| { |
| "case_id": "Case07", |
| "title": "Case07 — High-order harmonic generation as induced by a quantized field: Phase-space picture", |
| "atoms": [ |
| { |
| "criterion_id": "F1", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.", |
| "award_conditions": [ |
| "The complete no-RWA Rabi Hamiltonian and all four initial/coupling cases use consistent units, basis phases and physical initial states." |
| ], |
| "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": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent." |
| ], |
| "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 a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.", |
| "award_conditions": [ |
| "A computable complete moving lattice has a valid nonorthogonal initial Gram solution, same-branch metric and cross-branch atomic coupling." |
| ], |
| "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": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-4-5, Eqs.(17)-(24): nonorthogonal coherent-state initialization, moving-lattice metric and atomic cross-branch mixing." |
| ], |
| "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": "Trace the atom out of the propagated complete state and construct a normalized reduced-field phase-space object, accepting equivalent normalized representations explicitly mapped to that reduced state.", |
| "award_conditions": [ |
| "The atom is traced out of the complete propagated state and the reduced-field phase-space object is normalized and explicitly related to that state." |
| ], |
| "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": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-5-6, Sec.III.B, Eqs.(25)-(31), explicit reduced density operator paragraph: partial trace over atom and normalized field phase-space construction." |
| ], |
| "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": "F4", |
| "dimension": "F", |
| "points": 0.5, |
| "scientific_requirement": "Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.", |
| "award_conditions": [ |
| "The harmonic observable is the material dipole spectrum; derivative alternatives derive frequency reweighting without manufacturing ordering or mechanism." |
| ], |
| "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": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match." |
| ], |
| "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": "O1", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Present normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.", |
| "award_conditions": [ |
| "Normalized first-cycle Case-A phase-space evidence is correctly time-bound and resolves genuine full-model branch motion, mixing, broadening or interference.", |
| "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: all of: F2 (Derive a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.); F3 (Trace the atom out of the propagated complete state and construct a normalized reduced-field phase-space object, accepting equivalent normalized representations explicitly mapped to that reduced state.)", |
| "Preserve independently valid work in O2, 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": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model 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": "O2", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.", |
| "award_conditions": [ |
| "Case-B 20-cycle material-dipole spectral evidence is reconstructible and resolves principal peaks, plateau/cutoff and global morphology.", |
| "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: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F4 (Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.)", |
| "Preserve independently valid work in O3, O4, O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match." |
| ], |
| "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 a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.", |
| "award_conditions": [ |
| "Case-C 20-cycle material-dipole spectral evidence is reconstructible and resolves principal peaks, plateau/cutoff and global morphology.", |
| "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: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F4 (Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.)", |
| "Preserve independently valid work in O2, O4, O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match." |
| ], |
| "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": "O4", |
| "dimension": "O", |
| "points": 0.5, |
| "scientific_requirement": "Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.", |
| "award_conditions": [ |
| "Case-D 20-cycle material-dipole spectral evidence is reconstructible and resolves principal peaks, plateau/cutoff and global morphology.", |
| "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: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F4 (Construct the material-dipole HHG spectrum; any dipole/velocity/acceleration equivalence must derive and account for frequency reweighting without manufacturing harmonic ordering or mechanism.)", |
| "Preserve independently valid work in O2, O3, O1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match." |
| ], |
| "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 coherent-field branch motion/separation, return and full-model mixing, broadening or interference in the submitted Case-A evidence; the source's minimal two-state morphology is not required.", |
| "award_conditions": [ |
| "The candidate identifies branch motion/separation, return and complete-model changes in their own Case-A evidence without imposing minimal-two-state morphology." |
| ], |
| "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 normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.)", |
| "Preserve independently valid work in 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": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model 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": "I2", |
| "dimension": "I", |
| "points": 0.5, |
| "scientific_requirement": "Identify pronounced common harmonic peaks, plateau-like ranges and cutoffs in the submitted B-D spectra, rather than merely reporting spectrum generation.", |
| "award_conditions": [ |
| "The candidate identifies material peaks, plateau-like ranges and cutoffs in all submitted B-D spectra." |
| ], |
| "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: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.)", |
| "Preserve independently valid work in I1, I3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match." |
| ], |
| "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 the correct extension of the cutoff with initial amplitude and case-dependent changes in peak detail from B-D evidence.", |
| "award_conditions": [ |
| "The candidate identifies growing cutoff with coherent amplitude and actual case-dependent peak changes." |
| ], |
| "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: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.)", |
| "Preserve independently valid work in I1, I2. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match." |
| ], |
| "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": "Use any self-consistent Hamiltonian-term decomposition, analytic relation, intervention or equivalent evidence to explain the field/free-plus-interaction contribution to coherent-field or branch motion; atomic-term omission, closed trajectories and phase traces are accepted examples, not prescribed forms.", |
| "award_conditions": [ |
| "A valid Hamiltonian decomposition, analytic relation or intervention explains field/free-plus-interaction branch motion with an established physical consequence." |
| ], |
| "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 M2, M3. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent." |
| ], |
| "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": "M2", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Distinguish relevant full-Hamiltonian contributions to changing material dipole and radiation by a commutator with computed/analytic consequence, term intervention or equivalent evidence. Proving constant dipole after removing the atomic term is one accepted realization, not the sole control.", |
| "award_conditions": [ |
| "A commutator, full-vs-RWA or other valid intervention isolates relevant Hamiltonian-term contributions to the changing dipole/radiation, not merely model names." |
| ], |
| "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": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent." |
| ], |
| "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": "M3", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.", |
| "award_conditions": [ |
| "Submitted evidence closes the physical-term to branch change to time-dependent dipole to radiation causal chain; isolated line/weight changes are insufficient." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: M2 (Distinguish relevant full-Hamiltonian contributions to changing material dipole and radiation by a commutator with computed/analytic consequence, term intervention or equivalent evidence. Proving constant dipole after removing the atomic term is one accepted realization, not the sole control.)", |
| "Preserve independently valid work in M1, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient." |
| ], |
| "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": "Explain which Case-A complete-lattice phase-space structures arise from branch motion, atomic mixing and full-state reduction, without treating a smooth minimal two-state image as uniquely correct.", |
| "award_conditions": [ |
| "The candidate attributes actual complete-lattice phase-space structure to branch motion, atomic mixing and reduced-state construction rather than a prescribed smooth picture." |
| ], |
| "applicability_and_na": [ |
| "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item." |
| ], |
| "dependencies": [ |
| "Necessary scientific premise: I1 (Identify coherent-field branch motion/separation, return and full-model mixing, broadening or interference in the submitted Case-A evidence; the source's minimal two-state morphology is not required.)", |
| "Preserve independently valid work in M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model 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": "M5", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.", |
| "award_conditions": [ |
| "All B-D spectra ground the cutoff/peak amplitude-dependence explanation and distinguish it from frequency reweighting or display rescaling." |
| ], |
| "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 pronounced common harmonic peaks, plateau-like ranges and cutoffs in the submitted B-D spectra, rather than merely reporting spectrum generation.); I3 (Identify the correct extension of the cutoff with initial amplitude and case-dependent changes in peak detail from B-D evidence.)", |
| "Preserve independently valid work in M1, M3, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match." |
| ], |
| "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": "Connect reduced-field reorganization and material-dipole HHG evidence, explaining how they jointly constrain rather than replace the central physical picture.", |
| "award_conditions": [ |
| "Phase-space reorganization and material-dipole spectra jointly constrain the physical account; one does not substitute for the other." |
| ], |
| "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 coherent-field branch motion/separation, return and full-model mixing, broadening or interference in the submitted Case-A evidence; the source's minimal two-state morphology is not required.); I2 (Identify pronounced common harmonic peaks, plateau-like ranges and cutoffs in the submitted B-D spectra, rather than merely reporting spectrum generation.)", |
| "Preserve independently valid work in M3, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient." |
| ], |
| "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": "M7", |
| "dimension": "M", |
| "points": 0.5, |
| "scientific_requirement": "Reconcile auxiliary models/controls with the complete no-RWA calculation, answering term contributions and amplitude dependence with the strongest conclusion supported by common physical endpoints.", |
| "award_conditions": [ |
| "Auxiliary controls and complete no-RWA endpoints support a mutually consistent account of term contributions and coherent-amplitude dependence." |
| ], |
| "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: M3 (Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.); M5 (Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.); M6 (Connect reduced-field reorganization and material-dipole HHG evidence, explaining how they jointly constrain rather than replace the central physical picture.)", |
| "Preserve independently valid work in M1, M2, M4. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect." |
| ], |
| "equivalent_evidence": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient." |
| ], |
| "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": "V1", |
| "dimension": "V", |
| "points": 0.5, |
| "scientific_requirement": "Positively state the two-level, single-mode, complete no-RWA and four-case evidence domain, distinguishing general phase-space/HHG conclusions from model-specific detail.", |
| "award_conditions": [ |
| "The candidate positively states the two-level, single-mode, complete no-RWA four-case evidence domain and model-specific limits." |
| ], |
| "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": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-7-9, Sec.V peak-detail limitation and Sec.VI-VII generalization/scope; normalization and complete-lattice stability follow Eqs.(18),(24). Positive model scope and triggered validation are task duties, not a demand to reproduce one lattice size." |
| ], |
| "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": "V2", |
| "dimension": "V", |
| "points": 0.5, |
| "scientific_requirement": "Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.", |
| "award_conditions": [ |
| "Only a concrete triggered state, metric, transform or claim risk requires discriminating evidence or narrower 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": [ |
| "Consistent atomic phase, branch relabelling, coupling sign, phase-space reflection, Fourier and positive display-scale conventions are accepted after mapping invariant physical states.", |
| "A normalized phase-space representation is equivalent only with an explicit relation to the atom-traced reduced field state. A complete-lattice Wigner function may legitimately contain stable multi-lobe/interference structure absent from a minimal two-state source panel.", |
| "Any genuinely discriminating Hamiltonian-term intervention is accepted. A full-versus-RWA intervention qualifies for M2 when it has discernible dipole/spectrum consequences isolating the relevant contribution; naming the Hamiltonians alone does not.", |
| "Equivalent mechanisms must close the physical-term -> field separation/mixing -> changing dipole -> radiation chain. Showing only a line-position or weight change does not establish M3.", |
| "Derivative spectra require the transform relation and treatment of frequency weighting wherever it affects conclusions; matching peak frequencies alone does not establish equivalence." |
| ], |
| "source_support": [ |
| "Gombkoto et al. (2020), article pp.013418-7-9, Sec.V peak-detail limitation and Sec.VI-VII generalization/scope; normalization and complete-lattice stability follow Eqs.(18),(24). Positive model scope and triggered validation are task duties, not a demand to reproduce one lattice size." |
| ], |
| "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." |
| } |
| ], |
| "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.", |
| "The complete Hamiltonian, not an RWA or reduced free-field orbit, is the production target. A nonorthogonal moving basis requires initialization, same-branch metric and time-dependent cross-branch overlaps.", |
| "Clipping, smoothing or time-slice summation cannot manufacture source-panel resemblance. The minimal eight-snapshot montage and a fixed number of figures are not required.", |
| "No absolute spectral normalization is source-fixed. A declared positive display scale is allowed, but cannot support absolute-yield or exact cross-case-magnitude claims.", |
| "M3 can be supported by a valid term intervention reaching the changing-dipole endpoint without a compulsory additional Case-A phase-space identification premise; the separately commissioned phase-space branch remains assessed.", |
| "The canonical Hamiltonian is", |
| "$$\nH=\\frac{\\hbar\\omega_0}{2}\\sigma_z\n+\\hbar\\omega a^\\dagger a\n+\\hbar\\Omega\\sigma_x(a+a^\\dagger),\n$$", |
| "without RWA. A branch-dependent displacement diagonalizes the field plus interaction part $\\widetilde H=H-H_a$. For a $\\sigma_x$ eigenstate, an initial coherent state therefore follows an analytically moving coherent label and accumulates a branch phase. With $H_a$ restored, a complete moving von Neumann lattice expansion is nonorthogonal. Its static Gram problem fixes the initial coefficients, its same-branch Gram matrices provide the generalized metric, and its time-dependent cross-branch overlaps transmit the atomic-term coupling. Students must derive a physically equivalent end-to-end system; the complete recurrence is not stated in task.", |
| "The initial atomic ground-state phase in the $\\sigma_x$ basis and the sign of $\\Omega$ may be changed consistently. Grade invariant physical states after the corresponding branch rephasing or phase-space reflection.", |
| "The material dipole is proportional to $\\langle\\sigma_x\\rangle(t)$. The source HHG object is the squared Fourier modulus of that time record over the stated 20 cycles. A dipole-, velocity- or acceleration-form spectrum may be accepted only when the student derives the transform relation and shows that frequency reweighting does not manufacture the claimed harmonic ordering or mechanism. The reduced field state is obtained by tracing over the atom, and a standard normalized Wigner function provides the canonical phase-space observable. Equivalent normalized phase-space constructions are acceptable only when their relation to the reduced field state is explicit.", |
| "The source's smooth eight-snapshot Fig. 4 top uses a minimal two-moving-state approximation. The present task does not require that approximation or its montage. A correct complete-lattice Wigner function may contain stable multi-lobe or interference structure absent from that panel and must not be penalized for the difference. Conversely, smoothing, clipping or summing time slices cannot manufacture agreement.", |
| "Under $\\widetilde H$, one initial coherent label separates into two branch-dependent moving coherent components and returns after an optical cycle. The branch phase becomes more structured as the coherent amplitude grows.", |
| "Because $[\\widetilde H,\\sigma_x]=0$, the dipole expectation is constant if the atomic Hamiltonian is omitted. The atomic term mixes the moving branches and is essential for a changing dipole and secondary harmonic radiation.", |
| "A complete first-cycle field Wigner calculation must begin from the stated coherent field, preserve normalization and resolve genuine branch motion, mixing, broadening or interference supported by its own full-state data. The exact minimal-source morphology is not required.", |
| "Cases B-D show pronounced harmonic peaks, a plateau-like range and a cutoff. The cutoff extends with increasing $\\alpha_0$, while the detailed peak pattern changes. Fine-structure mechanism is outside the source's claimed scope.", |
| "No source-defined absolute spectral normalization exists. A declared positive display scale is acceptable but cannot support absolute-yield or exact cross-case-magnitude conclusions.", |
| "For F2-F4/M1-M3, article pp.013418-3-5, Eqs.(14),(18),(22)-(26), one consistent branch convention is $\\gamma=-\\Omega/\\omega$,\n$$\\alpha_\\pm(t)=\\pm\\gamma+(\\alpha\\mp\\gamma)e^{-i\\omega t},\\quad\ni\\hbar N^{++}\\dot c^+=(\\hbar\\omega_0/2)N^{+-}c^-,\\quad\ni\\hbar N^{--}\\dot c^-=(\\hbar\\omega_0/2)N^{-+}c^+.$$\nThe static Gram inverse initializes coefficients; the metric norm is $(c^+)^\\dagger N^{++}c^+ +(c^-)^\\dagger N^{--}c^-=1$. The invariant field object is $\\rho_f=\\mathrm{Tr}_a|\\Psi\\rangle\\langle\\Psi|$ and $\\int W(\\alpha)d^2\\alpha=1$. With $\\widetilde H=H-H_a$, $[\\widetilde H,\\sigma_x]=0$, whereas $\\dot{\\langle\\sigma_x\\rangle}=-\\omega_0\\langle\\sigma_y\\rangle$ in the usual Pauli convention for the full Hamiltonian. These identities explain why coherent-label motion alone is not harmonic radiation; equivalent causal term controls are accepted." |
| ], |
| "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 CL1, central physical object: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F2 (Derive a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.). 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 CL2, indispensable material component: O1 (Present normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.). Judge the role-specific failure facts, not the corresponding atom scores.", |
| "Required co primary claim CL3, indispensable material component: all of: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.). 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 CL2, principal mechanism or commissioned conclusion: M3 (Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.). Judge the role-specific failure facts, not the corresponding atom scores.", |
| "Required co primary claim CL3, principal mechanism or commissioned conclusion: M5 (Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.). Judge the role-specific failure facts, not the corresponding atom scores.", |
| "Required co primary claim CL4, principal mechanism or commissioned conclusion: M7 (Reconcile auxiliary models/controls with the complete no-RWA calculation, answering term contributions and amplitude dependence with the strongest conclusion supported by common physical endpoints.). 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 CL4, material validation/scope: V2 (Only when the submitted method, data, anomaly or claim triggers 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 CL1 central physical object: all of: F1 (Establish the complete no-RWA quantum Rabi Hamiltonian, specified initial states and four cases with consistent units, basis phases and coupling convention.); F2 (Derive a computable complete moving von Neumann lattice evolution with correct nonorthogonal initialization, Gram/metric treatment and cross-branch atomic-term coupling.).", |
| "Close CL2 indispensable material component: O1 (Present normalized first-cycle Case-A reduced-field phase-space evidence with valid object/time binding and full-model effects, exposing genuine branch motion, mixing, broadening or interference with reconstructible data.).", |
| "Close CL2 principal mechanism or commissioned conclusion: M3 (Explain from submitted intervention, phase-space or dipole evidence how relevant full-Hamiltonian terms produce field-branch separation/mixing, a changing material dipole and radiation. Atomic mixing of moving branches is canonical, not the only permissible formulation.).", |
| "Close CL3 indispensable material component: all of: O2 (Present a valid, reconstructible and adequately exposed Case-B 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O3 (Present a valid, reconstructible and adequately exposed Case-C 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.); O4 (Present a valid, reconstructible and adequately exposed Case-D 20-cycle material-dipole HHG spectrum with correct parameters, main harmonic structure, plateau/cutoff and comparable global morphology.).", |
| "Close CL3 principal mechanism or commissioned conclusion: M5 (Use all B-D spectra to explain cutoff extension and peak changes with initial amplitude, distinguishing physical trends from frequency reweighting or curve rescaling.).", |
| "Close CL4 principal mechanism or commissioned conclusion: M7 (Reconcile auxiliary models/controls with the complete no-RWA calculation, answering term contributions and amplitude dependence with the strongest conclusion supported by common physical endpoints.).", |
| "Close CL4 material validation/scope: V2 (Only when the submitted method, data, anomaly or claim triggers a concrete material risk, exclude it with discriminating evidence or narrow the threatened conclusion.).", |
| "Supporting claim CL5 is separately scored but does not determine overall closure: Positively state the two-level, single-mode, complete no-RWA and four-case evidence domain, distinguishing general phase-space/HHG conclusions from model-specific detail." |
| ] |
| }, |
| "references": [ |
| { |
| "citation": "Ákos Gombkötő, Sándor Varró, Péter Mati, and Péter Földi. 2020. *High-order harmonic generation as induced by a quantized field: Phase-space picture*. *Physical Review A*, 101, 013418.", |
| "url": "https://doi.org/10.1103/PhysRevA.101.013418", |
| "scientific_scope": "High-order harmonic generation as induced by a quantized field: Phase-space picture", |
| "anchors": [ |
| "Gombkoto et al. (2020), article pp.013418-2-3, Eqs.(1),(2),(8),(14) and paragraph preceding Eq.(15): complete no-RWA Hamiltonian, branch motion under field-plus-interaction and constant dipole if the atomic term is absent.", |
| "Gombkoto et al. (2020), article pp.013418-4-5, Eqs.(17)-(24): nonorthogonal coherent-state initialization, moving-lattice metric and atomic cross-branch mixing.", |
| "Gombkoto et al. (2020), article pp.013418-5-6, Sec.III.B, Eqs.(25)-(31), explicit reduced density operator paragraph: partial trace over atom and normalized field phase-space construction.", |
| "Gombkoto et al. (2020), article pp.013418-7-8, Eq.(34), Fig.5 upper/middle/lower spectra and caption: 20-cycle material-dipole spectra at increasing coherent amplitudes, peaks, plateau and growing cutoff. Peak fine detail is model-specific, not a compulsory exact match.", |
| "Gombkoto et al. (2020), article pp.013418-6-7, Eqs.(19),(24),(29), Fig.4(top) first-cycle illustration. The full moving-lattice task uses the complete reduced state; the minimal two-state discussion of Eqs.(32),(33) is illustrative and its smooth montage is not a unique full-model target.", |
| "Gombkoto et al. (2020), article pp.013418-3,6-8, Eqs.(16),(22),(23),(34), Sec.IV and final Sec.VI paragraphs: atomic term mixes branches and enables changing material dipole/radiation. Term interventions can establish equivalent causal evidence, but a changed line position alone is insufficient.", |
| "Gombkoto et al. (2020), article pp.013418-7-9, Sec.V peak-detail limitation and Sec.VI-VII generalization/scope; normalization and complete-lattice stability follow Eqs.(18),(24). Positive model scope and triggered validation are task duties, not a demand to reproduce one lattice size." |
| ] |
| } |
| ] |
| } |
|
|
