cases/case03/grading_rubric.json

{
  "case_id": "Case03",
  "title": "Case03 — Efficient time-sampling method in Coulomb-corrected strong-field approximation",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.",
      "award_conditions": [
        "All six signed-plane objects and coherent cell accumulation are defined, with absolute-area Jp/Jq separated from cell/proposal factors and normalization; determinant orientation is not a phase."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F2, O1, O2, O3, O4, O5, O6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases."
      ],
      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.",
      "award_conditions": [
        "The declared phase, launch, propagation, asymptotic continuation and finite-tail equations distinguish adiabatic QTMC from q-labelled nonadiabatic CCSFA."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F1, O1, O2, O3, O4, O5, O6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-2-4, Eqs.(7)-(16),(22)-(28),(33)-(36): direct amplitude, nonadiabatic launch, Coulomb dynamics and -2/r action. Operational finite asymptotic/tail closure is supplied by Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40), not explicitly by Xiao et al."
      ],
      "rc_relation": "Role: central physical object. Trigger: the material physical identity is absent or invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Reach the first-coverage milestone of the homogeneous no-Coulomb family N1 direct, N2 unweighted complex-time, N3 Jp-weighted complex-time: any one independently valid, reconstructible and adequately presented member suffices, without supplying the other members.",
      "award_conditions": [
        "At least one of N1/N2/N3 independently has a correct reconstructible and adequately presented no-Coulomb identity; no missing member is supplied by another.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F1, F2, O2, O3, I1, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Reach second coverage of N1 direct, N2 unweighted complex-time and N3 Jp-weighted complex-time: at least two independently object-valid, presentation-adequate and claim-adequate members share signed axes, pulse, phase and cell/binning conventions. No member supplies another.",
      "award_conditions": [
        "At least two independently valid N1/N2/N3 members are reconstructible and comparable in signed axes, pulse, phase and cell convention.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O1 (Reach the first-coverage milestone of the homogeneous no-Coulomb family N1 direct, N2 unweighted complex-time, N3 Jp-weighted complex-time: any one independently valid, reconstructible and adequately presented member suffices, without supplying the other members.)",
        "Preserve independently valid work in F1, F2, O3, I1, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.",
      "award_conditions": [
        "All three N1/N2/N3 members are independently valid and comparable; N2 omits only Jp, retains the induced distortion, and N3 approaches direct N1 at demonstrated resolution.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O2 (Reach second coverage of N1 direct, N2 unweighted complex-time and N3 Jp-weighted complex-time: at least two independently object-valid, presentation-adequate and claim-adequate members share signed axes, pulse, phase and cell/binning conventions. No member supplies another.)",
        "Preserve independently valid work in F1, F2, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.",
      "award_conditions": [
        "C1 is an independent coherent planar QTMC object with signed transverse launch, y=vy=py=0, regularized action and reached asymptotic-momentum bins; material support/envelope/arcs are resolved.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in O5, O6, I2, M3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-4,6, Eqs.(33),(34),(36), Fig.2(b): adiabatic planar QTMC with coherent final-momentum accumulation. The signed planar reduction and finite tail/asymptotic implementation follow the stated task and standard-method equivalence class."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O5",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.",
      "award_conditions": [
        "C2 actually samples q and solves contributing saddles under a declared converged prescription, uses nonadiabatic launch and common finite-tail/asymptotic treatment, and resolves material reached-momentum structure.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in O4, O6, I2, I3, M3, M4, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "O6",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.",
      "award_conditions": [
        "C3 independently samples complex time with Jq and the same q-labelled saddle/launch/action/tail/bin identity as C2; C2 data cannot replace it.",
        "Record object_valid, presentation_adequate and claim_adequate separately; all three must hold for this 0.5-point Output award. Examiner reconstruction cannot supply omitted candidate presentation or reasoning."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in O4, O5, I2, M3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit."
      ],
      "rc_relation": "Role: indispensable material component. Trigger: the required output object is absent or physically invalid. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure. Inadequate presentation or unsupported claim alone does not establish that an otherwise valid object is absent or physically invalid."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from submitted arrays/slices the nonuniform-measure failure of N2, including scarce support near px=0 when resolved, and convergence of N3 toward N1 under sampling/bin refinement, rather than generic image texture.",
      "award_conditions": [
        "The candidate identifies N2's nonuniform measure and resolved scarce support near px=0, and N3's convergence toward N1 using their own arrays or slices."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: O3 (Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.)",
        "Preserve independently valid work in F1, O1, O2, M1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from reached-p_infinity data the common-q C2/C3 agreement in global support, envelope and resolved major rings/ridges, limiting fine-structure equivalence to actually resolved features.",
      "award_conditions": [
        "Candidate identification establishes C2/C3 agreement of global support, envelope and resolved major rings/ridges at reached asymptotic momentum, bounding fine-structure claims."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.); O6 (Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.)",
        "Preserve independently valid work in O4, M3, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "I3",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify directly in C1 versus C2 the major CCSFA-family ridge/distribution shift toward larger final momentum relative to QTMC. Extend it to C3 only when I2 supports C2/C3 agreement; pointwise fringe matching is not required.",
      "award_conditions": [
        "The candidate identifies the direct C1/C2 local shift toward larger final momentum; extending it to C3 requires actual C2/C3 agreement."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: O4 (Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.); O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.)",
        "Preserve independently valid work in O6, I2, M4, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning \"In the present work\" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain how uniform sampling in (tr,ti) induces a nonuniform momentum measure rather than merely saying the weighted image is better.",
      "award_conditions": [
        "The time-to-momentum change of variables explains why uniform complex-time samples create a nonuniform momentum measure."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.)",
        "Preserve independently valid work in F2, I1, M2, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain how the absolute-area Jacobian corrects the variable transformation and distinguish it from deterministic cell measure or Monte Carlo proposal weights.",
      "award_conditions": [
        "The absolute-area Jacobian is derived/interpreted as the measure correction, distinct from estimator proposal probabilities and deterministic cell factors."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.)",
        "Preserve independently valid work in O1, I1, M1, M5. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain C2/C3 as two sampling directions of the same q-labelled saddle/launch ensemble, with Jq correcting only sampling measure followed by common propagation and reached-p_infinity binning.",
      "award_conditions": [
        "The candidate explains common-q C2/C3 equivalence through a common saddle/launch ensemble, propagation and asymptotic bins, with Jq changing only sampling measure."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.); I2 (Identify from reached-p_infinity data the common-q C2/C3 agreement in global support, envelope and resolved major rings/ridges, limiting fine-structure equivalence to actually resolved features.)",
        "Preserve independently valid work in O5, O6, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.",
      "award_conditions": [
        "The resolved local CCSFA shift is linked to its nonzero nonadiabatic longitudinal launch; the account is not asserted for the entire PMD."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.); I3 (Identify directly in C1 versus C2 the major CCSFA-family ridge/distribution shift toward larger final momentum relative to QTMC. Extend it to C3 only when I2 supports C2/C3 agreement; pointwise fringe matching is not required.)",
        "Preserve independently valid work in I2, M3, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning \"In the present work\" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the principal physical mechanism is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use convergence evidence to distinguish residual sample scarcity/bin asymmetry from physical structure and restrict N3 recovery of N1 to the resolved no-Coulomb validation; an unresolved map does not establish validation.",
      "award_conditions": [
        "Refinement evidence separates scarcity/bin asymmetry from physical structure and supports only resolved no-Coulomb recovery."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: I1 (Identify from submitted arrays/slices the nonuniform-measure failure of N2, including scarce support near px=0 when resolved, and convergence of N3 toward N1 under sampling/bin refinement, rather than generic image texture.)",
        "Preserve independently valid work in M1, M2, V1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Distinguish direct C1/C2 observations, extensions supported by C2/C3 agreement and unresolved fine structure; unresolved features cannot support a mechanism. Fine interference is optional strengthening evidence.",
      "award_conditions": [
        "Direct C1/C2 observation, inference via C2/C3 agreement and unresolved fine structure are distinguished; an unresolved fringe is not mechanism evidence."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in I2, I3, M3, M4, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning \"In the present work\" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Form the commissioned QTMC-CCSFA family conclusion from the resolved direct C1/C2 shift and local launch mechanism; extend it to C3 only when independently demonstrated C2/C3 agreement permits.",
      "award_conditions": [
        "The family conclusion closes with the direct resolved shift and local launch mechanism; C3 is included only to the extent its independent agreement supports."
      ],
      "applicability_and_na": [
        "This scientific obligation applies to an assessable submission; it is not a risk-triggered N/A item."
      ],
      "dependencies": [
        "Necessary scientific premise: all of: I3 (Identify directly in C1 versus C2 the major CCSFA-family ridge/distribution shift toward larger final momentum relative to QTMC. Extend it to C3 only when I2 supports C2/C3 agreement; pointwise fringe matching is not required.); M4 (Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.)",
        "Preserve independently valid work in I2, M6. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning \"In the present work\" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching."
      ],
      "rc_relation": "Role: principal mechanism or commissioned conclusion. Trigger: the commissioned scientific conclusion is absent or wrong. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "V1",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Supply code/commands reproducing all six arrays, branch-specific numerical choices, raw cell/density conventions, separate cell/proposal factors, seeds/counts, normalization and claim-relevant stability evidence; judge implemented local parts without reward for resource consumption or duplicate penalties.",
      "award_conditions": [
        "Code/commands and branch-specific records reproduce six arrays, raw cell/density measures, separate estimator factors, seeds/counts and claim-relevant stability without rewarding resource use."
      ],
      "applicability_and_na": [
        "This positive scientific scope/evidence duty is unconditional; N/A is not permitted."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F1, F2, O1, O2, O3, O4, O5, O6, I1, I2, I3, M1, M2, M3, M4, M5, M6, M7. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article p.053310-6, Sec.III.A sampling/bin-error discussion and p.053310-7 Table I (efficiency context only); Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40) for finite post-pulse treatment. Reproduction records, compatible complex-estimator replica aggregation and risk-triggered checks are task-defined; no source sample count or runtime is a scoring target."
      ],
      "rc_relation": "Role: no independent closure role. Trigger: no independent closure trigger. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    },
    {
      "criterion_id": "V2",
      "dimension": "V",
      "points": 0.5,
      "scientific_requirement": "Only when estimator/Jacobian placement, saddle/contour consistency, replica aggregation, asymptotic/tail treatment or sampling-scarcity claims create a material threat to a central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.",
      "award_conditions": [
        "Only a concrete central risk in estimator weights, saddles, replicas, asymptotic tails or scarcity triggers discriminating validation; otherwise the assessable item is N/A."
      ],
      "applicability_and_na": [
        "Applicable only when a concrete material risk arises from the submitted method, data, anomaly or claim and threatens a retained conclusion.",
        "If untriggered in an assessable attempt, record N/A with fixed 0.5-point contribution, exclude it from applicable functional-completion counts, make no positive validation-evidence claim and do not block RC4."
      ],
      "dependencies": [
        "Necessary scientific premise: No fixed upstream prerequisite; judge this scientific obligation on its own evidence.",
        "Preserve independently valid work in F1, F2, O1, O2, O3, O4, O5, O6, I1, I2, I3, M1, M2, M3, M4, M5, M6, M7, V1. Propagate only a failure of the actual necessary physical premise, not a composite atom's unrelated missing branch or display defect."
      ],
      "equivalent_evidence": [
        "Equivalent notation, physically reasonable standard saddle/contour prescriptions and converged numerical realizations are accepted when they preserve all branch identities; no examiner-specific root subset is required.",
        "A standard analytic Coulomb/Kepler end-of-pulse map or demonstrated equivalent continuation is accepted with a consistent finite regularized phase. Cell-representative matching and trajectory-specific regularized actions are accepted when tail and cell choices do not drive the conclusions.",
        "Global support, envelope, symmetry and resolved major ring/ridge relations are targets, not pointwise fine-fringe phase, contrast, count or position. Axis extensions, common factors, logarithmic display and regions of interest are acceptable when the physical object remains reviewable."
      ],
      "source_support": [
        "Xiao et al. (2016), article p.053310-6, Sec.III.A sampling/bin-error discussion and p.053310-7 Table I (efficiency context only); Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40) for finite post-pulse treatment. Reproduction records, compatible complex-estimator replica aggregation and risk-triggered checks are task-defined; no source sample count or runtime is a scoring target."
      ],
      "rc_relation": "Role: material validation/scope. Trigger: a triggered, conclusion-threatening material validation/scope risk remains unresolved. Assess the substantive role condition independently of the atomic award; an atom receiving zero does not automatically establish a closure failure."
    }
  ],
  "case_scientific_rules": [
    "Each of the exact twenty criteria is worth 0 or 0.5 points; the sum is Atomic Score on 0-10. Judge the essential scientific core: an immaterial notation or display imperfection alone does not remove credit. Do not interpolate or inherit numerical partial-credit ranges.",
    "Object existence, candidate presentation, candidate identification and physical inference are distinct evidence acts. Examiner-generated plots, slices, fits or diagnostics may verify an object but cannot supply omitted candidate presentation, identification, mechanism or validation.",
    "For every Output atom separately establish object_valid, presentation_adequate and claim_adequate. Credit requires all three. Assess physical identity, global pattern and important secondary structure, not a single superficial resemblance.",
    "Apply only scientifically necessary dependencies, branch-locally. A composite prerequisite failing for an unrelated part does not erase independently established evidence. Identify the exact failed premise and why the downstream argument cannot stand independently; do not turn a half-point result into a mechanical gate.",
    "Risk-triggered validation is applicable only to a concrete threat arising from the submitted method, data, anomaly or claim. In an assessable attempt, an untriggered criterion is N/A and contributes its fixed 0.5 points, but supplies no positive validation evidence and does not block RC4.",
    "Positive model/scope duties are unconditional where specified. Merely omitting an examiner-preferred convergence procedure, control or plot does not create a material risk. A valid run with no assessable scientific work is 0 and RC0 before atom summation; N/A cannot create credit for it.",
    "Research Closure is descriptive and independent of Atomic Score and criterion awards. Evaluate scientific role conditions against their specified facts, not zero-valued atoms; choose the lowest applicable level across required roles of all indispensable/co-primary claims. Supporting claims alone do not determine overall RC.",
    "Numerical defects matter where they damage a physical object or make a scientific conclusion false/unsupported; do not deduct the same defect again as generic incompleteness, missing convergence or validation. A fluent interpretation does not rescue a materially incorrect signal.",
    "Accept physically valid equivalent methods and representations after aligning identity, units, gauge/basis, normalization, signs, support and component relations as applicable. Do not invent a tolerance when the evidence cannot distinguish equivalence from error; retain a bounded issue for review.",
    "Reference verification is required when a material decision depends on resolution, fine structure, component completeness, formula identity or representational equivalence, including nonstandard projections, cropping or reconstruction used for full Output credit. Consult the applicable scientific source and appropriately scoped validated references after establishing observable, case/component and convention mapping. It cannot complete missing candidate reasoning.",
    "A provisional Atomic Score of at least 9.0 or provisional RC4 requires examiner-side focused verification of one central output and one principal-mechanism link against applicable scientific references, checking identity, sign, ordering and overall pattern. This is not an additional candidate deliverable or pixel-matching requirement.",
    "For the no-Coulomb map pz=-Ar(tr,ti), px=+/-sqrt(Ai(tr,ti)^2-2Ip), retain both signed branches and the admissible real domain. The CCSFA sampling map is to saddle/drift q, not asymptotic p_infinity.",
    "Only the absolute area Jacobian Jp is omitted in N2; all saddle prefactors, phases and cell/proposal weights remain. Apply Ms_eff=Ms J in weighted branches, not sqrt(J), an arbitrary factor, an oriented-sign phase or an invented q-to-p_infinity Jacobian.",
    "C2 samples q then solves roots and propagates; C3 samples complex time then maps to q. Both use the same nonadiabatic launch, action, contributing saddles, asymptotic map, tail convention and final cells. Ordinary CCSFA is not an asymptotic-momentum shooting problem.",
    "Independent replicas must be combined at a compatible complex-estimator level before power. Duplicate seeds are not independent samples. Document proposed/sampled, propagated-root/trajectory and outgoing counts separately.",
    "No-Coulomb coverage atoms are cumulative one/two/three-member milestones, not fixed assignments of N1, N2 and N3 to separate credits. Each Coulomb output C1, C2 and C3 is independently adjudicated.",
    "Joint tail-parameter and cell-width stability must support relative phases and PMDs. An arbitrary finite-time momentum, literal divergent post-pulse integral, or branch-dependent cutoff determining the comparison is not equivalent.",
    "When a major-feature mismatch would decide credit, compare like normalized objects against combined cell resolution and sampling uncertainty. No fixed image-correlation threshold is prescribed; unresolved physical-versus-numerical disagreement requires bounded review rather than an invented tolerance.",
    "| ID | Mathematical object | Required branch identity | Normalization and units |\n|---|---|---|---|\n| N1 | Direct no-Coulomb $\\vert M(p_x,p_z)\\vert ^2$ from the finite-endpoint length-gauge SFA integral | Direct time integration; no Coulomb | Momentum in a.u.; yield in arbitrary units; one momentum-independent factor is free |\n| N2 | $\\vert \\sum_b a_s^{(\\mathrm{nc})}\\vert ^2$ from complex-time samples with $J_p=\\vert \\det\\partial(p_x,p_z)/\\partial(t_r,t_i)\\vert $ omitted and all other estimator weights retained | Same saddles/prefactor/phase/binning as N3 | Same as N1; `unweighted` omits only $J_p$ |\n| N3 | $\\vert \\sum_b a_s^{(\\mathrm{nc})}J_p\\vert ^2$ | Same physical branch as N2 with the absolute area Jacobian | Same as N1 |\n| C1 | Coherent planar QTMC PMD with $y=v_y=p_y=0$ | Standard stated one-component signed transverse-$p_x$ ADK/Landau initialization; retained post-release equations and $-2/r$ action; post-pulse Coulomb/Kepler map and finite regularized phase | Reached $\\mathbf p_\\infty$ in a.u.; yield in arbitrary units |\n| C2 | Coherent ordinary CCSFA PMD | Sample saddle/drift $\\mathbf q$, solve contributing saddle roots, propagate, map the end-of-pulse state to $\\mathbf p_\\infty$, and bin there; nonadiabatic launch | Same as C1 |\n| C3 | Coherent time-sampled CCSFA PMD | Complex-time sampling $\\rightarrow\\mathbf q$ with $J_q=\\vert \\det\\partial(q_x,q_z)/\\partial(t_r,t_i)\\vert $; same launch/action/post-pulse map and phase/saddles/$\\mathbf p_\\infty$ binning as C2 | Same as C1 |",
    "The common physical construction for C1-C3 uses the planar reduction, a standard analytic Coulomb/Kepler end-of-pulse-to-asymptotic map or a demonstrated equivalent continuation, and a finite regularized post-pulse Coulomb phase within the tail-equivalence class stated in task. Cell-representative matching and trajectory-specific regularized actions are both acceptable when the submitted evidence shows that the selected tail and cell representation do not drive the claimed structures. Do not require a particular cutoff, radius, solver, grid, quadrature, caustic treatment, regularization, contour prescription, or root subset. Reject a comparison in which C2 and C3 use inconsistent declared saddle prescriptions, launch relations, asymptotic maps, Coulomb action factors, tail conventions, or $\\mathbf p_\\infty$ bin definitions. Saved raw arrays must identify cell-integrated versus density/average form, with deterministic cell measures or Monte Carlo proposal corrections documented separately from $J_p$ or $J_q$.",
    "Uniform complex-time sampling maps nonuniformly into momentum space. Omitting the absolute area Jacobian produces the wrong measure; the most explicit source signal is scarce samples/noise near $p_x=0$, not a mandatory `boxy` appearance. Deterministic cell measure or Monte Carlo proposal correction remains separate from that Jacobian.",
    "With the determinant and sufficient sampling, the time-sampled no-Coulomb result reproduces the direct SFA structures substantially better. Residual central noise and left-right asymmetry may remain at finite sampling/bin size.",
    "Time-sampled CCSFA should reproduce ordinary CCSFA because both construct the same $\\mathbf q$-labelled saddle/launch ensemble, propagate it, and bin by reached $\\mathbf p_\\infty$; only the sampling direction and $J_q$ differ.",
    "The source directly assigns the local larger-final-momentum shift to the ordinary CCSFA comparison relative to QTMC and connects it to nonzero initial longitudinal momentum in the nonadiabatic SFA launch. Applying that statement to the time-sampled result is conditional on demonstrated C2-C3 agreement.",
    "When sufficiently resolved, finer structures absent from QTMC can be connected to an additional direct trajectory in CCSFA and the resulting intercycle interference. Such fine-fringe evidence may strengthen the analysis but is not required for full credit under this rubric; unresolved structure must not be used to support the mechanism.",
    "Source anchors: article method section containing the direct SFA amplitude and saddle equations; time-sampling section defining the Jacobian and effective amplitude; no-Coulomb comparison caption and discussion; Coulomb comparison and trajectory-analysis discussion; runtime table; and Shvetsov-Shilovski et al. (2016), Section III.B, article p.013415-6, Eqs.(26)-(40), for the standard end-of-pulse Coulomb/Kepler asymptotic-momentum map and finite regularized post-pulse Coulomb phase.",
    "The target article's printed antiderivative corresponding to its Eq. (31) has an erroneous factor of two in the two sideband numerators. Direct integration of the displayed pulse gives",
    "$$\n  I_1(t)=-\\frac{A_0}{4}\\left[\n  \\frac{2\\cos(\\omega t+\\phi)}{\\omega}\n  +\\frac{\\cos((\\omega+2\\beta)t+\\phi)}{\\omega+2\\beta}\n  +\\frac{\\cos((\\omega-2\\beta)t+\\phi)}{\\omega-2\\beta}\n  \\right].\n  $$",
    "The bracketed expression printed for the antiderivative corresponding to Eq. (32) differentiates to $A_z^2/2$ with its printed $A_0^2/64$ prefactor. For an antiderivative of $A_z^2$, the same bracket therefore carries $A_0^2/32$. The required integrals are derived or numerically evaluated from the stated pulse; these corrections clarify the mathematical identity and do not impose one antiderivative notation.",
    "The target article invokes propagation to asymptotic momentum and an infinite post-release phase but does not itself give an operational finite post-pulse construction. Shvetsov-Shilovski et al. (2016) supplies one standard closure through the end-of-pulse energy, angular momentum and Runge--Lenz vector and the associated finite regularized phase. This reference establishes method provenance; it does not prescribe a unique reference or notation. A physically equivalent, declared and converged continuation receives full credit.",
    "Full analysis credit requires the corresponding computed structure to be identifiable. A self-consistent explanation of a materially wrong PMD is not full-credit physics.",
    "A student who correctly diagnoses nonconvergence may receive method/diagnostic credit but not credit for an unobserved source-supported conclusion.",
    "Reasonable axis extensions, color maps, logarithmic transforms, common factors, and regions of interest are acceptable when the mathematical object and structures remain reviewable.",
    "Do not require source annotations, panel letters, exact colors/crops, code-specific time windows, a particular root solver, grid, sample count, derivative formula, quadrature, cutoff, tolerance, optimization, or parallel strategy.",
    "Do not prescribe an asymptotic-momentum shooting problem, a $\\mathbf q\\!\\to\\!\\mathbf p_\\infty$ Jacobian, root windows/seeds/tracker, bin grid, caustic solver, tail regularization, cutoff, radius, or quadrature.",
    "Do not require a prescribed list of references, fixed file tree, numerical residual, or complete failed-run history.",
    "For F1-F2/O1-O6/M1-M4, use article pp.053310-2-4, Eqs.(7),(8),(18)-(28),(33),(34),(36)-(38), with $\\mathbf q$ denoting the launch/saddle label in the Coulomb branches:\n$$[q_z+A_z(t_s)]^2+q_x^2+2I_p=0,\\quad\nq_z=-\\Re A_z(t_s),\\quad q_x=\\pm\\sqrt{[\\Im A_z(t_s)]^2-2I_p},$$\n$$\\mathbf v_0=\\mathbf q+\\mathbf A(t_r),\\quad\n\\mathbf r_0=\\Re\\int_{t_s}^{t_r}[\\mathbf q+\\mathbf A(s)]ds,\\quad\nJ_q=\\left|\\det\\frac{\\partial(q_x,q_z)}{\\partial(t_r,t_i)}\\right|.$$\nFor the no-Coulomb map replace q by final p. Both signed transverse branches must be represented. Subsequent Coulomb equations are $\\dot{\\mathbf r}=\\mathbf v$, $\\dot{\\mathbf v}=-\\mathbf E-\\mathbf r/r^3$. The retained continuum action uses $-\\int(v^2/2-2/r+I_p)dt$, rather than the source's $-1/r$ action. Its infinite tail must be replaced by a declared finite regularized phase. For a post-pulse outgoing Coulomb trajectory, $p_\\infty=\\sqrt{v_f^2-2/r_f}$; an analytic Kepler vector map or demonstrated equivalent continuation fixes direction. The q-to-p_infinity propagation map is not the time-to-q sampling Jacobian. The specified pulse antiderivatives, rather than the misprinted source Eqs.(31)-(32), determine the vector potential; directly integrating the stated pulse is equivalent.\n\nFor the standard post-pulse example, Shvetsov-Shilovski et al. (2016), article p.013415-6, Sec.III.B, Eqs.(26)-(40), gives for unit Coulomb charge\n$$\\mathbf L=\\mathbf r_f\\times\\mathbf v_f,\\quad\\mathbf a=\\mathbf v_f\\times\\mathbf L-\\mathbf r_f/r_f,\\quad\n\\mathbf p_\\infty=p_\\infty\\frac{p_\\infty(\\mathbf L\\times\\mathbf a)-\\mathbf a}{1+p_\\infty^2L^2}.$$\nWriting $E=p_\\infty^2/2>0$, $b=1/(2E)$ and $g=\\sqrt{1+2EL^2}$, one finite Coulomb tail contribution after removal of common divergent phases is\n$$\\widetilde\\Phi_C=-\\sqrt b\\left[\\ln g+\\operatorname{arsinh}\\frac{\\mathbf r_f\\cdot\\mathbf v_f}{g\\sqrt b}\\right].$$\nThis is a supported standard closure, not required notation or permission to replace the task's own launch/action identity. A declared converged equivalent continuation remains accepted. For the no-Coulomb direct reference, Xiao et al. article p.053310-2, Eqs.(7),(8), uses $M_{\\mathbf p}=i\\int_{t_0}^{t_f}dt\\,e^{i\\widetilde S_{\\mathbf p}(t)}\\langle\\mathbf p+\\mathbf A(t)|\\mathbf r\\cdot\\mathbf E(t)|\\psi_0\\rangle$, with $\\partial_t\\widetilde S_{\\mathbf p}=[\\mathbf p+\\mathbf A(t)]^2/2+I_p$ and one common finite endpoint convention."
  ],
  "closure_requirements": {
    "RC0": [
      "The central physical object is absent or materially invalid, or a valid run contains no assessable scientific work. This is a scientific fact determination, not a low-score rule.",
      "Required indispensable claim CL1, central physical object: all of: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.); F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC1": [
      "With a valid central object, an indispensable material component needed for the commissioned research question is absent or invalid. Presentation or claim inadequacy alone does not establish object absence/invalidity.",
      "Required indispensable claim CL1, indispensable material component: all of: O3 (Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.); O4 (Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.); O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.); O6 (Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC2": [
      "With the central object and indispensable components present, a required principal mechanism, state-dependence account or commissioned conclusion remains absent or wrong.",
      "Required co primary claim CL2, principal mechanism or commissioned conclusion: all of: M1 (Explain how uniform sampling in (tr,ti) induces a nonuniform momentum measure rather than merely saying the weighted image is better.); M2 (Explain how the absolute-area Jacobian corrects the variable transformation and distinguish it from deterministic cell measure or Monte Carlo proposal weights.); M5 (Use convergence evidence to distinguish residual sample scarcity/bin asymmetry from physical structure and restrict N3 recovery of N1 to the resolved no-Coulomb validation; an unresolved map does not establish validation.). Judge the role-specific failure facts, not the corresponding atom scores.",
      "Required co primary claim CL3, principal mechanism or commissioned conclusion: all of: M3 (Explain C2/C3 as two sampling directions of the same q-labelled saddle/launch ensemble, with Jq correcting only sampling measure followed by common propagation and reached-p_infinity binning.); M4 (Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.); M7 (Form the commissioned QTMC-CCSFA family conclusion from the resolved direct C1/C2 shift and local launch mechanism; extend it to C3 only when independently demonstrated C2/C3 agreement permits.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC3": [
      "With the central object, indispensable components and principal mechanism established, a concrete material validation/scope risk remains unresolved and threatens a central conclusion. It is not triggered by omission of a preferred named check.",
      "Before assigning RC3, establish all six elements: 1. Identify the concrete unexcluded failure mode. 2. Explain its origin in the submitted method, data or conclusion. 3. Identify a fair basis in the task or standard scientific reasoning for recognizing this risk. 4. Identify the threatened central conclusion. 5. Explain why submitted evidence cannot expose/exclude the failure; naming it alone does not resolve it. 6. Give examples of functionally equivalent remedies without prescribing one method.",
      "Required co primary claim CL3, material validation/scope: V2 (Only when estimator/Jacobian placement, saddle/contour consistency, replica aggregation, asymptotic/tail treatment or sampling-scarcity claims create a material threat to a central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.). Judge the role-specific failure facts, not the corresponding atom scores."
    ],
    "RC4": [
      "All required scientific roles of every indispensable and co-primary claim close, including applicable material-risk treatment and evidence-bounded scope. Supporting claims do not independently determine RC; untriggered risk N/A does not block RC4.",
      "Choose the lowest applicable level when required role failures coexist. RC has no score cap, floor or multiplier and cannot be inferred mechanically from criterion awards. A scope restriction removes unsupported breadth but cannot repair a wrong signal, absent component or missing principal mechanism.",
      "Close CL1 central physical object: all of: F1 (State the common six-branch physical objects, signed-plane coordinates, final-momentum cells, coherent accumulation, normalization and cell/proposal conventions, including absolute-area Jp/Jq bookkeeping for no-Coulomb time-to-p and CCSFA time-to-q maps. A determinant sign is not a phase. O1-O6 independently judge branch validity.); F2 (State the phase, launch, real-time propagation, asymptotic continuation, finite regularized tail and reached-p_infinity binning equations/conventions needed to interpret each branch, keeping QTMC adiabatic and CCSFA nonadiabatic launches distinct. O4-O6 independently judge branch construction and output.).",
      "Close CL1 indispensable material component: all of: O3 (Reach full coverage of N1 direct, N2 unweighted and N3 Jp-weighted: all three members are independently valid, reconstructible, adequately presented and comparable under common signed axes, pulse, phase and cell/binning conventions. N2 retains its nonuniform-measure distortion and N3 recovers N1; a boxy texture is not compulsory.); O4 (Present an independent planar QTMC C1 PMD with y=v_y=p_y=0, a declared one-component signed-px adiabatic launch, coherent Coulomb propagation/action, finite regularized tail and reached-p_infinity binning; resolve global low-energy support, envelope and material arcs/ridges without cylindrical or py-marginal substitution.); O5 (Present an independent ordinary momentum-sampled CCSFA C2 PMD: sample q, solve all contributing saddles under a physically reasonable declared prescription and converged root domain, use nonadiabatic launch/action and consistent asymptotic/tail treatment, and bin at reached p_infinity. Global support, envelope and material major rings/ridges must be physically valid, reconstructible and adequately exposed.); O6 (Present an independent time-sampled/Jq-corrected CCSFA C3 PMD with the same q-labelled saddle/nonadiabatic-launch/action/asymptotic-tail/reached-p_infinity physical identity as C2. The complex-time-to-q absolute-area Jacobian corrects sampling measure; C2 results cannot supply C3 evidence.).",
      "Close CL2 principal mechanism or commissioned conclusion: all of: M1 (Explain how uniform sampling in (tr,ti) induces a nonuniform momentum measure rather than merely saying the weighted image is better.); M2 (Explain how the absolute-area Jacobian corrects the variable transformation and distinguish it from deterministic cell measure or Monte Carlo proposal weights.); M5 (Use convergence evidence to distinguish residual sample scarcity/bin asymmetry from physical structure and restrict N3 recovery of N1 to the resolved no-Coulomb validation; an unresolved map does not establish validation.).",
      "Close CL3 principal mechanism or commissioned conclusion: all of: M3 (Explain C2/C3 as two sampling directions of the same q-labelled saddle/launch ensemble, with Jq correcting only sampling measure followed by common propagation and reached-p_infinity binning.); M4 (Connect the resolved local larger-final-momentum shift to the nonzero initial longitudinal momentum allowed by the nonadiabatic SFA launch; do not generalize that local mechanism to the entire PMD.); M7 (Form the commissioned QTMC-CCSFA family conclusion from the resolved direct C1/C2 shift and local launch mechanism; extend it to C3 only when independently demonstrated C2/C3 agreement permits.).",
      "Close CL3 material validation/scope: V2 (Only when estimator/Jacobian placement, saddle/contour consistency, replica aggregation, asymptotic/tail treatment or sampling-scarcity claims create a material threat to a central conclusion, provide targeted discriminating evidence; otherwise record N/A with fixed credit and no evidence claim.)."
    ]
  },
  "references": [
    {
      "citation": "Xiang-Ru Xiao, Mu-Xue Wang, Wei-Hao Xiong, and Liang-You Peng. 2016. *Efficient time-sampling method in Coulomb-corrected strong-field approximation*. *Physical Review E*, 94, 053310.",
      "url": "https://doi.org/10.1103/PhysRevE.94.053310",
      "scientific_scope": "Efficient time-sampling method in Coulomb-corrected strong-field approximation",
      "anchors": [
        "Xiao et al. (2016), article pp.053310-3-5, Eqs.(18)-(21),(37),(38) and Sec.III.A: complex-time-to-momentum sampling and Jacobian compensation. Absolute area and separate proposal/cell bookkeeping are mathematical/task clarifications, not determinant-sign phases.",
        "Xiao et al. (2016), article pp.053310-2-4, Eqs.(7)-(16),(22)-(28),(33)-(36): direct amplitude, nonadiabatic launch, Coulomb dynamics and -2/r action. Operational finite asymptotic/tail closure is supplied by Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40), not explicitly by Xiao et al.",
        "Xiao et al. (2016), article pp.053310-5-6, Fig.1(a-c) and slices (d-f), Sec.III.A: direct/unweighted/Jacobian-corrected no-Coulomb comparison, scarce sampling near px=0 and bin-induced asymmetry. The one/two/three coverage milestones are task rubric structure, not source panel obligations.",
        "Xiao et al. (2016), article pp.053310-4,6, Eqs.(33),(34),(36), Fig.2(b): adiabatic planar QTMC with coherent final-momentum accumulation. The signed planar reduction and finite tail/asymptotic implementation follow the stated task and standard-method equivalence class.",
        "Xiao et al. (2016), article pp.053310-3-6, Eqs.(22)-(28),(37),(38), Fig.2(c,d): ordinary and time-sampled CCSFA represent the same nonadiabatic launch family. In Coulomb propagation the sampled saddle label q is not the reached asymptotic momentum; this distinction is task-explicit.",
        "Xiao et al. (2016), article p.053310-6, Sec.III.B paragraph beginning \"In the present work\" and Fig.2(b,c) boxed region: local larger-final-momentum CCSFA shift is linked to nonzero longitudinal launch. Extension to Fig.2(d) requires demonstrated c/d agreement. Article p.053310-7, Fig.3 is optional fine-trajectory context, not mandatory fringe matching.",
        "Xiao et al. (2016), article p.053310-6, Sec.III.A sampling/bin-error discussion and p.053310-7 Table I (efficiency context only); Shvetsov-Shilovski et al. (2016), Sec.III.B, article p.013415-6, Eqs.(26)-(40) for finite post-pulse treatment. Reproduction records, compatible complex-estimator replica aggregation and risk-triggered checks are task-defined; no source sample count or runtime is a scoring target."
      ]
    },
    {
      "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": "Standard post-pulse Coulomb/Kepler asymptotic-momentum map and finite regularized Coulomb phase; equivalent declared converged continuations remain accepted.",
      "anchors": [
        "Article p.013415-6, Section III.B, Eqs.(26)-(29): end-of-pulse Coulomb/Kepler map; Eqs.(30)-(40): removal of common divergent phase and finite regularized tail."
      ]
    }
  ]
}