reconstructible complex response resolving material enhancement and phase organization across an adequate resonance domain.", |
| "The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "F3: Construct a reconstructible complex HHG response from the propagated state, consistently binding amplitude, harmonic order, detuning, phase origin and normalization. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in O2, I3, I4, M3, M5, M6 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "Judge bright resonance binding locally. A dark-binding defect within F2 does not invalidate correct bright output.", |
| "Bright and dark branch correctness is local; one failed resonance does not erase the other. A dark temporal inference requires the actual H13/H15 inter-harmonic phase, not merely a correct bright phase scan." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-4-5, Fig. 4(a,b) and following bright-resonance paragraphs: Bright H17 is locally enhanced, H19 responds and H15 is much weaker in intensity; H17/H19 have approximately one phase-cycle variation, distinct from H15." |
| ], |
| "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "O2", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Provide a locally correctly bound even-parity dark (1,1), 14-photon complex HHG output family, physically valid, reconstructible and adequately presented to audit its material amplitude and phase structure.", |
| "award_conditions": [ |
| "The correctly bound dark family provides reconstructible complex response resolving its neighboring-harmonic line-shape and phase organization.", |
| "The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "F3: Construct a reconstructible complex HHG response from the propagated state, consistently binding amplitude, harmonic order, detuning, phase origin and normalization. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in O1, I1, I2, M2 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "Judge dark resonance binding locally. A bright-binding defect within F2 does not invalidate correct dark output.", |
| "Bright and dark branch correctness is local; one failed resonance does not erase the other. A dark temporal inference requires the actual H13/H15 inter-harmonic phase, not merely a correct bright phase scan." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-5-6, Figs. 5, 6(a,b) and adjacent dark-resonance discussion: The dark state acts through laser-dressed pathways; H13/H15 maxima are displaced and H13 has a destructive minimum. Fig. 5 is contextual, not an extra required output." |
| ], |
| "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "O3", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Provide comparable bright/dark evidence under common observable, phase and normalization definitions, explicitly preserving the boundary on absolute-scale comparisons.", |
| "award_conditions": [ |
| "Bright/dark evidence uses compatible observable and relative-scale/phase definitions, and explicitly avoids unsupported absolute enhancement ratios.", |
| "The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "All of [O1: Provide a locally correctly bound odd-parity bright (1,2), 17-photon complex HHG output family, physically valid, reconstructible and adequately presented to audit its material amplitude and phase structure.; O2: Provide a locally correctly bound even-parity dark (1,1), 14-photon complex HHG output family, physically valid, reconstructible and adequately presented to audit its material amplitude and phase structure.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in I1, I2, I3, I4, M2, M3, M5, M6 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "Honest qualitative comparison can remain valid when absolute scale is not comparable; a failed comparison does not erase correct within-branch identifications or mechanisms.", |
| "Cross-class strength comparisons need common relative scales; independently normalized branches may preserve local line-shape evidence without establishing an absolute enhancement ratio." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-4-6, Figs. 4(a,b), 6(a,b) and Sec. V: A common complex-response and relative-scale convention is needed to compare resonance classes. Reconstruction and absolute-scale restrictions are task obligations, not source file requirements." |
| ], |
| "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "I1", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify from the candidate's bright output localized H17 enhancement and the relative intensity responses of H15 and H19.", |
| "award_conditions": [ |
| "The candidate identifies local H17 enhancement, a response in H19 and the much weaker bright intensity response of H15 from their own data.", |
| "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "O1: Provide a locally correctly bound odd-parity bright (1,2), 17-photon complex HHG output family, physically valid, reconstructible and adequately presented to audit its material amplitude and phase structure. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in I2, I3, I4 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "Bright and dark branch correctness is local; one failed resonance does not erase the other. A dark temporal inference requires the actual H13/H15 inter-harmonic phase, not merely a correct bright phase scan." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-4-5, Fig. 4(a,b) and following bright-resonance paragraphs: Bright H17 is locally enhanced, H19 responds and H15 is much weaker in intensity; H17/H19 have approximately one phase-cycle variation, distinct from H15." |
| ], |
| "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "I2", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify the bright phase-response class: about one phase cycle for H17/H19 and a smaller variation for H15.", |
| "award_conditions": [ |
| "The candidate identifies approximately one phase-cycle response in bright H17/H19 and the smaller variation of H15 under a consistent phase convention.", |
| "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "O1: Provide a locally correctly bound odd-parity bright (1,2), 17-photon complex HHG output family, physically valid, reconstructible and adequately presented to audit its material amplitude and phase structure. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in I1, I3, I4 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "Intensity identification remains independent of phase-class identification, and conversely.", |
| "Bright and dark branch correctness is local; one failed resonance does not erase the other. A dark temporal inference requires the actual H13/H15 inter-harmonic phase, not merely a correct bright phase scan." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-4-5, Fig. 4(a,b) and following bright-resonance paragraphs: Bright H17 is locally enhanced, H19 responds and H15 is much weaker in intensity; H17/H19 have approximately one phase-cycle variation, distinct from H15." |
| ], |
| "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "I3", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify from the candidate's dark output displaced H13/H15 maxima and the H13 destructive minimum as a distinct line-shape family.", |
| "award_conditions": [ |
| "The candidate identifies dark H13/H15 displaced maxima and the H13 destructive minimum rather than reusing the bright line-shape narrative.", |
| "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "O2: Provide a locally correctly bound even-parity dark (1,1), 14-photon complex HHG output family, physically valid, reconstructible and adequately presented to audit its material amplitude and phase structure. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in I1, I2, I4, M5, M6 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "If both neighboring enhancements exist but one line-shape distinction is unresolved, localize that identification gap here. Judge O2, I4 and mechanisms not using that distinction on their own evidence.", |
| "Bright and dark branch correctness is local; one failed resonance does not erase the other. A dark temporal inference requires the actual H13/H15 inter-harmonic phase, not merely a correct bright phase scan." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-5-6, Figs. 5, 6(a,b) and adjacent dark-resonance discussion: The dark state acts through laser-dressed pathways; H13/H15 maxima are displaced and H13 has a destructive minimum. Fig. 5 is contextual, not an extra required output." |
| ], |
| "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "I4", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify the resonance-linked dark H13/H15 inter-harmonic phase change as a signal usable for temporal inference.", |
| "award_conditions": [ |
| "The candidate identifies the resonance-linked dark inter-harmonic phase change relevant to temporal inference.", |
| "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "O2: Provide a locally correctly bound even-parity dark (1,1), 14-photon complex HHG output family, physically valid, reconstructible and adequately presented to audit its material amplitude and phase structure. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in F4, I1, I2, I3 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "The identified dark phase signal depends on valid presented dark phase output, not a complete F4 phase-to-time definition. Preserve independent dark-intensity and bright work.", |
| "Bright and dark branch correctness is local; one failed resonance does not erase the other. A dark temporal inference requires the actual H13/H15 inter-harmonic phase, not merely a correct bright phase scan." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article p. 053506-6, Eq. (4), unnumbered emission-time relation and Eqs. (5)-(6): The H15-H13 phase difference determines relative emission timing and is not the resonant-minus-background phase of one harmonic." |
| ], |
| "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "M1", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Use at least one candidate resonance branch to explain how detuning-dependent interference between nonresonant and resonant complex amplitudes changes intensity and phase together.", |
| "award_conditions": [ |
| "At least one valid branch supports a complex resonant/nonresonant interference account that changes intensity and phase together as detuning varies.", |
| "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "At least one of [I1: Identify from the candidate's bright output localized H17 enhancement and the relative intensity responses of H15 and H19.; I3: Identify from the candidate's dark output displaced H13/H15 maxima and the H13 destructive minimum as a distinct line-shape family.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in M2, M3, M5, M6 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "Either valid branch can establish general complex-path interference. Full cross-class distinction is separately required by M4; preserve an independent dark timing chain." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article p. 053506-6, paragraph preceding Eq. (4), Eq. (4) and following phase analysis; pp. 053506-4-5, Figs. 4 and 6: Complex resonant and nonresonant amplitudes interfere; their different detuning phases link amplitude and phase and distinguish bright/direct from dark/dressed response." |
| ], |
| "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "M2", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Use the candidate's bright signals to explain the odd-parity bright state's direct radiative pathway and its physical role.", |
| "award_conditions": [ |
| "The bright-state explanation connects direct radiative coupling to the identified bright response, not just its parity label.", |
| "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "I1: Identify from the candidate's bright output localized H17 enhancement and the relative intensity responses of H15 and H19. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in M3, M5, M6 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "Bright and dark branch correctness is local; one failed resonance does not erase the other. A dark temporal inference requires the actual H13/H15 inter-harmonic phase, not merely a correct bright phase scan." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-4-5, Fig. 4(a,b) and following bright-resonance paragraphs: Bright H17 is locally enhanced, H19 responds and H15 is much weaker in intensity; H17/H19 have approximately one phase-cycle variation, distinct from H15." |
| ], |
| "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "M3", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Use the candidate's dark signals to explain how the even-parity dark state affects neighboring odd harmonics through laser-dressed pathways.", |
| "award_conditions": [ |
| "The dark-state explanation uses laser dressing to connect an even state with neighboring odd-harmonic response.", |
| "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "I3: Identify from the candidate's dark output displaced H13/H15 maxima and the H13 destructive minimum as a distinct line-shape family. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in M2 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "Bright and dark branch correctness is local; one failed resonance does not erase the other. A dark temporal inference requires the actual H13/H15 inter-harmonic phase, not merely a correct bright phase scan." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-5-6, Figs. 5, 6(a,b) and adjacent dark-resonance discussion: The dark state acts through laser-dressed pathways; H13/H15 maxima are displaced and H13 has a destructive minimum. Fig. 5 is contextual, not an extra required output." |
| ], |
| "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "M4", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Use amplitude/phase features of both classes to distinguish direct bright and dressed dark pathways rather than merely repeating selection-rule labels.", |
| "award_conditions": [ |
| "Feature-level amplitude and phase evidence from both classes distinguishes their direct versus dressed pathways.", |
| "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "All of [M1: Use at least one candidate resonance branch to explain how detuning-dependent interference between nonresonant and resonant complex amplitudes changes intensity and phase together.; M2: Use the candidate's bright signals to explain the odd-parity bright state's direct radiative pathway and its physical role.; M3: Use the candidate's dark signals to explain how the even-parity dark state affects neighboring odd harmonics through laser-dressed pathways.; I2: Identify the bright phase-response class: about one phase cycle for H17/H19 and a smaller variation for H15.; I4: Identify the resonance-linked dark H13/H15 inter-harmonic phase change as a signal usable for temporal inference.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in M5, M6 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "Full cross-class pathway distinction needs both pathway classes and material phase evidence; a dark temporal inference can remain independently scoreable when cross-class comparison fails.", |
| "Cross-class strength comparisons need common relative scales; independently normalized branches may preserve local line-shape evidence without establishing an absolute enhancement ratio." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article p. 053506-6, paragraph preceding Eq. (4), Eq. (4) and following phase analysis; pp. 053506-4-5, Figs. 4 and 6: Complex resonant and nonresonant amplitudes interfere; their different detuning phases link amplitude and phase and distinguish bright/direct from dark/dressed response." |
| ], |
| "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "M5", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Derive the supported emission-time relation from the dark H13/H15 inter-harmonic phase difference.", |
| "award_conditions": [ |
| "The dark inter-harmonic phase gives a consistent relative emission time/delay through the 2 omega_l spacing, with phase-origin and branch changes handled consistently.", |
| "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "All of [F4: Define the dark H13/H15 inter-harmonic emission-phase difference and distinguish it from the resonant-minus-nonresonant phase difference.; I4: Identify the resonance-linked dark H13/H15 inter-harmonic phase change as a signal usable for temporal inference.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in M1, M2, M3, M4 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article p. 053506-6, Eq. (4), unnumbered emission-time relation and Eqs. (5)-(6): The H15-H13 phase difference determines relative emission timing and is not the resonant-minus-background phase of one harmonic." |
| ], |
| "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "M6", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Relate the inferred dark emission-delay scale to the autoionizing-state lifetime or inverse width in proportion to the evidence.", |
| "award_conditions": [ |
| "The inferred dark delay is compared proportionately with the lifetime/inverse-width scale without asserting an unjustified exact equality.", |
| "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "M5: Derive the supported emission-time relation from the dark H13/H15 inter-harmonic phase difference. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in M1, M2, M3, M4 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "A lifetime/width interpretation requires a defensible delay relation, but a failed scale interpretation does not erase a correct phase-to-time construction." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article p. 053506-6, Eqs. (5)-(6), lifetime paragraph and Fig. 7: The source obtains a delay near 300 as, comparable with but not equal to the inverse-width scale near 470 as. These are scale anchors, not exact mandatory values." |
| ], |
| "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "M7", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Compare similarities and differences of bright/dark enhancement and phase organization under common definitions, limiting strength comparisons to what the candidate's relative-scale evidence supports.", |
| "award_conditions": [ |
| "The bright/dark scientific comparison distinguishes common response features and material differences and respects what the common relative scale actually permits.", |
| "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "All of [O3: Provide comparable bright/dark evidence under common observable, phase and normalization definitions, explicitly preserving the boundary on absolute-scale comparisons.; M4: Use amplitude/phase features of both classes to distinguish direct bright and dressed dark pathways rather than merely repeating selection-rule labels.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.", |
| "Preserve independent correct work in M5, M6, V2 and all branches not using the failed premise.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.", |
| "Cross-class strength comparisons need common relative scales; independently normalized branches may preserve local line-shape evidence without establishing an absolute enhancement ratio." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-4-6, Figs. 4(a,b), 6(a,b) and Sec. V: A common complex-response and relative-scale convention is needed to compare resonance classes. Reconstruction and absolute-scale restrictions are task obligations, not source file requirements." |
| ], |
| "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "V1", |
| "dimension": "V", |
| "points": 0.5, |
| "scientific_requirement": "When candidate method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or restrict the threatened conclusion to a safe scope.", |
| "award_conditions": [ |
| "An actual phase, scale, sampling, window or detuning-domain threat is resolved by equivalent evidence or a justified restriction; otherwise apply N/A." |
| ], |
| "applicability_and_na": [ |
| "Activate only for a concrete material risk arising from the candidate method, data, anomaly or claim; no fixed test is required in the absence of a trigger.", |
| "Without a triggered risk record N/A and award 0.5 without positive validation evidence; this neither blocks RC4 nor triggers RC3.", |
| "When triggered, accept functionally equivalent discriminating evidence or a justified restriction of the threatened claim." |
| ], |
| "dependencies": [ |
| "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-2, 053506-4 and 053506-6, model definition, pulse paragraph and Sec. VI: The reduced correlated model and finite resonance domain bound inference. Phase-origin/unwrapping, normalization and finite-detuning risks are judged only when material." |
| ], |
| "rc_relation": "RC3: an unresolved applicable material risk, only after signals and principal mechanisms are substantially supported and all six risk-proof requirements are met. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| }, |
| { |
| "criterion_id": "V2", |
| "dimension": "V", |
| "points": 0.5, |
| "scientific_requirement": "Limit conclusions to correlated one-dimensional helium, the specified strong-field pulse and sampled resonance neighborhoods, not a universal experimental retrieval.", |
| "award_conditions": [ |
| "The conclusion remains about the correlated one-dimensional model, stated finite pulse and investigated resonances, not universal experimental retrieval." |
| ], |
| "applicability_and_na": [ |
| "Applicable to the stated scientific commission; N/A is not permitted." |
| ], |
| "dependencies": [ |
| "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.", |
| "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty." |
| ], |
| "equivalent_evidence": [ |
| "Dipole, velocity, acceleration or equivalent complex-amplitude extraction is accepted when observable and phase conventions are consistently established; time-origin changes are accepted when phases and timing transform consistently.", |
| "Accept declared common normalization, equivalent frequency/detuning variables, complex phase conventions modulo 2 pi and reconstructible alternative evidence preserving relative structures.", |
| "A reconstructed XUV pulse or another time-domain check can support temporal inference but is not required. No source grid, absorber, exact full width, sampling, absolute intensity, colors or panel arrangement is prescribed." |
| ], |
| "source_support": [ |
| "Strelkov (2023), article pp. 053506-2, 053506-4 and 053506-6, model definition, pulse paragraph and Sec. VI: The reduced correlated model and finite resonance domain bound inference. Phase-origin/unwrapping, normalization and finite-detuning risks are judged only when material." |
| ], |
| "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure." |
| } |
| ], |
| "case_scientific_rules": [ |
| "The ground and dark (1,1) spatial states are even, and the bright (1,2) state is odd, with the exchange-symmetric two-electron spatial wavefunction. Dark and bright neighborhoods correspond to even 14-photon and odd 17-photon conditions; a single-active-electron target is not equivalent.", |
| "A valid complex response is Dq(omega_l) = integral w(t) a(t;omega_l) exp(i q omega_l t) dt, with intensity proportional to |Dq|^2 and phase arg(Dq). A phase appended to an independently normalized real spectrum is not a substitute. The pulse has 4-8-4 cycles, intensity 8e14 W/cm^2, field-amplitude sine-squared ramps and a cosine carrier fixing the phase origin.", |
| "Bright anchors are localized dominant H17 enhancement near fundamental energy 3.02-3.03 eV, much weaker H15 intensity response and material H19 response on the lower-frequency side; H17/H19 change by about a phase cycle and H15 by roughly 1-2 radians. Far enough off resonance, endpoint phases agree modulo 2 pi. These are structure classes, not pointwise tolerances.", |
| "Dark anchors are neighboring H13/H15 enhancements with displaced maxima and an H13 destructive minimum near 14-photon energy 44.6 eV without the same H15 feature. H15/H17 have approximately cycle-scale phase changes, H13 several radians and H11 weaker variation. Exact maxima, widths, phase spans or sampling points are not targets.", |
| "Detuning changes the relative complex resonant and nonresonant amplitudes, producing linked strength/phase interference. The bright state radiates directly to the ground state; the dark even state affects odd harmonics through laser dressing. Parity labels alone do not establish the candidate's mechanism.", |
| "Define delta phi_q = phi_q(resonant) - phi_q(nonresonant). Dark emission time is te = (phi15 - phi13)/(2 omega_l); a delay tau implies delta phi15 - delta phi13 = 2 tau omega_l. The source scale is about 300 as, comparable to inverse-width scale about 470 as, not a digit-level target. Do not impose this dark H13/H15 relation as the construction rule for the bright H15/H17/H19 scan.", |
| "Dark and bright enhancement can be comparable under the stated conditions, but independent normalization cannot establish an absolute enhancement ratio. Preserve correct intensity work if phase evidence fails and restrict only the phase-dependent inference.", |
| "Concrete risks include resonance/harmonic misbinding, phase-branch or time-origin artifacts, transform/sampling creation or loss of a minimum/cycle, inadequate detuning support and manufactured cross-family normalization. No fixed phase-unwrapping algorithm, scan endpoints, window or reconstructed XUV pulse is required.", |
| "The score is the sum of twenty material-core criteria, each worth either 0 or 0.5, for a maximum of 10.0. Research Closure is descriptive and never caps, floors, rescales or repairs the score.", |
| "Judge physical object identity and correctness before display similarity. For each output record object_valid, presentation_adequate and claim_adequate separately; all three must hold for its atomic award. A presentation or claim defect alone is not evidence that an existing physical object is absent or invalid.", |
| "Candidate-created data, candidate presentation, candidate identification, physical inference and validation are distinct evidential acts. Examiner inspection or reconstruction may verify an object but cannot create missing candidate identification, reasoning or risk resolution.", |
| "A dependency propagates only the failed necessary physical fact, not the whole upstream atomic verdict or unrelated missing detail. Name the failed premise, the downstream obligation needing it, and why independent candidate-presented evidence does not establish it. Preserve unaffected branches, independent work and honest scope.", |
| "Numerical reliability has no separate generic penalty. Charge a defect where it materially damages a physical object or evidence, and a dependent conclusion only when that same defect makes the conclusion false or unsupported. Missing a preferred convergence study, control, solver or named self-check is not itself a failure.", |
| "Risk-triggered validation applies only to a concrete material risk arising from the candidate method, data, anomaly or claim. With no such risk record N/A and award the fixed atomic credit without treating it as positive validation evidence; N/A does not block RC4. Unconditional scope obligations cannot be N/A.", |
| "Before assigning RC3 establish all six: the concrete failure mode; its origin in candidate work; the fair task or standard-knowledge basis; the threatened central conclusion; why submitted evidence cannot expose or exclude it; and examples of functionally equivalent discriminating evidence or an honest scope restriction that would resolve it. A generic possibility of further testing is insufficient.", |
| "Use bounded examiner-side source/reference readback only to resolve a material scientific uncertainty, not to demand pixels, an undeclared tolerance or additional candidate deliverables. A provisional score of at least 9.0 or provisional RC4 triggers one bounded central-output-anchor check and one principal-mechanism-link check. Reference conflict or insufficiency remains an explicit unresolved decision, not an invented target.", |
| "Evaluate closure-role trigger facts independently of atomic awards and select the most severe failed required role across all indispensable and co-primary claims. Supporting claims do not independently set overall closure. A point loss alone is not a closure-gate fact.", |
| "A valid candidate-caused incomplete or timeout attempt with no scientifically assessable required submission has score 0.0 and RC0 before N/A bookkeeping. Assessable incomplete work is graded from the submitted evidence; unsubmitted scratch or logs do not become scientific answers.", |
| "Use a reconstructible complex harmonic response $D_q=\\int dt\\,w(t)d(t)e^{iq\\omega_l t}$, or a consistently converted velocity/acceleration equivalent; $I_q\\propto|D_q|^2$ and $\\phi_q=\\arg D_q$. Write $D_q=D_q^{\\rm nr}+D_q^{\\rm r}$ so interference contributes $2\\operatorname{Re}(D_q^{\\rm nr}D_q^{{\\rm r}*})$. This is the complex-amplitude entailment of Sec. V, not an extra source-numbered equation.", |
| "With the stated Fourier/time convention, $\\Delta\\phi=\\phi_{15}-\\phi_{13}$ gives $t_e=\\Delta\\phi/(2\\omega_l)$, while $\\delta\\phi_q=\\phi_q^{\\rm r}-\\phi_q^{\\rm nr}$ compares pathways of the same harmonic. The delay is $\\tau=(\\Delta\\phi^{\\rm r}-\\Delta\\phi^{\\rm nr})/(2\\omega_l)$ (Eqs. (4)-(6)). Convert phase branches and time origin consistently; compare the evidence-supported scale to $\\hbar/\\Gamma$, not an exact equality." |
| ], |
| "closure_requirements": { |
| "RC0": [ |
| "Required claim CL1, central object: All of [F1: Establish the shared physical object of the supplied correlated one-dimensional two-electron Hamiltonian, exchange-symmetric ground state and specified strong-field pulse.; F3: Construct a reconstructible complex HHG response from the propagated state, consistently binding amplitude, harmonic order, detuning, phase origin and normalization.]. Judge role-trigger facts, not the sum or pattern of atomic scores.", |
| "Apply for a missing or materially invalid required central object; a presentation-only or claim-only defect does not establish object invalidity.", |
| "No scientifically assessable required submission gives the terminal 0.0/RC0 disposition." |
| ], |
| "RC1": [ |
| "Required claim CL1, indispensable component: F2: Bind the even-parity dark (1,1), 14-photon neighborhood and odd-parity bright (1,2), 17-photon neighborhood to their correct resonance branches.. Judge role-trigger facts, not the sum or pattern of atomic scores.", |
| "Required claim CL2, indispensable component: O1: Provide a locally correctly bound odd-parity bright (1,2), 17-photon complex HHG output family, physically valid, reconstructible and adequately presented to audit its material amplitude and phase structure.. Judge role-trigger facts, not the sum or pattern of atomic scores.", |
| "Required claim CL3, indispensable component: All of [F4: Define the dark H13/H15 inter-harmonic emission-phase difference and distinguish it from the resonant-minus-nonresonant phase difference.; O2: Provide a locally correctly bound even-parity dark (1,1), 14-photon complex HHG output family, physically valid, reconstructible and adequately presented to audit its material amplitude and phase structure.]. Judge role-trigger facts, not the sum or pattern of atomic scores.", |
| "Required claim CL4, indispensable component: O3: Provide comparable bright/dark evidence under common observable, phase and normalization definitions, explicitly preserving the boundary on absolute-scale comparisons.. Judge role-trigger facts, not the sum or pattern of atomic scores.", |
| "The central object is established but a required physical component is absent or materially invalid. Preserve independent valid branches; do not invent a hidden canonical plot, sampling grid or implementation duty." |
| ], |
| "RC2": [ |
| "Required claim CL2, principal mechanism: M2: Use the candidate's bright signals to explain the odd-parity bright state's direct radiative pathway and its physical role.. Judge role-trigger facts, not the sum or pattern of atomic scores.", |
| "Required claim CL3, principal mechanism: All of [M3: Use the candidate's dark signals to explain how the even-parity dark state affects neighboring odd harmonics through laser-dressed pathways.; M5: Derive the supported emission-time relation from the dark H13/H15 inter-harmonic phase difference.; M6: Relate the inferred dark emission-delay scale to the autoionizing-state lifetime or inverse width in proportion to the evidence.]. Judge role-trigger facts, not the sum or pattern of atomic scores.", |
| "Required claim CL4, principal mechanism: All of [M1: Use at least one candidate resonance branch to explain how detuning-dependent interference between nonresonant and resonant complex amplitudes changes intensity and phase together.; M4: Use amplitude/phase features of both classes to distinguish direct bright and dressed dark pathways rather than merely repeating selection-rule labels.; M7: Compare similarities and differences of bright/dark enhancement and phase organization under common definitions, limiting strength comparisons to what the candidate's relative-scale evidence supports.]. Judge role-trigger facts, not the sum or pattern of atomic scores.", |
| "Required signal objects/components exist, but an indispensable principal mechanism or co-primary scientific conclusion is missing, wrong or unsupported by candidate-presented and identified evidence. Correct data do not let an examiner supply missing reasoning." |
| ], |
| "RC3": [ |
| "Required claim CL4, material validation: V1: When candidate method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or restrict the threatened conclusion to a safe scope.. Judge role-trigger facts, not the sum or pattern of atomic scores.", |
| "All indispensable signal and principal-mechanism roles are substantially supported, but a concrete triggered material risk remains unresolved and inadequately restricted.", |
| "Establish the failure mode, candidate origin, fair task/knowledge basis, threatened central conclusion, insufficiency of submitted evidence, and equivalent resolution or scope restriction. Missing an examiner-preferred check alone never suffices." |
| ], |
| "RC4": [ |
| "Every nonempty required role in every indispensable and co-primary claim above is scientifically established from candidate evidence, with the correct case/model/observable identities and evidence-bounded conclusion.", |
| "All applicable material risks are discriminated or honestly restricted; no unresolved material ambiguity remains. Risk N/A does not block closure or supply positive validation evidence. Honest limitations cannot repair a false signal or mechanism.", |
| "Select the most severe failed required role if any; otherwise RC4. No score threshold, score ceiling or required display/solver checklist determines this classification." |
| ] |
| }, |
| "references": [ |
| { |
| "citation": "V. V. Strelkov. 2023. Dark and bright autoionizing states in resonant high-order harmonic generation: Simulation via a one-dimensional helium model. Physical Review A, 107, 053506.", |
| "url": "https://doi.org/10.1103/PhysRevA.107.053506", |
| "scientific_scope": "Complex HHG amplitude/phase near bright and dark autoionizing resonances, interference pathways and dark-branch temporal inference. Source figures support physical structure, not fixed displays, exact widths or arbitrary-unit absolute ratios.", |
| "anchors": [ |
| "article p. 053506-2, Eqs. (1)-(2), Fig. 1 and Sec. III parity discussion; p. 053506-4, Sec. V pulse paragraph", |
| "article pp. 053506-4-6, Figs. 4(a,b), 6(a,b) and Sec. V", |
| "article p. 053506-6, Eq. (4), unnumbered emission-time relation and Eqs. (5)-(6)", |
| "article pp. 053506-4-5, Fig. 4(a,b) and following bright-resonance paragraphs", |
| "article pp. 053506-5-6, Figs. 5, 6(a,b) and adjacent dark-resonance discussion", |
| "article p. 053506-6, paragraph preceding Eq. (4), Eq. (4) and following phase analysis; pp. 053506-4-5, Figs. 4 and 6", |
| "article p. 053506-6, Eqs. (5)-(6), lifetime paragraph and Fig. 7", |
| "article pp. 053506-2, 053506-4 and 053506-6, model definition, pulse paragraph and Sec. VI" |
| ] |
| } |
| ] |
| } |
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