{
  "case_id": "Case34",
  "title": "Semiclassical two-step model with quantum input: Quantum-classical approach to strong-field ionization",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Bind target, pulse, ground state, TDSE outgoing-wave construction and same-case conventional-trajectory/direct-quantum references.",
      "award_conditions": [
        "Target, pulse, ground state, outgoing TDSE construction and conventional/direct-quantum references describe the same case."
      ],
      "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": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article pp. 053411-2-3, Eqs. (1)-(4), TDSE and ground-state paragraphs: The one-dimensional soft-core target, finite pulse, outgoing TDSE wave and same-case references bind production."
      ],
      "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": "Construct complex Gabor quantum-input seeding and physically correct phase-space weighting.",
      "award_conditions": [
        "The newly removed wave produces complex Gabor seeding with physically correct phase-space weights rather than probability-only input."
      ],
      "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": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article pp. 053411-4-5, Eqs. (19)-(21), Fig. 1(a,b) and sampling paragraphs: The complex Gabor transform of the newly absorbed wave, not its probability alone, seeds a phase-space-weighted ensemble."
      ],
      "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": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Propagate with semiclassical/post-pulse phase, define the reconstructible momentum observable and perform asymptotic coherent accumulation as one production-observable identity.",
      "award_conditions": [
        "Correct semiclassical/post-pulse phase, asymptotic momentum and coherent accumulation establish the production momentum observable."
      ],
      "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.",
        "Preserve independent correct work in F1, F2, O1, O2, O3, O4, O5 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": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article pp. 053411-4-5, Eqs. (13)-(18), (23)-(24): The quantum-input momentum observable coherently combines complex Gabor weights with the production trajectory phase and finite post-pulse remainder in asymptotic momentum."
      ],
      "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": "O5",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide a physically valid reconstructible adequately presented launch-content control or equivalent discriminating evidence independently exposing accessible nonzero longitudinal launch-momentum support, without requiring the phase-control branch.",
      "award_conditions": [
        "An independently valid launch-content control or equivalent discriminator exposes nonzero longitudinal launch support without requiring the phase-control branch.",
        "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": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Preserve independent correct work in O4, I2, M3 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.",
        "Launch-control output is judged on its own object/presentation/claim statuses, with no phase-control prerequisite.",
        "Failure of launch-content evidence does not erase independent phase-control output, phase identification or phase mechanism credit.",
        "Launch-content control is independently scoreable without phase control. Unrelated changes in complex phase or propagation cannot establish a launch-only cause."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article pp. 053411-7-8, Fig. 4(b), Fig. 5 and launch-momentum discussion: Restricting accessible longitudinal launch momenta changes support and provides an independent discriminator; the source comparisons use different display normalizations and do not impose raw height matching."
      ],
      "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": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide the same-case direct-TDSE momentum reference with physically valid reconstructible and adequately presented data.",
      "award_conditions": [
        "A physically valid same-case direct-TDSE momentum reference is reconstructible and adequately presented.",
        "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": [
        "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": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article p. 053411-6, Fig. 2(a-c), captions and comparison discussion: TDSE, conventional SCTS and full SCTSQI share the same physical case. SCTSQI improves support and interference positions while peak heights and near-zero extraction remain evidence-bounded, not pixel targets."
      ],
      "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 the same-case conventional SCTS momentum distribution with physically valid reconstructible and adequately presented data.",
      "award_conditions": [
        "A physically valid same-case conventional SCTS distribution is reconstructible and adequately presented.",
        "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": [
        "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": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article p. 053411-6, Fig. 2(a-c), captions and comparison discussion: TDSE, conventional SCTS and full SCTSQI share the same physical case. SCTSQI improves support and interference positions while peak heights and near-zero extraction remain evidence-bounded, not pixel targets."
      ],
      "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 the full quantum-input semiclassical SCTSQI asymptotic momentum distribution with physically valid reconstructible and adequately presented data.",
      "award_conditions": [
        "A physically valid full SCTSQI asymptotic momentum distribution is reconstructible and adequately presented.",
        "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": [
        "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": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article p. 053411-6, Fig. 2(a-c), captions and comparison discussion: TDSE, conventional SCTS and full SCTSQI share the same physical case. SCTSQI improves support and interference positions while peak heights and near-zero extraction remain evidence-bounded, not pixel targets."
      ],
      "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": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide a physically valid reconstructible adequately presented phase control or equivalent discriminating evidence isolating material complex-phase information and distinguishing Gabor seeding phase from trajectory phase, without requiring the launch-content branch.",
      "award_conditions": [
        "An independently valid phase control or equivalent discriminator isolates complex input phase while distinguishing it from trajectory phase.",
        "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": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Preserve independent correct work in O5, I3, 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.",
        "Phase-control output is judged on its own object/presentation/claim statuses, with no launch-control prerequisite.",
        "Failure of phase evidence does not erase independent launch-control output, launch identification or launch mechanism credit.",
        "Phase control is independently scoreable without launch-content control. Its physical change must isolate complex Gabor information rather than also remove trajectory phase or alter accessible launch support."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article p. 053411-7, Eq. (25), Fig. 4(a) and phase-removal discussion: Replacing complex G by its modulus while retaining trajectory phase is a canonical phase-only discriminator. Gabor-input phase and trajectory phase are not the same object."
      ],
      "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": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify same-case support, global morphology, claim-relevant interference positions and model ordering, separating nonessential peak-height mismatch.",
      "award_conditions": [
        "The candidate identifies same-case support, global morphology, claim-relevant interference positions and model ordering without treating nonessential heights as targets.",
        "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 [O1: Provide the same-case direct-TDSE momentum reference with physically valid reconstructible and adequately presented data.; O2: Provide the same-case conventional SCTS momentum distribution with physically valid reconstructible and adequately presented data.; O3: Provide the full quantum-input semiclassical SCTSQI asymptotic momentum distribution with physically valid reconstructible and adequately presented data.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "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": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article p. 053411-6, Fig. 2(a-c), captions and comparison discussion: TDSE, conventional SCTS and full SCTSQI share the same physical case. SCTSQI improves support and interference positions while peak heights and near-zero extraction remain evidence-bounded, not pixel targets."
      ],
      "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 material complex-phase information from the candidate's discriminating evidence, distinguishing Gabor seeding phase from trajectory phase.",
      "award_conditions": [
        "The candidate identifies the effect of complex Gabor-input phase from their independent discriminating output.",
        "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": [
        "O4: Provide a physically valid reconstructible adequately presented phase control or equivalent discriminating evidence isolating material complex-phase information and distinguishing Gabor seeding phase from trajectory phase, without requiring the launch-content branch. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O5, I3, 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.",
        "Phase-information identification requires the independently valid O4 phase-control output.",
        "Launch-content output, identification and mechanism remain independently judgeable when phase evidence fails.",
        "Phase control is independently scoreable without launch-content control. Its physical change must isolate complex Gabor information rather than also remove trajectory phase or alter accessible launch support."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article p. 053411-7, Eq. (25), Fig. 4(a) and phase-removal discussion: Replacing complex G by its modulus while retaining trajectory phase is a canonical phase-only discriminator. Gabor-input phase and trajectory phase are not the same object."
      ],
      "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 accessible longitudinal launch-momentum content independently of phase information from the candidate's discriminating evidence.",
      "award_conditions": [
        "The candidate identifies accessible longitudinal launch-momentum information independently of the phase-control conclusion.",
        "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": [
        "O5: Provide a physically valid reconstructible adequately presented launch-content control or equivalent discriminating evidence independently exposing accessible nonzero longitudinal launch-momentum support, without requiring the phase-control branch. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O4, I2, M3 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.",
        "Launch-content identification requires the independently valid O5 launch-control output.",
        "Phase-control output, identification and mechanism remain independently judgeable when launch evidence fails.",
        "Launch-content control is independently scoreable without phase control. Unrelated changes in complex phase or propagation cannot establish a launch-only cause."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article pp. 053411-7-8, Fig. 4(b), Fig. 5 and launch-momentum discussion: Restricting accessible longitudinal launch momenta changes support and provides an independent discriminator; the source comparisons use different display normalizations and do not impose raw height matching."
      ],
      "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": "Judge whether quantum-input SCTSQI improves on conventional SCTS relative to direct TDSE using the candidate's signal.",
      "award_conditions": [
        "Candidate momentum signals support the improvement/failure judgment of SCTSQI relative to conventional SCTS and direct TDSE.",
        "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 same-case support, global morphology, claim-relevant interference positions and model ordering, separating nonessential peak-height mismatch. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in 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 comparative conclusion depends on I1 same-case distribution evidence, not on closure of phase or launch-control branches. Preserve their independent identification/mechanism credit."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article p. 053411-6, Fig. 2(a-c), captions and comparison discussion: TDSE, conventional SCTS and full SCTSQI share the same physical case. SCTSQI improves support and interference positions while peak heights and near-zero extraction remain evidence-bounded, not pixel targets."
      ],
      "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": "Separate qualitative support agreement from quantitative agreement of interference positions.",
      "award_conditions": [
        "The judgment distinguishes qualitative support agreement from quantitative interference-position agreement.",
        "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 same-case support, global morphology, claim-relevant interference positions and model ordering, separating nonessential peak-height mismatch. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in 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.",
        "Qualitative/quantitative comparison depends on I1, not on closure of phase or launch controls. A non-full output verdict does not mechanically cap a properly bounded valid comparison."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article p. 053411-6, Fig. 2(a-c), captions and comparison discussion: TDSE, conventional SCTS and full SCTSQI share the same physical case. SCTSQI improves support and interference positions while peak heights and near-zero extraction remain evidence-bounded, not pixel targets."
      ],
      "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": "Physically distinguish complex Gabor-input phase from the accumulated trajectory phase.",
      "award_conditions": [
        "The candidate physically separates complex Gabor phase already present at seeding from subsequently accumulated trajectory/post-pulse phase.",
        "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.",
        "Explicitly distinguish the complex phase already carried by the Gabor input from the subsequent semiclassical trajectory/post-pulse phase; removing one is not removing the other."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "I2: Identify material complex-phase information from the candidate's discriminating evidence, distinguishing Gabor seeding phase from trajectory phase. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "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.",
        "phase mechanism credit requires the independent I2 phase-information signal.",
        "Phase control is independently scoreable without launch-content control. Its physical change must isolate complex Gabor information rather than also remove trajectory phase or alter accessible launch support."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article p. 053411-7, Eq. (25), Fig. 4(a) and phase-removal discussion: Replacing complex G by its modulus while retaining trajectory phase is a canonical phase-only discriminator. Gabor-input phase and trajectory phase are not the same object."
      ],
      "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": "Distinguish the effects of phase information and longitudinal launch-momentum support.",
      "award_conditions": [
        "The candidate distinguishes phase-information effects from accessible longitudinal launch-momentum effects using the separate evidence.",
        "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.",
        "Use independently discriminating launch-content evidence to separate accessible nonzero longitudinal momentum from phase information; an uncontrolled multi-object comparison is insufficient."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "I3: Identify accessible longitudinal launch-momentum content independently of phase information from the candidate's discriminating evidence. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "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.",
        "launch-content mechanism credit requires the independent I3 launch signal.",
        "Launch-content control is independently scoreable without phase control. Unrelated changes in complex phase or propagation cannot establish a launch-only cause."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article pp. 053411-7-8, Fig. 4(b), Fig. 5 and launch-momentum discussion: Restricting accessible longitudinal launch momenta changes support and provides an independent discriminator; the source comparisons use different display normalizations and do not impose raw height matching."
      ],
      "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": "Explain why the submitted controls or equivalent evidence isolate material quantum-input information rather than confound unrelated physical changes.",
      "award_conditions": [
        "The candidate explains why their controls isolate material information without unrelated physical changes; one confounded comparison cannot close both roles.",
        "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 [I2: Identify material complex-phase information from the candidate's discriminating evidence, distinguishing Gabor seeding phase from trajectory phase.; I3: Identify accessible longitudinal launch-momentum content independently of phase information from the candidate's discriminating evidence.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "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.",
        "joint attribution requires both independently scored phase and launch-content branches; either branch retains its own credit when the other fails.",
        "Both roles must be independently discriminated for the joint information attribution; a confounded comparison can support at most the physical fact it actually isolates."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article p. 053411-7, Fig. 4(a,b), Eq. (25) and separate-control discussion: Phase and launch-content comparisons isolate different quantum information. A comparison changing both does not independently identify each cause; either control can earn its own local credit."
      ],
      "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": "Address a material competing explanation emerging from candidate work or honestly restrict the affected claim.",
      "award_conditions": [
        "An actual material competing explanation is addressed or the affected scientific claim is honestly restricted.",
        "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": [
        "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": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article pp. 053411-6-7, extraction caveat, Fig. 3(a,b) and comparison/control discussion: Absorber, transform phase, sampling and confounded controls matter only where an actual material threat arises; source convergence procedures are not universal candidate duties."
      ],
      "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": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Limit conclusions to the submitted one-dimensional soft-core target/pulse and reliably established momentum/observable domain.",
      "award_conditions": [
        "The conclusion remains within the submitted one-dimensional soft-core pulse/target and reliably established momentum/observable domain.",
        "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": [
        "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.",
        "Evidence-bounded scope is independently judged from actual extraction and signal; the source mask caveat is not an automatic near-zero exclusion for another valid method."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article pp. 053411-6-8, near-zero mask-method caveat and Conclusion: Conclusion and reconstructibility follow the actual one-dimensional target/pulse and extraction domain. The source near-zero caveat is not automatically imposed on a different valid extraction."
      ],
      "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": "V1",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Provide reconstructible same-case signals and state extraction, representation and sampling limitations commensurate with the claim.",
      "award_conditions": [
        "Same-case signals are reconstructible and the actual extraction, representation and sampling limitations match the claim."
      ],
      "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.",
        "Evidence-bounded scope is independently judged from actual extraction and signal; the source mask caveat is not an automatic near-zero exclusion for another valid method."
      ],
      "equivalent_evidence": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article pp. 053411-6-8, near-zero mask-method caveat and Conclusion: Conclusion and reconstructibility follow the actual one-dimensional target/pulse and extraction domain. The source near-zero caveat is not automatically imposed on a different valid extraction."
      ],
      "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": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "If incoherent accumulation, transform phase, absorber, undersampling, confounded control, normalization or weak-TDSE-reference risk concretely emerges, discriminate it or restrict scope; otherwise record N/A with fixed credit.",
      "award_conditions": [
        "An actual coherent-sum, transform-phase, absorber, sampling, confounded-control, normalization or reference threat is discriminated or restricted; otherwise 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": [
        "Accept declared physically equivalent TDSE extraction, complex Gabor/phase-space representation, trajectory/asymptotic mapping and common normalization preserving complex input, trajectory phase, coherent accumulation and accessible momentum support.",
        "Functionally equivalent controls, reductions or interventions can replace canonical phase-removal and momentum-restriction comparisons when they independently isolate the same information without unrelated physical changes.",
        "Accept alternative signal displays/resolution mappings and evidence-bounded domain restrictions. Source bins, seed, Gabor width, propagation horizon, exact peak heights and original crop are not grading conditions."
      ],
      "source_support": [
        "Shvetsov-Shilovski and Lein (2019), article pp. 053411-6-7, extraction caveat, Fig. 3(a,b) and comparison/control discussion: Absorber, transform phase, sampling and confounded controls matter only where an actual material threat arises; source convergence procedures are not universal candidate duties."
      ],
      "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."
    }
  ],
  "case_scientific_rules": [
    "Let Psi_removed = (1-M) Psi be newly removed absorber wavefunction. The quantum input is G(x0,p0,t) = (1/sqrt(2 pi)) integral Psi_removed(x_prime,t) exp[-(x_prime-x0)^2/(2 delta0^2)] exp(-i p0 x_prime) dx_prime. Preserve its complex phase and phase-space weights, not only |G|^2.",
    "Sample initial points in the two outgoing absorbing-region phase-space domains, propagate under the stated soft-core force and attach the position-to-momentum semiclassical phase including convergent relative post-pulse potential contribution. Accumulate R(k) = |sum_m sum_{j to k} G(t_m,x0j,p0j) exp(i Phi_j)|^2 coherently in asymptotic momentum.",
    "A probability sum changes the central observable. Removing Gabor phase for a controlled comparison is not the same as removing trajectory phase. The source T = 4 t_f horizon is one implementation, not a hidden condition; any adequately supported horizon/asymptotic treatment is allowed.",
    "For the same target/pulse conventional SCTS is qualitatively consistent with TDSE but underestimates momentum width. Full SCTSQI better reproduces overall support and interference-extremum positions outside extraction-sensitive near-zero momentum. Nonessential peak-height differences are not absolute/pixel targets.",
    "A prominent peak or broad support alone is insufficient for a full comparison: inspect global morphology and claim-relevant secondary interference families after legitimate resolution, orientation, units, transform and normalization mapping. Honest restrictions can support a correct narrower comparison even when an output atom is not full.",
    "One canonical phase intervention replaces complex G by |G| while retaining Phi and produces severe qualitative loss. One launch intervention restricts longitudinal initial-momentum support while keeping other physics fixed; it narrows the distribution without making it identical to conventional SCTS. These are examples, not unique prescribed controls.",
    "Phase and launch-content output controls are independently scoreable. Neither requires the other control to exist. A single confounded comparison changing both ingredients cannot independently establish their roles. Merely varying numerical accuracy is mechanism evidence only if it actually exposes a claim-changing alternative.",
    "Both phase information and accessible longitudinal momentum can matter to support/interference; their demonstration does not establish exclusive causation or universal method superiority. A near-zero mask limitation is applicable only when the candidate's actual extraction/evidence exposes an equivalent risk, not as an automatic domain exclusion.",
    "Concrete risks include incoherent accumulation, transform-origin/phase errors, contaminated absorber input, interference-erasing undersampling, multi-object controls, independently scaled apparent model ordering and an under-resolved TDSE reference. No fixed Gabor width, mask, sample count, seed, momentum range or preferred control 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.",
    "For newly removed wave $\\widetilde\\Psi=(1-M)\\Psi$, $G(x_0,p_0,t)=(2\\pi)^{-1/2}\\int dx\\,\\widetilde\\Psi(x,t)e^{-(x-x_0)^2/(2\\delta_0^2)}e^{-ip_0x}$ (Eq. (19)). The observable is $R(k)=|\\sum_{m,j\\to k}G(t_m,x_{0j},p_{0j})e^{i\\Phi_{0j}}|^2$ (Eq. (24)); $|G|^2$ alone or incoherent accumulation changes the production object.",
    "The SCTSQI production phase is $\\Phi_0=-\\int_{t_0}^{\\infty}[v^2/2-x^2/(x^2+a^2)^{3/2}-1/\\sqrt{x^2+a^2}]dt$ (Eq. (23)). Do not import the conventional SCTS launch endpoint or $I_pt_0$ again into this quantum-seeded phase; the incoming complex quantum phase is carried by G.",
    "The finite relative post-pulse term can use $\\int_{t_f}^{\\infty}[x(t)^2/(x(t)^2+a^2)^{3/2}-2Et^2/(2Et^2+a^2)^{3/2}]dt$ (Eq. (18)), discarding only the same-bin common divergence. An equivalent convergent asymptotic treatment is accepted. Phase-only control replaces G by $|G|$ while preserving $e^{i\\Phi_0}$ (Eq. (25)); a launch-support control is physically distinct."
  ],
  "closure_requirements": {
    "RC0": [
      "Required claim CL1, central object: All of [F1: Bind target, pulse, ground state, TDSE outgoing-wave construction and same-case conventional-trajectory/direct-quantum references.; F2: Construct complex Gabor quantum-input seeding and physically correct phase-space weighting.; F3: Propagate with semiclassical/post-pulse phase, define the reconstructible momentum observable and perform asymptotic coherent accumulation as one production-observable identity.]. 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: All of [O1: Provide the same-case direct-TDSE momentum reference with physically valid reconstructible and adequately presented data.; O2: Provide the same-case conventional SCTS momentum distribution with physically valid reconstructible and adequately presented data.; O3: Provide the full quantum-input semiclassical SCTSQI asymptotic momentum distribution with physically valid reconstructible and adequately presented data.]. 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: All of [M1: Judge whether quantum-input SCTSQI improves on conventional SCTS relative to direct TDSE using the candidate's signal.; M2: Separate qualitative support agreement from quantitative agreement of interference positions.; M3: Physically distinguish complex Gabor-input phase from the accumulated trajectory phase.; M4: Distinguish the effects of phase information and longitudinal launch-momentum support.; M5: Explain why the submitted controls or equivalent evidence isolate material quantum-input information rather than confound unrelated physical changes.]. 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 CL2, material validation: V2: If incoherent accumulation, transform phase, absorber, undersampling, confounded control, normalization or weak-TDSE-reference risk concretely emerges, discriminate it or restrict scope; otherwise record N/A with fixed credit.. 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": "N. I. Shvetsov-Shilovski and M. Lein. 2019. Semiclassical two-step model with quantum input: Quantum-classical approach to strong-field ionization. Physical Review A, 100, 053411.",
      "url": "https://doi.org/10.1103/PhysRevA.100.053411",
      "scientific_scope": "Same-case quantum-input semiclassical momentum distributions, phase/coherent accumulation and separately discriminating phase versus longitudinal-launch information. Source fine-scale implementation settings and external feasibility metrics are not numerical targets.",
      "anchors": [
        "article pp. 053411-2-3, Eqs. (1)-(4), TDSE and ground-state paragraphs",
        "article pp. 053411-4-5, Eqs. (19)-(21), Fig. 1(a,b) and sampling paragraphs",
        "article pp. 053411-4-5, Eqs. (13)-(18), (23)-(24)",
        "article p. 053411-6, Fig. 2(a-c), captions and comparison discussion",
        "article p. 053411-7, Eq. (25), Fig. 4(a) and phase-removal discussion",
        "article pp. 053411-7-8, Fig. 4(b), Fig. 5 and launch-momentum discussion",
        "article p. 053411-7, Fig. 4(a,b), Eq. (25) and separate-control discussion",
        "article pp. 053411-6-7, extraction caveat, Fig. 3(a,b) and comparison/control discussion",
        "article pp. 053411-6-8, near-zero mask-method caveat and Conclusion"
      ]
    }
  ]
}