{
  "case_id": "Case22",
  "title": "Vacuum pair production in zeptosecond pulses: Peculiar momentum spectra and striking particle acceleration by bipolar pulses",
  "atoms": [
    {
      "criterion_id": "F1",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Correctly instantiate both counterpropagating spacetime pulses, all three phase classes, direction conventions, units and continuum normalization; do not replace them with one homogeneous pulse.",
      "award_conditions": [
        "Both counterpropagating spacetime pulses, phase assignments, orientation and continuum units are correctly represented; one homogeneous pulse is not equivalent."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint p. 2, Eqs. (2)-(5), Fig. 1(b): Counterpropagating spacetime dependence and phase-specific energy matching define the comparison; field-amplitude changes enter density at fourth power."
      ],
      "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": "F2",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Derive or correctly implement equal-energy amplitudes, distinguishing matched like-pulse amplitudes from the common mixed-case amplitude, preserving leading fourth-power field normalization.",
      "award_conditions": [
        "Equal-energy amplitudes are derived for the two like-pulse classes, while the mixed case keeps its prescribed common amplitude; leading fourth-power density scaling is retained.",
        "Equal-energy amplitudes are derived for the actual like/mixed assignments and combined with the leading fourth-power density scaling."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint p. 2, Eqs. (2)-(5), Fig. 1(b): Counterpropagating spacetime dependence and phase-specific energy matching define the comparison; field-amplitude changes enter density at fourth power."
      ],
      "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": "F3",
      "dimension": "F",
      "points": 0.5,
      "scientific_requirement": "Establish the shared leading nonvanishing perturbative-QED coherent two-pulse kernel/object with counterpropagating spacetime dependence, phase-sensitive branches and declared continuum normalization; equivalent time-domain or Volkov representations are accepted.",
      "award_conditions": [
        "The leading two-pulse coherent perturbative object retains the correct phase-sensitive branches and normalization, in a kernel, time-domain or equivalent Volkov representation."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Preserve independent correct work in O1, O2, O3, O4 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge the common leading two-pulse object independently. Local unipolar/bipolar/mixed duration, asymptotic convention or yield-domain defects do not establish global central-object invalidity or RC0."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint p. 2, Eqs. (7)-(8), leading-order theoretical-description paragraphs; Supplemental Eqs. (S1)-(S7): A coherent two-pulse leading perturbative kernel is required, not a homogeneous tunneling rate."
      ],
      "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": "Convert differential density to total pair number per transverse normalization area by a three-dimensional momentum integral; distinguish a p_y = 0 slice integral from total yield.",
      "award_conditions": [
        "The defined total observable integrates all three momentum components per declared transverse area; a py=0 slice is explicitly distinguished."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "F3: Establish the shared leading nonvanishing perturbative-QED coherent two-pulse kernel/object with counterpropagating spacetime dependence, phase-sensitive branches and declared continuum normalization; equivalent time-domain or Volkov representations are accepted. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in O1, O2, O3, I1, I2, M5 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "A wrong total-yield integration dimension does not erase correct differential spectra or mixed-direction evidence."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint pp. 2 and 4, Eq. (6), Fig. 4 and adjacent total-yield discussion: The total yield integrates all three momentum components; Fig. 4 supports broad duration ordering/crossover/productivity, not an exact quadrature target or a slice-as-total substitution."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "O1",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide at least one correctly duration-bound equal-energy unipolar-pair momentum density with correct case/orientation, even longitudinal symmetry, major support/lobes and auditable unscaled density.",
      "award_conditions": [
        "At least one duration-bound unipolar-pair spectrum has even longitudinal symmetry, correct major support and auditable unscaled density.",
        "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.",
        "Judge each local duration and phase branch on its own physical density. A missing counterpart limits contrast, not the validity of an existing branch. Reflection equivalence requires the pulse-phase assignment to transform with the longitudinal direction."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint p. 3, Fig. 2 left/right columns and numerical-results paragraphs: Like-phase spectra are even longitudinally; bipolar pulses reach much larger longitudinal momenta as duration shortens while density falls. Panel rescalings are not yields."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "O2",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide at least one correctly duration-bound equal-energy bipolar-pair density with even longitudinal symmetry, bandwidth/density scale and major lobes, permitting the comparable contrast/duration evolution with the unipolar branch; retain unscaled data.",
      "award_conditions": [
        "At least one duration-bound bipolar-pair spectrum has correct even symmetry, density/bandwidth and support, allowing the actual submitted contrast to be checked.",
        "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.",
        "Judge each local duration and phase branch on its own physical density. A missing counterpart limits contrast, not the validity of an existing branch. Reflection equivalence requires the pulse-phase assignment to transform with the longitudinal direction."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint p. 3, Fig. 2 left/right columns and numerical-results paragraphs: Like-phase spectra are even longitudinally; bipolar pulses reach much larger longitudinal momenta as duration shortens while density falls. Panel rescalings are not yields."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "O3",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide at least one correctly bound mixed-phase density with both pulse-phase orientations and longitudinal convention, resolving broken symmetry and directed support; duration coverage is separately judged by I2/M5 within the claim domain.",
      "award_conditions": [
        "A mixed-phase spectrum is bound to both opposite pulse assignments and the longitudinal convention, resolving directed asymmetric support.",
        "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.",
        "Judge each local duration and phase branch on its own physical density. A missing counterpart limits contrast, not the validity of an existing branch. Reflection equivalence requires the pulse-phase assignment to transform with the longitudinal direction."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint p. 3, Fig. 3 left/right panels and mixed-phase paragraph; Eq. (8) on p. 2: Opposite pulse phases break longitudinal reflection symmetry and produce directed support. Exchanging phase assignments with the longitudinal reflection is equivalent."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "O4",
      "dimension": "O",
      "points": 0.5,
      "scientific_requirement": "Provide a correctly equal-energy/class-bound three-dimensional total-yield bounded duration scan, not a p_y = 0 slice. Missing one broad regime does not erase credit for an otherwise valid bounded scan.",
      "award_conditions": [
        "An equal-energy class-bound bounded duration scan uses the three-dimensional yield; a missing broad regime does not erase an otherwise valid local scan.",
        "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.",
        "A valid three-dimensional bounded yield scan retains its local output/identification credit when one broad duration regime is missing; the complete most-productive-regime conclusion remains separately judgeable."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint pp. 2 and 4, Eq. (6), Fig. 4 and adjacent total-yield discussion: The total yield integrates all three momentum components; Fig. 4 supports broad duration ordering/crossover/productivity, not an exact quadrature target or a slice-as-total substitution."
      ],
      "rc_relation": "RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "I1",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify from any valid like-pulse branch its even longitudinal symmetry, density/bandwidth/support and duration signal; if both branches are valid identify their contrast, without mistaking display scaling for density.",
      "award_conditions": [
        "The candidate identifies symmetry, support/bandwidth and duration behavior from at least one valid like-pulse branch and contrast where both exist.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "At least one of [O1: Provide at least one correctly duration-bound equal-energy unipolar-pair momentum density with correct case/orientation, even longitudinal symmetry, major support/lobes and auditable unscaled density.; O2: Provide at least one correctly duration-bound equal-energy bipolar-pair density with even longitudinal symmetry, bandwidth/density scale and major lobes, permitting the comparable contrast/duration evolution with the unipolar branch; retain unscaled data.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I2, I3 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Either valid like-pulse branch can establish its own morphology; full contrast needs both branches. A local branch failure neither backfills nor erases the other branch.",
        "Judge each local duration and phase branch on its own physical density. A missing counterpart limits contrast, not the validity of an existing branch. Reflection equivalence requires the pulse-phase assignment to transform with the longitudinal direction."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint p. 3, Fig. 2 left/right columns and numerical-results paragraphs: Like-phase spectra are even longitudinally; bipolar pulses reach much larger longitudinal momenta as duration shortens while density falls. Panel rescalings are not yields."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "I2",
      "dimension": "I",
      "points": 0.5,
      "scientific_requirement": "Identify broken longitudinal symmetry, directed momentum transfer and orientation sign from at least one valid mixed-phase case; judge one-sided support or duration persistence only within the submitted evidence.",
      "award_conditions": [
        "The candidate identifies directed momentum and broken longitudinal symmetry with an explicit orientation sign, restricting duration persistence to actual evidence.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "O3: Provide at least one correctly bound mixed-phase density with both pulse-phase orientations and longitudinal convention, resolving broken symmetry and directed support; duration coverage is separately judged by I2/M5 within the claim domain. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I1, I3 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge each local duration and phase branch on its own physical density. A missing counterpart limits contrast, not the validity of an existing branch. Reflection equivalence requires the pulse-phase assignment to transform with the longitudinal direction."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint p. 3, Fig. 3 left/right panels and mixed-phase paragraph; Eq. (8) on p. 2: Opposite pulse phases break longitudinal reflection symmetry and produce directed support. Exchanging phase assignments with the longitudinal reflection is equivalent."
      ],
      "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 ordering/crossover or productivity actually covered by the valid three-dimensional bounded yield scan, stating which very-short or Compton-scale regimes remain uncovered.",
      "award_conditions": [
        "The candidate identifies only the ordering/crossover/productivity supported by the valid three-dimensional scan and states uncovered broad regimes.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "O4: Provide a correctly equal-energy/class-bound three-dimensional total-yield bounded duration scan, not a p_y = 0 slice. Missing one broad regime does not erase credit for an otherwise valid bounded scan. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I1, I2 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "A valid three-dimensional bounded yield scan retains its local output/identification credit when one broad duration regime is missing; the complete most-productive-regime conclusion remains separately judgeable."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint pp. 2 and 4, Eq. (6), Fig. 4 and adjacent total-yield discussion: The total yield integrates all three momentum components; Fig. 4 supports broad duration ordering/crossover/productivity, not an exact quadrature target or a slice-as-total substitution."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M1",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use specific spectra and yields to distinguish momentum reach from production probability and bind their tradeoff to pulse class and duration.",
      "award_conditions": [
        "Spectra and yields are used together to distinguish large momentum reach from large production probability and explain the duration/class tradeoff.",
        "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 from any valid like-pulse branch its even longitudinal symmetry, density/bandwidth/support and duration signal; if both branches are valid identify their contrast, without mistaking display scaling for density.; I3: Identify ordering/crossover or productivity actually covered by the valid three-dimensional bounded yield scan, stating which very-short or Compton-scale regimes remain uncovered.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M2, M3, M4, M5, M6, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge each local duration and phase branch on its own physical density. A missing counterpart limits contrast, not the validity of an existing branch. Reflection equivalence requires the pulse-phase assignment to transform with the longitudinal direction."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint pp. 3-4, Figs. 2-4 and contrast/yield discussion: Equal energy does not equate momentum reach and probability; the spectral-density and integrated-yield tradeoff must be separated."
      ],
      "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": "M2",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Answer that equal-energy unipolar and bipolar classes are not physically equivalent, using spectral/yield differences rather than image area or display multipliers.",
      "award_conditions": [
        "The equal-energy answer uses physical density and yield differences rather than display multipliers or plot area.",
        "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 at least one correctly duration-bound equal-energy unipolar-pair momentum density with correct case/orientation, even longitudinal symmetry, major support/lobes and auditable unscaled density.; O2: Provide at least one correctly duration-bound equal-energy bipolar-pair density with even longitudinal symmetry, bandwidth/density scale and major lobes, permitting the comparable contrast/duration evolution with the unipolar branch; retain unscaled data.; I3: Identify ordering/crossover or productivity actually covered by the valid three-dimensional bounded yield scan, stating which very-short or Compton-scale regimes remain uncovered.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I1, M1, M3, M4, M5, M6, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Full equal-energy comparison needs both like-pulse classes and the candidate yield signal. Preserve local one-branch or one-observable output/identification credit if the complete conclusion fails.",
        "Judge each local duration and phase branch on its own physical density. A missing counterpart limits contrast, not the validity of an existing branch. Reflection equivalence requires the pulse-phase assignment to transform with the longitudinal direction."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint pp. 3-4, Figs. 2-4 and contrast/yield discussion: Equal energy does not equate momentum reach and probability; the spectral-density and integrated-yield tradeoff must be separated."
      ],
      "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": "M3",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain how polarity/phase changes the coherent leading observable through phase-sensitive two-pulse Fourier factors or equivalent time-domain/Volkov construction; homogeneous tunneling is not an equivalent mechanism.",
      "award_conditions": [
        "Phase-dependent two-pulse Fourier/time-domain structure explains the observable; a homogeneous tunneling or classical-impulse narrative is not substituted.",
        "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 from any valid like-pulse branch its even longitudinal symmetry, density/bandwidth/support and duration signal; if both branches are valid identify their contrast, without mistaking display scaling for density.; I2: Identify broken longitudinal symmetry, directed momentum transfer and orientation sign from at least one valid mixed-phase case; judge one-sided support or duration persistence only within the submitted evidence.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M1, M2, M4, M5, M6, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint pp. 2-3, Eqs. (7)-(8) and short-duration paragraphs; Supplemental Eqs. (S8)-(S11): Cosh/sinh Fourier factors create distinct support and fixed-momentum scaling; the bipolar support grows as inverse duration, so pointwise density alone does not determine yield."
      ],
      "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M4",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "When both like-pulse branches are valid, explain very-short-duration fixed-momentum scaling, bipolar support growing as inverse duration and their combined total-yield tradeoff.",
      "award_conditions": [
        "With both like-pulse branches available, the argument combines short-duration fixed-momentum suppression with bipolar inverse-duration momentum support to explain yield tradeoff.",
        "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 at least one correctly duration-bound equal-energy unipolar-pair momentum density with correct case/orientation, even longitudinal symmetry, major support/lobes and auditable unscaled density.; O2: Provide at least one correctly duration-bound equal-energy bipolar-pair density with even longitudinal symmetry, bandwidth/density scale and major lobes, permitting the comparable contrast/duration evolution with the unipolar branch; retain unscaled data.; I3: Identify ordering/crossover or productivity actually covered by the valid three-dimensional bounded yield scan, stating which very-short or Compton-scale regimes remain uncovered.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in I1, M3, M5, M6, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "The complete short-duration tradeoff needs both differential branches and candidate three-dimensional yield evidence. A local unipolar defect does not imply RC0 or erase bipolar, mixed or bounded-yield work."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint pp. 2-3, Eqs. (7)-(8) and short-duration paragraphs; Supplemental Eqs. (S8)-(S11): Cosh/sinh Fourier factors create distinct support and fixed-momentum scaling; the bipolar support grows as inverse duration, so pointwise density alone does not determine yield."
      ],
      "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": "M5",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Explain that the mixed assignment binds distinct Fourier/time-domain structures to opposite counterpropagating branches, breaking the interchange/reflection symmetry producing an even longitudinal spectrum; give the direction convention and restrict duration extrapolation to evidence.",
      "award_conditions": [
        "Opposite phase structures assigned to counterpropagating branches explain broken reflection symmetry and the direction of mixed-case support within the demonstrated domain.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "I2: Identify broken longitudinal symmetry, directed momentum transfer and orientation sign from at least one valid mixed-phase case; judge one-sided support or duration persistence only within the submitted evidence. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M1, M2, M3, M4, M6, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "Judge each local duration and phase branch on its own physical density. A missing counterpart limits contrast, not the validity of an existing branch. Reflection equivalence requires the pulse-phase assignment to transform with the longitudinal direction."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint p. 3, Fig. 3 left/right panels and mixed-phase paragraph; Eq. (8) on p. 2: Opposite pulse phases break longitudinal reflection symmetry and produce directed support. Exchanging phase assignments with the longitudinal reflection is equivalent."
      ],
      "rc_relation": "RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M6",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Use computed three-dimensional yields to determine the most productive duration regime, separately closing very-short ordering, crossover and Compton-scale peak behavior. Missing one broad regime loses this complete-conclusion obligation without deleting local O4/I3 credit.",
      "award_conditions": [
        "The complete productivity conclusion addresses very-short ordering, crossover and Compton-scale peak behavior from computed three-dimensional yields.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "I3: Identify ordering/crossover or productivity actually covered by the valid three-dimensional bounded yield scan, stating which very-short or Compton-scale regimes remain uncovered. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.",
        "Preserve independent correct work in M1, M2, M3, M4, M5, M7 and all branches not using the failed premise.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty.",
        "A valid bounded scan can retain O4/I3 credit even if it lacks a broad regime needed for this complete productivity conclusion. Source narrative cannot supply missing candidate yields.",
        "A valid three-dimensional bounded yield scan retains its local output/identification credit when one broad duration regime is missing; the complete most-productive-regime conclusion remains separately judgeable."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint pp. 2 and 4, Eq. (6), Fig. 4 and adjacent total-yield discussion: The total yield integrates all three momentum components; Fig. 4 supports broad duration ordering/crossover/productivity, not an exact quadrature target or a slice-as-total substitution."
      ],
      "rc_relation": "No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure."
    },
    {
      "criterion_id": "M7",
      "dimension": "M",
      "points": 0.5,
      "scientific_requirement": "Give an evidence-bounded conclusion separating leading-order idealized counterpropagating fields from unsupported nonperturbative, long-duration, focused-field or experimental generalization.",
      "award_conditions": [
        "The conclusion distinguishes idealized leading-order counterpropagating production from unsupported nonperturbative, focused or experimental claims.",
        "Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link."
      ],
      "applicability_and_na": [
        "Applicable to the stated scientific commission; N/A is not permitted."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint pp. 1-2, Setup and perturbative-validity paragraphs; p. 4, concluding discussion: Leading perturbation, counterpropagating geometry and demonstrated duration domain bound the claim. Data provenance and triggered risk discrimination are task obligations, not extra canonical plots."
      ],
      "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": "Positively state the actual leading-order representation, normalization, orientation, duration/momentum domain and data provenance without imposing a canonical grid, quadrature, cutoff, plot or source coordinate.",
      "award_conditions": [
        "Actual representation, normalization, phase orientation, momentum/duration coverage and reconstructible data provenance are stated."
      ],
      "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.",
        "Positive scope omissions are owned here; material overclaims or unexcluded risks are owned only by triggered V2. Ordinary omission does not trigger RC3; do not charge it again at M7."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint pp. 1-2, Setup and perturbative-validity paragraphs; p. 4, concluding discussion: Leading perturbation, counterpropagating geometry and demonstrated duration domain bound the claim. Data provenance and triggered risk discrimination are task obligations, not extra canonical plots."
      ],
      "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 or claim exposes a concrete risk that can overturn or materially weaken the central conclusion, discriminate it or narrow the claim; otherwise record N/A without validation-evidence credit.",
      "award_conditions": [
        "Actual cutoff, momentum-integral, phase/normalization or perturbative-domain threats are resolved or restricted; absent a material trigger apply N/A."
      ],
      "applicability_and_na": [
        "Activate only for a concrete material risk arising from the candidate method, data, anomaly or claim; no fixed test is required in the absence of a trigger.",
        "Without a triggered risk record N/A and award 0.5 without positive validation evidence; this neither blocks RC4 nor triggers RC3.",
        "When triggered, accept functionally equivalent discriminating evidence or a justified restriction of the threatened claim."
      ],
      "dependencies": [
        "Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation.",
        "Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty."
      ],
      "equivalent_evidence": [
        "Accept algebraically equivalent Fourier/kernel, leading time-domain, one-Volkov-pulse or direct lowest-order two-pulse representations preserving coherent observable, phase binding, branch symmetry, short-duration support, normalization and three-dimensional yield.",
        "Shifted-Gaussian Fourier evaluation, light-cone kernel rewrites, converged quadratures and declared continuum conventions are accepted. Pulse interchange plus longitudinal reflection and explicit leading field-amplitude rescaling are allowed.",
        "Accept reconstructible alternative displays and bounded self-chosen duration sampling; preserve local correct branch/scan credit independently from broader regime coverage. No author grid, cutoff, source panel multiplier or exact curve coordinate is required."
      ],
      "source_support": [
        "Aleksandrov and Rosanov (2024), preprint pp. 1-2, Setup and perturbative-validity paragraphs; p. 4, concluding discussion: Leading perturbation, counterpropagating geometry and demonstrated duration domain bound the claim. Data provenance and triggered risk discrimination are task obligations, not extra canonical plots."
      ],
      "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 each supplied pulse, W^(zeta) = sqrt(pi)/2^(3/2) E0_zeta^2 tau [1 - exp(-sigma^2/2) cos(2 phi_zeta)]. At sigma = 1 equal energy gives E0_B/E0_U = tanh(1/4)^(-1/2) = 2.0206405..., with task amplitudes E0_U = 0.1 Ec and E0_B = 0.20206405... Ec. The mixed case instead uses common amplitude 0.1 Ec. Smaller amplitudes with explicit leading E0^4 conversion are accepted.",
    "One canonical density is f(p) = pi^(-2) (E0/Ec)^4 (m tau/sigma)^4 integral dpz_prime G(p,pz_prime) |F_plus(q_plus) F_minus(q_minus)|^2. Here q_plus/minus = [p0 + p0_prime +/- (pz + pz_prime)] tau/(2 sigma), p0 = sqrt(m^2 + p^2), p0_prime = sqrt(m^2 + px^2 + py^2 + pz_prime^2).",
    "The Fourier factors are F_zeta(q) = sqrt(pi) sigma exp[-sigma^2(q^2+1)/4] {sin(phi_zeta) cosh(sigma^2 q/2) + i cos(phi_zeta) sinh(sigma^2 q/2)}. The kernel is G = {[(p0^2-pz^2)(p0 p0_prime-pz pz_prime-p0^2+pz^2+8 px^2)-8 px^4] m^4}/{p0 p0_prime (p0^2-pz^2)^2 (p0+p0_prime+pz+pz_prime)^2 (p0+p0_prime-pz-pz_prime)^2}. All denominator factors multiply.",
    "Total pair number per transverse normalization area is N = integral f(p) d^3p. A p_y = 0 slice integrated over px,pz is not N. Equivalent continuum normalizations need an explicit conversion.",
    "Equal-phase pairs have even pz spectra. Unipolar sub-Compton spectra remain within longitudinal momenta of a few m; bipolar spectra broaden strongly as duration shortens, reaching order 20 m at tau = 0.1 tau_C. Judge support, lobes, symmetry, density and duration contrast, not exact rms values or panel multipliers.",
    "Mixed (phi_plus,phi_minus) = (0,pi/2) breaks pz reflection symmetry and yields directed support; the shorter case has broad one-sided U-shaped support. Exchanging phase assignments with pz reflection is equivalent, but reflection without the corresponding pulse map is not.",
    "Equal-energy total yields rise from very short duration, peak at order tau_C and fall afterward. Unipolar yield is larger in the very-short regime including tau <= about 0.5 tau_C; ordering reverses before the maxima and bipolar reaches the higher peak. Exact crossover or peak coordinates are not data targets.",
    "At fixed momentum very-short unipolar density scales as tau^4 and bipolar as tau^7. Bipolar longitudinal support grows as 1/tau, leaving relative total-yield suppression of two rather than three duration powers. This explains higher momentum reach with smaller probability.",
    "Homogeneous Schwinger rates, locally constant field models and omission of one pulse are not equivalent to the leading coherent two-pulse object. Concrete risks include energy matching, branch loss/duplication, finite-domain tail/yield distortion, display scaling, wrong integration dimension or overextended perturbative scope.",
    "The source total-yield curve supports broad ordering, crossover and peak-scale structure; no independent exact three-dimensional yield reference is implied. Fine-scale ambiguity requires bounded source/formula adjudication or an unresolved decision, not invented numerical tolerances.",
    "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.",
    "The leading density is $f(\\mathbf p)=\\pi^{-2}(E_0/E_{\\rm cr})^4(m\\tau/\\sigma)^4\\int dp_z^{\\prime}G(\\mathbf p,p_z^{\\prime})|F^{(+)}(q_+)F^{(-)}(q_-)|^2$, $q_\\pm=[p_0+p_0^{\\prime}\\pm(p_z+p_z^{\\prime})]\\tau/(2\\sigma)$ (Eq. (7)). The shared Fourier profile is $F^{(\\zeta)}(q)=\\sqrt\\pi\\sigma e^{-\\sigma^2(q^2+1)/4}[\\sin\\phi_\\zeta\\cosh(\\sigma^2q/2)+i\\cos\\phi_\\zeta\\sinh(\\sigma^2q/2)]$ (Eq. (8)); use the coherent kernel or an equivalent two-pulse formulation.",
    "Total pairs per declared transverse normalization area are $N=\\int d^3p\\,f(\\mathbf p)$ (Eq. (6)); $\\int dp_xdp_z f(p_x,0,p_z)$ is only a slice integral. Perturbative interpretation requires the declared small-parameter domain, conventionally $\\xi=(E_0/E_{\\rm cr})m\\tau\\ll1$; source formal amplitude rescalings do not certify arbitrary physical intensities.",
    "For $E_x^{(\\zeta)}(t,z)=E_{0\\zeta}e^{(\\zeta)}(\\sigma(t-\\zeta z)/\\tau)$ and $e^{(\\zeta)}(\\eta)=e^{-(\\eta/\\sigma)^2}\\sin(\\eta+\\phi_\\zeta)$, $W^{(\\zeta)}=\\sqrt\\pi E_{0\\zeta}^2\\tau[1-e^{-\\sigma^2/2}\\cos(2\\phi_\\zeta)]/2^{3/2}$ (Eqs. (2)-(5)). Thus the bipolar/like-unipolar matched amplitude ratio is $[\\tanh(\\sigma^2/4)]^{-1/2}$. The mixed case instead uses the task-prescribed common amplitudes $E_{0+}=E_{0-}=E_*=0.1E_{\\rm cr}$; no mixed-case equal-energy rescaling is imposed."
  ],
  "closure_requirements": {
    "RC0": [
      "Required claim CL1, central object: F3: Establish the shared leading nonvanishing perturbative-QED coherent two-pulse kernel/object with counterpropagating spacetime dependence, phase-sensitive branches and declared continuum normalization; equivalent time-domain or Volkov representations are accepted.. 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 [O1: Provide at least one correctly duration-bound equal-energy unipolar-pair momentum density with correct case/orientation, even longitudinal symmetry, major support/lobes and auditable unscaled density.; O2: Provide at least one correctly duration-bound equal-energy bipolar-pair density with even longitudinal symmetry, bandwidth/density scale and major lobes, permitting the comparable contrast/duration evolution with the unipolar branch; retain unscaled data.]. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL3, indispensable component: O3: Provide at least one correctly bound mixed-phase density with both pulse-phase orientations and longitudinal convention, resolving broken symmetry and directed support; duration coverage is separately judged by I2/M5 within the claim domain.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL4, indispensable component: O4: Provide a correctly equal-energy/class-bound three-dimensional total-yield bounded duration scan, not a p_y = 0 slice. Missing one broad regime does not erase credit for an otherwise valid bounded scan.. 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 CL3, principal mechanism: M5: Explain that the mixed assignment binds distinct Fourier/time-domain structures to opposite counterpropagating branches, breaking the interchange/reflection symmetry producing an even longitudinal spectrum; give the direction convention and restrict duration extrapolation to evidence.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "Required claim CL4, principal mechanism: M3: Explain how polarity/phase changes the coherent leading observable through phase-sensitive two-pulse Fourier factors or equivalent time-domain/Volkov construction; homogeneous tunneling is not an equivalent mechanism.. 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 or claim exposes a concrete risk that can overturn or materially weaken the central conclusion, discriminate it or narrow the claim; otherwise record N/A without validation-evidence credit.. Judge role-trigger facts, not the sum or pattern of atomic scores.",
      "All indispensable signal and principal-mechanism roles are substantially supported, but a concrete triggered material risk remains unresolved and inadequately restricted.",
      "Establish the failure mode, candidate origin, fair task/knowledge basis, threatened central conclusion, insufficiency of submitted evidence, and equivalent resolution or scope restriction. Missing an examiner-preferred check alone never suffices."
    ],
    "RC4": [
      "Every nonempty required role in every indispensable and co-primary claim above is scientifically established from candidate evidence, with the correct case/model/observable identities and evidence-bounded conclusion.",
      "All applicable material risks are discriminated or honestly restricted; no unresolved material ambiguity remains. Risk N/A does not block closure or supply positive validation evidence. Honest limitations cannot repair a false signal or mechanism.",
      "Select the most severe failed required role if any; otherwise RC4. No score threshold, score ceiling or required display/solver checklist determines this classification."
    ]
  },
  "references": [
    {
      "citation": "I. A. Aleksandrov and N. N. Rosanov. 2024. Vacuum pair production in zeptosecond pulses: Peculiar momentum spectra and striking particle acceleration by bipolar pulses. Physical Review D, 110, L111901.",
      "url": "https://doi.org/10.1103/PhysRevD.110.L111901",
      "scientific_scope": "Leading perturbative pair production by counterpropagating spacetime pulses, equal-energy comparison, phase-directed momentum structure, three-dimensional productivity and duration scaling. Source displays and fine-scale curve coordinates are not extra duties.",
      "anchors": [
        "preprint p. 2, Eqs. (2)-(5), Fig. 1(b)",
        "preprint p. 2, Eqs. (7)-(8), leading-order theoretical-description paragraphs; Supplemental Eqs. (S1)-(S7)",
        "preprint pp. 2 and 4, Eq. (6), Fig. 4 and adjacent total-yield discussion",
        "preprint p. 3, Fig. 2 left/right columns and numerical-results paragraphs",
        "preprint p. 3, Fig. 3 left/right panels and mixed-phase paragraph; Eq. (8) on p. 2",
        "preprint pp. 3-4, Figs. 2-4 and contrast/yield discussion",
        "preprint pp. 2-3, Eqs. (7)-(8) and short-duration paragraphs; Supplemental Eqs. (S8)-(S11)",
        "preprint pp. 1-2, Setup and perturbative-validity paragraphs; p. 4, concluding discussion"
      ]
    }
  ]
}