{
  "case_id": "Case31",
  "title": "Semiclassical two-step model for strong-field ionization",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Bind target/pulse, instantaneous field-magnitude and Stark-shifted launch density, and the physically outgoing-side tunnel exit.",
      "award_conditions": [
        "Target, pulse, instantaneous magnitude/Stark-shifted tunneling weight and physically outgoing-side exit define the launch consistently."
      ],
      "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.",
        "This obligation is independently judgeable; no upstream failure is propagated into it.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article pp. 013415-3-4, Eqs. (9)-(14): Instantaneous field magnitude, Stark-shifted binding and the outgoing parabolic exit define the launch. The field sign is not substituted for its magnitude in the tunneling weight."
      ],
      "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": "Correctly instantiate the 800-nm nonzero-longitudinal-velocity launch case while retaining the same transverse weight family.",
      "award_conditions": [
        "The 800-nm nonzero-longitudinal-velocity launch is instantiated without changing the specified transverse weight family."
      ],
      "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.",
        "This obligation is independently judgeable; no upstream failure is propagated into it.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article pp. 013415-9-10, Eqs. (47)-(48), Fig. 6(a-c), Fig. 7 and discussion: The nonzero-longitudinal-velocity 800-nm launch is an independent first-step change under the same transverse weight; candidate-presented contrast is needed for identification."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Construct an unbiased coherent complex-amplitude photoelectron estimator, using importance sampling, explicit amplitude weights or a functionally equivalent unbiased route.",
      "award_conditions": [
        "The sampling density and any explicit amplitude weights give an unbiased coherent complex-amplitude estimator.",
        "Show that the chosen sampling density and explicit amplitude weights preserve the intended coherent amplitude measure; unit weights require the corresponding amplitude-level sampling, not an uncorrected probability-density draw."
      ],
      "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.",
        "The coherent estimator identity is independently judgeable and may be implemented by importance sampling, explicit amplitude weights or another unbiased coherent route.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Estimator correctness, SCTS action, QTMC comparator and finite-tail interpretation are independently judgeable physical facts. One failure propagates only where that exact fact is necessary, not to all four obligations."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article pp. 013415-4 and 013415-6-7, Eq. (15), importance-sampling discussion and Eq. (41): The estimator sums amplitudes coherently with unbiased sampling/weights, not probabilities. Sampling the probability and then using unit amplitudes is not automatically equivalent."
      ],
      "rc_relation": "RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "F4",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Map post-pulse trajectories to outgoing asymptotic momentum using Kepler/scattering-equivalent dynamics rather than pulse-end momentum.",
      "award_conditions": [
        "Pulse-end trajectories are mapped to outgoing asymptotic momenta by the correct Coulomb/scattering dynamics."
      ],
      "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.",
        "This obligation is independently judgeable; no upstream failure is propagated into it.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article p. 013415-6, Sec. III.B, Eqs. (26)-(29): Outgoing Kepler asymptotic momentum differs from finite pulse-end momentum; a scattering-equivalent mapping is accepted."
      ],
      "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": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide a reconstructible 800-nm coherent SCTS distribution resolving broad support, above-threshold-ionization/radial structure and material low-energy interference.",
      "award_conditions": [
        "The coherent 800-nm SCTS distribution is reconstructible and resolves broad support, ATI/radial structure and material low-energy interference.",
        "The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [F3: Construct an unbiased coherent complex-amplitude photoelectron estimator, using importance sampling, explicit amplitude weights or a functionally equivalent unbiased route.; F4: Map post-pulse trajectories to outgoing asymptotic momentum using Kepler/scattering-equivalent dynamics rather than pulse-end momentum.] 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.",
        "All named physical premises are necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "A shared outgoing observable and case binding are required for the comparison. Preserve a valid independent TDSE reference or one valid semiclassical branch even when another branch/action fails."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article p. 013415-8, Fig. 1(a-c), Fig. 2, and baseline comparison text: The 800-nm coherent QTMC/TDSE/SCTS objects share broad support and ATI structure but differ materially in low-energy interference; source layout and exact node positions are not targets."
      ],
      "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": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide a reconstructible 800-nm coherent QTMC distribution preserving the independent comparator action and outgoing-observable identity.",
      "award_conditions": [
        "The coherent 800-nm QTMC output retains its independent assigned action and the same outgoing-observable identity.",
        "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": [
        "F4: Map post-pulse trajectories to outgoing asymptotic momentum using Kepler/scattering-equivalent dynamics rather than pulse-end momentum. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "A shared outgoing observable and case binding are required for the comparison. Preserve a valid independent TDSE reference or one valid semiclassical branch even when another branch/action fails."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article p. 013415-8, Fig. 1(a-c), Fig. 2, and baseline comparison text: The 800-nm coherent QTMC/TDSE/SCTS objects share broad support and ATI structure but differ materially in low-energy interference; source layout and exact node positions are not 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": "Establish a reconstructible 800-nm single-active-electron TDSE/reference object and common-observable bridge to the semiclassical comparison.",
      "award_conditions": [
        "An independent single-active-electron 800-nm TDSE/reference object is reconstructible and physically comparable to the semiclassical observable.",
        "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.",
        "This obligation is independently judgeable; no upstream failure is propagated into it.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "A shared outgoing observable and case binding are required for the comparison. Preserve a valid independent TDSE reference or one valid semiclassical branch even when another branch/action fails."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article pp. 013415-7-9, TDSE-method Eqs. (43)-(44), Figs. 1-2 and Fig. 4(a,b): The independent 800-nm quantum reference supports specific low-energy/interference comparisons, not universal quantitative superiority over all energies."
      ],
      "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 reconstructible 800/1200/1600-nm semiclassical transfer evidence with auditable branch/case identities and uncertainty.",
      "award_conditions": [
        "800/1200/1600-nm transfer evidence retains branch/case identities and uncertainty in comparable semiclassical quantities.",
        "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.",
        "This obligation is independently judgeable; no upstream failure is propagated into it.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article p. 013415-9, Fig. 4(a-f), Fig. 5(a-c) and wavelength/Keldysh discussion: 800/1200/1600-nm transfer probes the changing domain. Peak-normalized energy and yield-normalized angular reductions are distinct; fewer wavelengths permit narrower domain claims only."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify material low-energy interference relations and their supported domain from the candidate's SCTS, QTMC and 800-nm reference evidence.",
      "award_conditions": [
        "The candidate identifies low-energy interference relationships and their supported domain across SCTS, QTMC and the 800-nm reference.",
        "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 a reconstructible 800-nm coherent SCTS distribution resolving broad support, above-threshold-ionization/radial structure and material low-energy interference.; O2: Provide a reconstructible 800-nm coherent QTMC distribution preserving the independent comparator action and outgoing-observable identity.; O3: Establish a reconstructible 800-nm single-active-electron TDSE/reference object and common-observable bridge to the semiclassical comparison.] 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.",
        "All named physical premises are necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "A shared outgoing observable and case binding are required for the comparison. Preserve a valid independent TDSE reference or one valid semiclassical branch even when another branch/action fails."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article p. 013415-8, Fig. 1(a-c), Fig. 2, and baseline comparison text: The 800-nm coherent QTMC/TDSE/SCTS objects share broad support and ATI structure but differ materially in low-energy interference; source layout and exact node positions are not 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": "Use computed evidence to identify the relative-action and finite-remainder effects distinguishing SCTS and QTMC.",
      "award_conditions": [
        "The candidate identifies computed effects of the relative-action difference and finite post-pulse remainder.",
        "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 a reconstructible 800-nm coherent SCTS distribution resolving broad support, above-threshold-ionization/radial structure and material low-energy interference.; O2: Provide a reconstructible 800-nm coherent QTMC distribution preserving the independent comparator action and outgoing-observable identity.] 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.",
        "All named physical premises are necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "A shared outgoing observable and case binding are required for the comparison. Preserve a valid independent TDSE reference or one valid semiclassical branch even when another branch/action fails."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article p. 013415-8, Fig. 3(a-d) and phase discussion; p. 013415-6, Eq. (40): Finite post-pulse Coulomb relative phase changes low-energy interference; the optional single-cycle panels and named phase-ablation layout are not compulsory."
      ],
      "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 the first-step launch effect on support/agreement solely from candidate-presented 800-nm zero/nonzero-longitudinal-velocity comparisons; a prescription description or examiner discovery in unpresented data cannot replace this identification.",
      "award_conditions": [
        "The candidate explicitly identifies the launch effect from presented 800-nm zero/nonzero-longitudinal comparisons, not an unshown array or prescription alone.",
        "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": [
        "F2: Correctly instantiate the 800-nm nonzero-longitudinal-velocity launch case while retaining the same transverse weight family. 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.",
        "Only the named physical premise is necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "The zero/nonzero-longitudinal launch effect requires candidate-presented 800-nm evidence and identification; continuum-action evidence alone does not establish it."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article pp. 013415-9-10, Eqs. (47)-(48), Fig. 6(a-c), Fig. 7 and discussion: The nonzero-longitudinal-velocity 800-nm launch is an independent first-step change under the same transverse weight; candidate-presented contrast is needed for identification."
      ],
      "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": "Establish same-bin relative phases equal to the defined SCTS mixed-generating-function action, preserving endpoint, sign, integrand and finite-part identity.",
      "award_conditions": [
        "Same-bin relative phases equal the assigned mixed-generating-function SCTS action, including endpoint, sign, integrand and finite-part identity.",
        "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.",
        "Show the same-bin relative-phase mapping, including the negative launch endpoint and doubled Coulomb term, or a genuinely equal generating-function rearrangement; a different action cannot be accepted merely by relabeling."
      ],
      "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.",
        "The SCTS action identity is judged independently from the estimator implementation and its later physical interpretation.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Estimator correctness, SCTS action, QTMC comparator and finite-tail interpretation are independently judgeable physical facts. One failure propagates only where that exact fact is necessary, not to all four obligations."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article pp. 013415-5-6, Eqs. (18)-(25), (30)-(40): The mixed position-to-momentum generating function fixes endpoint sign, the doubled Coulomb integrand and the trajectory-dependent finite post-pulse part."
      ],
      "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": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain that the common same-bin asymptotic divergence cancels while the trajectory-dependent finite post-pulse Coulomb remainder must be retained.",
      "award_conditions": [
        "The common same-bin asymptotic divergence is correctly removed while the trajectory-dependent finite Coulomb remainder is retained.",
        "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.",
        "Distinguish the common energy-dependent divergence from the finite trajectory-dependent Coulomb remainder; only the former may be discarded."
      ],
      "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.",
        "The finite-part explanation is judged on its own evidence; a formula transcription defect in M1 is not allowed to erase an independently correct explanation, or vice versa.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Estimator correctness, SCTS action, QTMC comparator and finite-tail interpretation are independently judgeable physical facts. One failure propagates only where that exact fact is necessary, not to all four obligations."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article p. 013415-6, Sec. III.B, Eqs. (30)-(40) and regularization derivation: Only common same-bin divergences cancel; the angular-momentum-dependent finite Coulomb remainder survives."
      ],
      "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": "Establish an independent same-bin comparator action explicitly mapped to the defined QTMC phase.",
      "award_conditions": [
        "The independently implemented comparator is explicitly equal to the assigned QTMC same-bin phase, not another action renamed as QTMC.",
        "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.",
        "This obligation is independently judgeable; no upstream failure is propagated into it.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "Estimator correctness, SCTS action, QTMC comparator and finite-tail interpretation are independently judgeable physical facts. One failure propagates only where that exact fact is necessary, not to all four obligations."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article pp. 013415-4-5, Eq. (17) and paragraph comparing it with Eqs. (22),(25): QTMC is a separately defined comparator action, not a renamed SCTS result; equivalent phase bookkeeping requires equality of same-bin relative phases."
      ],
      "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": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Causally connect the candidate's low-energy interference relation to the correct SCTS/QTMC relative-action and finite-Coulomb difference.",
      "award_conditions": [
        "The candidate explains the low-energy interference relation using the actual SCTS/QTMC action and finite-Coulomb differences.",
        "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 [I1: Identify material low-energy interference relations and their supported domain from the candidate's SCTS, QTMC and 800-nm reference evidence.; I2: Use computed evidence to identify the relative-action and finite-remainder effects distinguishing SCTS and QTMC.; M2: Explain that the common same-bin asymptotic divergence cancels while the trajectory-dependent finite post-pulse Coulomb remainder must be retained.; M3: Establish an independent same-bin comparator action explicitly mapped to the defined QTMC 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.",
        "All named physical premises are necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "A shared outgoing observable and case binding are required for the comparison. Preserve a valid independent TDSE reference or one valid semiclassical branch even when another branch/action fails."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article p. 013415-8, Fig. 3(a-d) and phase discussion; p. 013415-6, Eq. (40): Finite post-pulse Coulomb relative phase changes low-energy interference; the optional single-cycle panels and named phase-ablation layout are not compulsory."
      ],
      "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": "State which observables, energy domains and quantitative scales the 800-nm quantum reference actually supports for model credibility.",
      "award_conditions": [
        "The credibility conclusion states which observable, energy domain and quantitative scales the quantum reference actually supports.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "All of [O3: Establish a reconstructible 800-nm single-active-electron TDSE/reference object and common-observable bridge to the semiclassical comparison.; I1: Identify material low-energy interference relations and their supported domain from the candidate's SCTS, QTMC and 800-nm reference 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.",
        "All named physical premises are necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "A shared outgoing observable and case binding are required for the comparison. Preserve a valid independent TDSE reference or one valid semiclassical branch even when another branch/action fails."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article pp. 013415-7-9, TDSE-method Eqs. (43)-(44), Figs. 1-2 and Fig. 4(a,b): The independent 800-nm quantum reference supports specific low-energy/interference comparisons, not universal quantitative superiority over all energies."
      ],
      "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": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Distinguish the independent effects of continuum-phase treatment and first-step longitudinal launch input.",
      "award_conditions": [
        "Continuum-phase effects and longitudinal launch-input effects are separately identified and causally distinguished.",
        "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: Use computed evidence to identify the relative-action and finite-remainder effects distinguishing SCTS and QTMC.; I3: Identify the first-step launch effect on support/agreement solely from candidate-presented 800-nm zero/nonzero-longitudinal-velocity comparisons; a prescription description or examiner discovery in unpresented data cannot replace this identification.] 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.",
        "All named physical premises are necessary for this downstream claim.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "The zero/nonzero-longitudinal launch effect requires candidate-presented 800-nm evidence and identification; continuum-action evidence alone does not establish it."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article pp. 013415-8-10, Fig. 3, Figs. 6-7 and Conclusion: Continuum-action and launch-input changes are distinct physical causes and need separately discriminating evidence."
      ],
      "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Bound the conclusion using completed wavelength/Keldysh and low/high-energy evidence. Fewer than three wavelengths can earn narrower evidenced-domain credit but cannot be called complete three-wavelength coverage.",
      "award_conditions": [
        "The conclusion is bounded by completed wavelength, Keldysh and low/high-energy evidence; narrower coverage is not called a complete three-wavelength test.",
        "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.",
        "A supported narrower domain is independently judgeable from the full three-wavelength O4 coverage atom.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice.",
        "A sound narrower wavelength/energy/Keldysh conclusion is not erased solely because the three-wavelength coverage atom O4 is incomplete."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article p. 013415-9, Fig. 4(a-f), Fig. 5(a-c) and wavelength/Keldysh discussion: 800/1200/1600-nm transfer probes the changing domain. Peak-normalized energy and yield-normalized angular reductions are distinct; fewer wavelengths permit narrower domain claims only."
      ],
      "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": "Limit conclusions to single-active-electron hydrogen, the stated pulse/launch/wavelength cases and semiclassical/tunneling assumptions.",
      "award_conditions": [
        "The claim is explicitly restricted to single-active-electron hydrogen, supplied cases and semiclassical/tunneling assumptions."
      ],
      "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.",
        "This obligation is independently judgeable; no upstream failure is propagated into it.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article pp. 013415-2-3, tunneling/semiclassical assumptions; pp. 013415-9-10, domain and Conclusion: Single-active-electron hydrogen and the tested pulse/launch/Keldysh domain bound the result. Material phase/launch/binning risks need a concrete trigger, not a fixed trajectory count."
      ],
      "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": "Only when candidate method, data, anomaly or claim triggers a concrete material risk capable of changing the central conclusion, discriminate it or restrict the affected scope.",
      "award_conditions": [
        "A concrete candidate-arising phase, launch, sampling, reference or domain threat is discriminated or restricted; otherwise apply N/A."
      ],
      "applicability_and_na": [
        "Activate only for a concrete material risk arising from the candidate method, data, anomaly or claim; no fixed test is required in the absence of a trigger.",
        "Without a triggered risk record N/A and award 0.5 without positive validation evidence; this neither blocks RC4 nor triggers RC3.",
        "When triggered, accept functionally equivalent discriminating evidence or a justified restriction of the threatened claim."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "This obligation is independently judgeable; no upstream failure is propagated into it.",
        "Credit for branches not using the failed premise is preserved; the same defect is not charged twice."
      ],
      "equivalent_evidence": [
        "Accept physically equivalent gauges, generating functions, endpoint placement, Coulomb-tail regularization, coordinates, momentum measures and common normalizations only with an explicit same-bin phase mapping to the assigned actions.",
        "Accept importance sampling, direct explicit amplitude weights or other unbiased coherent estimators, and scattering-equivalent asymptotic mappings. No fixed trajectory count, seed, bin or analytic-tail formula is required.",
        "Alternative reconstructible distributions/reductions, controlled rearrangements and launch/action contrasts may replace source panels. Preserve correct narrower domain credit without falsely claiming full wavelength coverage."
      ],
      "source_support": [
        "Shvetsov-Shilovski et al. (2016), article pp. 013415-2-3, tunneling/semiclassical assumptions; pp. 013415-9-10, domain and Conclusion: Single-active-electron hydrogen and the tested pulse/launch/Keldysh domain bound the result. Material phase/launch/binning risks need a concrete trigger, not a fixed trajectory count."
      ],
      "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": [
    "For V(r) = -Z/r, the assigned SCTS mixed initial-position/final-momentum phase is Phi_SCTS = -p0 dot r0 + Ip t0 - FP integral_{t0}^infinity [p^2/2 + V - r dot grad V] dt = -p0 dot r0 + Ip t0 - FP integral [p^2/2 - 2Z/r] dt.",
    "The independent assigned comparator is Phi_QTMC = Ip t0 - FP integral_{t0}^infinity [p^2/2 + V] dt = Ip t0 - FP integral [p^2/2 - Z/r] dt. Renaming another action SCTS/QTMC does not establish equivalence. Alternative generating functions must explicitly reproduce same-bin relative phases, including the endpoint when p0 dot r0 is nonzero.",
    "After the pulse positive-energy trajectories follow outgoing Kepler hyperbolae. Map to scattering-equivalent asymptotic momentum, not momentum at pulse end. The same-final-cell common divergent phase cancels; the trajectory-dependent finite Coulomb remainder remains. No particular analytic tail formula is compulsory.",
    "Use the instantaneous field magnitude in tunneling weight/parabolic-exit equations. For positive Fz the positive-eta exit gives z0 = -eta0/2; field reversal reverses the laboratory side. An inner or opposite-side root changes the launch identity, not a harmless numerical convention.",
    "The coherent distribution is the modulus square of the complex trajectory-amplitude sum in each asymptotic momentum cell. Sampling from sqrt(w) with unit amplitudes or direct sampling with explicit weights is accepted when unbiased. Summing probabilities gives incoherent CTMC, not the required interference observable.",
    "At 800 nm, eight cycles and 9e13 W/cm^2, the distributions are axial/symmetric with ATI/radial structure. Material low-energy SCTS nodal structure is closer to the quantum reference than QTMC under supported resolution; different Coulomb phases explain this relation. No exact node coordinates, hidden low-momentum crop or display floor is required.",
    "Finite post-pulse Coulomb phase can materially alter low-energy interference. A source single-cycle control is context only; any computed comparison isolating the same action difference without unrelated ingredient changes is accepted.",
    "The 800/1200/1600-nm semiclassical cases test wavelength/Keldysh transfer. Only 800-nm TDSE is a required quantum-reference branch; full longer-wavelength TDSE is not hidden work. Higher-energy mismatch can arise from quasistatic longitudinal launch support, independently of continuum action.",
    "For 800 nm the specified nonzero initial longitudinal velocity changes first-step kinematics while retaining transverse weights and can improve spread/energy-angular agreement. Claim this only from presented comparison evidence; examiner reconstruction cannot create the candidate's launch-effect identification.",
    "Relevant risks include wrong exit, inequivalent action, sampling/bin aliasing, incorrect finite part, pulse-end momentum, insufficient reference resolution, normalization-manufactured ordering and unsupported tunneling-domain extrapolation. Source figures establish robust structures; external feasibility reports do not provide local pointwise numerical standards.",
    "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 Coulomb $V=-Z/r$, the assigned SCTS action is $\\Phi_{\\rm SCTS}=-\\mathbf v_0\\cdot\\mathbf r_0+I_pt_0-\\int_{t_0}^{\\infty}[p^2/2-2Z/r]dt$ (Eq. (22)); generally the integrand is $p^2/2+V-\\mathbf r\\cdot\\nabla V$ (Eq. (25)). The QTMC comparator is $\\Phi_{\\rm QTMC}=I_pt_0-\\int_{t_0}^{\\infty}[p^2/2-Z/r]dt$ (Eq. (17)), under the assigned endpoint convention. Gauge/generating-function changes must prove equality of same-bin relative phases; renaming a different action is not equivalence.",
    "For hydrogen $Z=1$, let $E>0$, $b=(2E)^{-1}$, $g=\\sqrt{1+2EL^2}$. After removal of common same-bin divergences, the finite Coulomb remainder is $\\widetilde\\Phi_f^C=-Z\\sqrt b[\\ln g+\\operatorname{arsinh}(\\mathbf r_f\\cdot\\mathbf p_f/(g\\sqrt b))]$ (Eq. (40)). It is trajectory dependent and cannot be discarded with the common divergent phase.",
    "The estimator has $R(\\mathbf k)\\propto|\\sum_{j\\to\\mathbf k}a_je^{i\\Phi_j}|^2$ with an unbiased amplitude measure (Eq. (15), importance-sampling discussion). Outgoing energy obeys $k^2/2=p_f^2/2-1/r_f$ and the direction follows the outgoing Coulomb/Kepler map (Eqs. (26)-(29)); finite pulse-end momentum is not the asymptotic observable.",
    "The launch weight is $w(t_0,v_\\perp)\\propto\\exp[-2\\kappa^3/(3F(t_0))]\\exp[-\\kappa v_\\perp^2/F(t_0)]$, with the assigned Stark binding and $F=|\\mathbf F|$ (Eqs. (9),(13)). The parabolic exit uses the outgoing side of Eqs. (10)-(12); changing longitudinal launch must not silently change this transverse weight or action branch."
  ],
  "closure_requirements": {
    "RC0": [
      "Required claim CL1, central object: All of [F1: Bind target/pulse, instantaneous field-magnitude and Stark-shifted launch density, and the physically outgoing-side tunnel exit.; F3: Construct an unbiased coherent complex-amplitude photoelectron estimator, using importance sampling, explicit amplitude weights or a functionally equivalent unbiased route.; F4: Map post-pulse trajectories to outgoing asymptotic momentum using Kepler/scattering-equivalent dynamics rather than pulse-end momentum.; O1: Provide a reconstructible 800-nm coherent SCTS distribution resolving broad support, above-threshold-ionization/radial structure and material low-energy interference.; M1: Establish same-bin relative phases equal to the defined SCTS mixed-generating-function action, preserving endpoint, sign, integrand and finite-part identity.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL2, central object: M3: Establish an independent same-bin comparator action explicitly mapped to the defined QTMC phase.. 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 CL2, indispensable component: All of [O2: Provide a reconstructible 800-nm coherent QTMC distribution preserving the independent comparator action and outgoing-observable identity.; O3: Establish a reconstructible 800-nm single-active-electron TDSE/reference object and common-observable bridge to the semiclassical comparison.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL3, indispensable component: All of [F2: Correctly instantiate the 800-nm nonzero-longitudinal-velocity launch case while retaining the same transverse weight family.; O4: Provide reconstructible 800/1200/1600-nm semiclassical transfer evidence with auditable branch/case identities and uncertainty.]. 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 CL1, principal mechanism: M2: Explain that the common same-bin asymptotic divergence cancels while the trajectory-dependent finite post-pulse Coulomb remainder must be retained.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL2, principal mechanism: M4: Causally connect the candidate's low-energy interference relation to the correct SCTS/QTMC relative-action and finite-Coulomb difference.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL3, principal mechanism: M6: Distinguish the independent effects of continuum-phase treatment and first-step longitudinal launch input.. 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 CL5, material validation: V2: Only when candidate method, data, anomaly or claim triggers a concrete material risk capable of changing the central conclusion, discriminate it or restrict the affected scope.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "All indispensable signal and principal-mechanism roles are substantially supported, but a concrete triggered material risk remains unresolved and inadequately restricted.",
      "Establish the failure mode, candidate origin, fair task/knowledge basis, threatened central conclusion, insufficiency of submitted evidence, and equivalent resolution or scope restriction. Missing an examiner-preferred check alone never suffices."
    ],
    "RC4": [
      "Every nonempty required role in every indispensable and co-primary claim above is scientifically established from candidate evidence, with the correct case/model/observable identities and evidence-bounded conclusion.",
      "All applicable material risks are discriminated or honestly restricted; no unresolved material ambiguity remains. Risk N/A does not block closure or supply positive validation evidence. Honest limitations cannot repair a false signal or mechanism.",
      "Select the most severe failed required role if any; otherwise RC4. No score threshold, score ceiling or required display/solver checklist determines this classification."
    ]
  },
  "references": [
    {
      "citation": "N. I. Shvetsov-Shilovski, M. Lein, L. B. Madsen, E. Räsänen, C. Lemell, J. Burgdörfer, D. G. Arbó, and K. Tőkési. 2016. Semiclassical two-step model for strong-field ionization. Physical Review A, 94, 013415.",
      "url": "https://doi.org/10.1103/PhysRevA.94.013415",
      "scientific_scope": "Coherent semiclassical outgoing distributions, independent SCTS/QTMC action identities and finite Coulomb remainder, 800-nm quantum comparison, launch sensitivity and wavelength-domain limits. Source nodes and external feasibility metrics are not exact numerical targets.",
      "anchors": [
        "article pp. 013415-3-4, Eqs. (9)-(14)",
        "article pp. 013415-9-10, Eqs. (47)-(48), Fig. 6(a-c), Fig. 7 and discussion",
        "article pp. 013415-4 and 013415-6-7, Eq. (15), importance-sampling discussion and Eq. (41)",
        "article p. 013415-6, Sec. III.B, Eqs. (26)-(29)",
        "article p. 013415-8, Fig. 1(a-c), Fig. 2, and baseline comparison text",
        "article pp. 013415-7-9, TDSE-method Eqs. (43)-(44), Figs. 1-2 and Fig. 4(a,b)",
        "article p. 013415-9, Fig. 4(a-f), Fig. 5(a-c) and wavelength/Keldysh discussion",
        "article p. 013415-8, Fig. 3(a-d) and phase discussion; p. 013415-6, Eq. (40)",
        "article pp. 013415-5-6, Eqs. (18)-(25), (30)-(40)",
        "article p. 013415-6, Sec. III.B, Eqs. (30)-(40) and regularization derivation",
        "article pp. 013415-4-5, Eq. (17) and paragraph comparing it with Eqs. (22),(25)",
        "article pp. 013415-8-10, Fig. 3, Figs. 6-7 and Conclusion",
        "article pp. 013415-2-3, tunneling/semiclassical assumptions; pp. 013415-9-10, domain and Conclusion"
      ]
    }
  ]
}