cases/case21/grading_rubric.md

# Grading Rubric — Case21

Spectral fringes without subcycles in Schwinger pair production and Dirac materials

## Atomic Scoring Criteria

Each criterion awards 0 or 0.5 points, for a maximum of 10. Explicit N/A rules apply where stated.

### F1 — F — 0.5 points

**Scientific requirement**

Establish a common field/vector-potential convention for both supplied single-lobe fields, exact scalar-QED mode or equivalent exact kinetic evolution, in-vacuum and asymptotic occupation readout; WKB does not replace exact production signals.

**Conditions for credit**

- Both single-lobe fields share a consistent vector-potential/charge convention, incoming vacuum and exact scalar production readout; WKB alone is not the production solution.

**Applicability and N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- 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.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, Fig. 1(a,b), Eqs. (1)-(2) and exact-mode paragraph; Supplemental pp. i-ii, Eqs. (S1)-(S12): Gaussian versus deformed exact scalar occupations are different production objects; display multipliers and WKB predictions do not replace unscaled exact occupations.

**Research Closure 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.

### F2 — F — 0.5 points

**Scientific requirement**

Establish the visible gapped-Dirac Hamiltonian, filled-valence incoming state and exact asymptotic post-pulse conduction occupation, consistently treating charge, field/vector potential and gap.

**Conditions for credit**

- The gapped-Dirac equations use the stated gap, filled-valence incoming state and asymptotic conduction population under the same field convention.

**Applicability and N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- 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.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 3, Eqs. (6)-(7), Fig. 3(a,b); Supplemental Eqs. (S14)-(S48): Filled-valence gapped-Dirac dynamics is read as post-pulse conduction occupation, with the specified gap and durations.

**Research Closure 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.

### F3 — F — 0.5 points

**Scientific requirement**

Develop a testable complex-time turning-point, coherent-contribution, analytic-continuation or physically equivalent interference-analysis route, distinct from the exact production-signal identity.

**Conditions for credit**

- The proposed mechanism representation is computable and can test onset and coherent contribution competition independently of the exact production solver.

**Applicability and N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- 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.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, Eqs. (2)-(5), Fig. 2 and its caption; Supplemental Eqs. (S1)-(S13): The deformed-pulse imaginary-axis turning point loses effective sole dominance near the finite critical integral; onset evidence is distinct from a complete active-weight demonstration.

**Research Closure 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.

### O1 — O — 0.5 points

**Scientific requirement**

Provide the correctly bound deformed-pulse gamma = 2 exact scalar-QED asymptotic longitudinal occupation, resolving symmetric center suppression and material off-center structure and preserving unscaled data.

**Conditions for credit**

- The deformed gamma=2 scalar output is an unscaled asymptotic exact occupation with symmetric center suppression and material off-center structure.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- 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.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, Fig. 1(a,b), Eqs. (1)-(2) and exact-mode paragraph; Supplemental pp. i-ii, Eqs. (S1)-(S12): Gaussian versus deformed exact scalar occupations are different production objects; display multipliers and WKB predictions do not replace unscaled exact occupations.

**Research Closure 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.

### O2 — O — 0.5 points

**Scientific requirement**

Provide the remaining visible scalar branches so the Gaussian/deformed contrast and prescribed duration/nonadiabatic dependence are independently judgeable, retaining unscaled data.

**Conditions for credit**

- The other visible scalar cases expose Gaussian/deformed and prescribed-duration contrast on recoverable unscaled occupations.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- 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.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, Fig. 1(a,b), Eqs. (1)-(2) and exact-mode paragraph; Supplemental pp. i-ii, Eqs. (S1)-(S12): Gaussian versus deformed exact scalar occupations are different production objects; display multipliers and WKB predictions do not replace unscaled exact occupations.

**Research Closure 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.

### O3 — O — 0.5 points

**Scientific requirement**

Provide a reconstructible case-bound auditable mechanism-evidence object adequately presenting separately judgeable onset/dominance change and competition among comparable active contributions; this output atom does not require the candidate already to have made either identification or mechanism conclusion.

**Conditions for credit**

- The mechanism evidence object separately exposes onset/dominance change and comparable active contribution competition; its existence does not presume candidate identification.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- 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 onset/dominance change and a demonstration of active comparable weights are separate facts. Credit correct onset without pretending that it already proves every claimed coherent contribution.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, Eqs. (2)-(5), Fig. 2 and its caption; Supplemental Eqs. (S1)-(S13): The deformed-pulse imaginary-axis turning point loses effective sole dominance near the finite critical integral; onset evidence is distinct from a complete active-weight demonstration.

**Research Closure 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.

### O4 — O — 0.5 points

**Scientific requirement**

Provide at least one correctly bound nonadiabatic deformed-Dirac post-pulse occupation with the filled-valence/readout identity and judgeable center suppression or material off-center structure; remaining family/duration transfer coverage is judged separately by I4/M4/M6.

**Conditions for credit**

- At least one correctly bound nonadiabatic deformed-Dirac case has a valid post-pulse occupation resolving suppression or off-center structure; other transfer coverage remains separate.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- 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.

- One valid nonadiabatic deformed-Dirac occupation can satisfy O4. Missing additional Gaussian/duration branches affects the transfer/coverage claim locally, not the existing occupation object or independently correct scalar branch.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 3, Eqs. (6)-(7), Fig. 3(a,b); Supplemental Eqs. (S14)-(S48): Filled-valence gapped-Dirac dynamics is read as post-pulse conduction occupation, with the specified gap and durations.

**Research Closure 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.

### I1 — I — 0.5 points

**Scientific requirement**

Identify material Gaussian/deformed differences and their gamma dependence from valid scalar spectra, not from display scaling or numerical noise.

**Conditions for credit**

- The candidate identifies material pulse-family differences and gamma dependence from exact scalar spectra, not curve multipliers or noise.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- O2: Provide the remaining visible scalar branches so the Gaussian/deformed contrast and prescribed duration/nonadiabatic dependence are independently judgeable, retaining unscaled data. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.

- Preserve independent correct work in O1, I2, I3, I4 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 pulse-family/gamma comparison depends on the comparison morphology in O2, not merely the single O1 branch. Incomplete comparisons do not erase correct deformed gamma = 2, onset or Dirac work.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, Fig. 1(a,b), Eqs. (1)-(2) and exact-mode paragraph; Supplemental pp. i-ii, Eqs. (S1)-(S12): Gaussian versus deformed exact scalar occupations are different production objects; display multipliers and WKB predictions do not replace unscaled exact occupations.

**Research Closure 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.

### I2 — I — 0.5 points

**Scientific requirement**

Identify from submitted mechanism evidence the crossover/onset where the leading deformed-pulse contribution loses sole dominance.

**Conditions for credit**

- The candidate identifies loss of effective sole dominance in their onset evidence rather than merely quoting the critical integral.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- O3: Provide a reconstructible case-bound auditable mechanism-evidence object adequately presenting separately judgeable onset/dominance change and competition among comparable active contributions; this output atom does not require the candidate already to have made either identification or mechanism conclusion. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.

- Preserve independent correct work in I1, I3, I4 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 onset/dominance change and a demonstration of active comparable weights are separate facts. Credit correct onset without pretending that it already proves every claimed coherent contribution.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, Eqs. (2)-(5), Fig. 2 and its caption; Supplemental Eqs. (S1)-(S13): The deformed-pulse imaginary-axis turning point loses effective sole dominance near the finite critical integral; onset evidence is distinct from a complete active-weight demonstration.

**Research Closure 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.

### I3 — I — 0.5 points

**Scientific requirement**

Identify that beyond crossover several physically active contributions have comparable weights and interfere through relative actions/phases, rather than only saying there are multiple paths.

**Conditions for credit**

- The candidate identifies physically active comparable contributions and relative phases/actions; a list of multiple roots alone does not establish interference weights.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- O3: Provide a reconstructible case-bound auditable mechanism-evidence object adequately presenting separately judgeable onset/dominance change and competition among comparable active contributions; this output atom does not require the candidate already to have made either identification or mechanism conclusion. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.

- Preserve independent correct work in I1, I2, I4 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 onset/dominance change and a demonstration of active comparable weights are separate facts. Credit correct onset without pretending that it already proves every claimed coherent contribution.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, Fig. 2 caption and semiclassical-mechanism paragraphs; Supplemental Eqs. (S1)-(S13): Several physically active comparable contributions with relative actions are needed to identify interference; merely finding multiple zeros does not establish comparable weights.

**Research Closure 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.

### I4 — I — 0.5 points

**Scientific requirement**

Identify from valid Dirac occupations the pulse-family contrast, center suppression/multiple extrema and gamma_D-dependent crossover.

**Conditions for credit**

- The candidate identifies the Dirac pulse-family/nonadiabatic crossover from actual occupations and available duration comparisons.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- O4: Provide at least one correctly bound nonadiabatic deformed-Dirac post-pulse occupation with the filled-valence/readout identity and judgeable center suppression or material off-center structure; remaining family/duration transfer coverage is judged separately by I4/M4/M6. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.

- Preserve independent correct work in I1, 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.

- One valid nonadiabatic deformed-Dirac occupation can satisfy O4. Missing additional Gaussian/duration branches affects the transfer/coverage claim locally, not the existing occupation object or independently correct scalar branch.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 3, Eqs. (6)-(7), Fig. 3(a,b); Supplemental Eqs. (S14)-(S48): Filled-valence gapped-Dirac dynamics is read as post-pulse conduction occupation, with the specified gap and durations.

**Research Closure 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.

### M1 — M — 0.5 points

**Scientific requirement**

Use specific scalar-spectrum evidence to answer whether smooth carrier-free single-lobe fields produce spectral interference without real-time subcycles.

**Conditions for credit**

- The answer uses scalar signal features to establish whether fringes can occur without real-time carrier subcycles.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- I1: Identify material Gaussian/deformed differences and their gamma dependence from valid scalar spectra, not from display scaling or numerical noise. 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.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, Fig. 1(a,b), Eqs. (1)-(2) and exact-mode paragraph; Supplemental pp. i-ii, Eqs. (S1)-(S12): Gaussian versus deformed exact scalar occupations are different production objects; display multipliers and WKB predictions do not replace unscaled exact occupations.

**Research Closure 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.

### M2 — M — 0.5 points

**Scientific requirement**

Correctly explain onset as loss of effective single-contribution dominance and competition among multiple contributions, excluding carrier cycles or numerical noise as false origins. Whether active comparable weights are discriminated is independently judged by I3 and triggered V2.

**Conditions for credit**

- The onset explanation correctly invokes loss of single-contribution dominance, not nonexistent real-time oscillations or numerical noise.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- I2: Identify from submitted mechanism evidence the crossover/onset where the leading deformed-pulse contribution loses sole dominance. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.

- Preserve independent correct work in I3, M1, M4, M5, M6, M7, V2 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 correct onset/dominance-change explanation is not automatically false because physically active/comparable contribution evidence is incomplete. Wrong origin is a mechanism/RC2 failure; a materially threatened stronger attribution with correct mechanism direction belongs to I3 and specifically triggered V2/RC3.

- A valid onset/dominance change and a demonstration of active comparable weights are separate facts. Credit correct onset without pretending that it already proves every claimed coherent contribution.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, Eqs. (2)-(5), Fig. 2 and its caption; Supplemental Eqs. (S1)-(S13): The deformed-pulse imaginary-axis turning point loses effective sole dominance near the finite critical integral; onset evidence is distinct from a complete active-weight demonstration.

**Research Closure 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.

### M3 — M — 0.5 points

**Scientific requirement**

Connect the identified dominance-change onset to scalar center suppression, off-center extrema and nonadiabatic case dependence; stronger comparable-active-weight claims still need independent I3/V2 discrimination.

**Conditions for credit**

- The candidate connects their identified onset to center suppression, side extrema and gamma-dependent scalar morphology, without pretending onset alone proves every active weight.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- All of [I1: Identify material Gaussian/deformed differences and their gamma dependence from valid scalar spectra, not from display scaling or numerical noise.; I2: Identify from submitted mechanism evidence the crossover/onset where the leading deformed-pulse contribution loses sole dominance.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.

- Preserve independent correct work in I3, M1, M2, M4, M5, M6, M7, V2 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 onset-to-spectrum linkage needs the candidate scalar comparison and identified onset, not prior closure of the stronger I3 contribution-weight risk. Do not back-propagate that sufficiency gap into an established linkage.

- A valid onset/dominance change and a demonstration of active comparable weights are separate facts. Credit correct onset without pretending that it already proves every claimed coherent contribution.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, Fig. 1(b), Fig. 2 and Eqs. (3)-(5): Connect the dominance transition to central suppression, side extrema and nonadiabatic dependence in the scalar signal.

**Research Closure 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.

### M4 — M — 0.5 points

**Scientific requirement**

Test qualitative transfer of the contribution-competition crossover using Dirac pulse-family/nonadiabatic evidence, not superficial visual similarity.

**Conditions for credit**

- Pulse-family and nonadiabatic Dirac evidence substantiate qualitative transfer of the competition mechanism, not only visual similarity.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- All of [M2: Correctly explain onset as loss of effective single-contribution dominance and competition among multiple contributions, excluding carrier cycles or numerical noise as false origins. Whether active comparable weights are discriminated is independently judged by I3 and triggered V2.; I4: Identify from valid Dirac occupations the pulse-family contrast, center suppression/multiple extrema and gamma_D-dependent crossover.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.

- Preserve independent correct work in M1, 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.

- Mechanism transfer requires the established scalar mechanism and candidate Dirac main-branch identification; no examiner-created visual inference. Dirac broad coverage remains separately owned.

- One valid nonadiabatic deformed-Dirac occupation can satisfy O4. Missing additional Gaussian/duration branches affects the transfer/coverage claim locally, not the existing occupation object or independently correct scalar branch.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article pp. 3-4, Fig. 3(a,b), Eqs. (6)-(7), and Fig. 4(a,b): The pulse-family/nonadiabatic crossover transfers qualitatively to Dirac carriers, not as equality of yields or critical scales. Fig. 4 is optional broad-domain context; its visibility scalar is not an exact target.

**Research Closure 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.

### M5 — M — 0.5 points

**Scientific requirement**

Distinguish qualitative mechanism transfer from equality of absolute yields, momentum scales or critical parameters across systems.

**Conditions for credit**

- The transfer conclusion explicitly distinguishes mechanism similarity from equality of momentum scales, yields or critical parameters.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- 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.

- One valid nonadiabatic deformed-Dirac occupation can satisfy O4. Missing additional Gaussian/duration branches affects the transfer/coverage claim locally, not the existing occupation object or independently correct scalar branch.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article pp. 3-4, Fig. 3(a,b), Eqs. (6)-(7), and Fig. 4(a,b): The pulse-family/nonadiabatic crossover transfers qualitatively to Dirac carriers, not as equality of yields or critical scales. Fig. 4 is optional broad-domain context; its visibility scalar is not an exact target.

**Research Closure 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.

### M6 — M — 0.5 points

**Scientific requirement**

Beyond the valid main deformed-Dirac branch in O4, explain coverage of the other Gaussian/deformed profiles and prescribed durations for transfer/onset. Missing comparisons affect this branch-local obligation; broader domain claims may use equivalent self-chosen variation, not a compulsory source two-dimensional map.

**Conditions for credit**

- The argument addresses the remaining prescribed pulse/duration comparisons within its actual transfer/onset domain; a broad source two-dimensional map is not mandatory.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- O4: Provide at least one correctly bound nonadiabatic deformed-Dirac post-pulse occupation with the filled-valence/readout identity and judgeable center suppression or material off-center structure; remaining family/duration transfer coverage is judged separately by I4/M4/M6. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate.

- Preserve independent correct work in I4, 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.

- Missing remaining profiles/durations or a broad map does not erase established O4/I4/M4 main-branch credit. Demand equivalent parameter variation only for an actual broader claim.

- One valid nonadiabatic deformed-Dirac occupation can satisfy O4. Missing additional Gaussian/duration branches affects the transfer/coverage claim locally, not the existing occupation object or independently correct scalar branch.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article pp. 3-4, Fig. 3(a,b), Eqs. (6)-(7), and Fig. 4(a,b): The pulse-family/nonadiabatic crossover transfers qualitatively to Dirac carriers, not as equality of yields or critical scales. Fig. 4 is optional broad-domain context; its visibility scalar is not an exact target.

**Research Closure 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.

### M7 — M — 0.5 points

**Scientific requirement**

Synthesize exact signals, mechanism and cross-system evidence into the strongest supported conclusion limited to the specified homogeneous external-field models, pulse family and evidence-supported nonadiabatic domain.

**Conditions for credit**

- The final research answer integrates exact scalar and Dirac signals with the mechanism and retains a homogeneous external-model/nonadiabatic scope.

- 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 N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- 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.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 4, Discussion and outlook and preceding zero-area paragraph: The demonstrated result is bounded to homogeneous prescribed fields and the established model/domain; source experimental suggestions are not required conclusions.

**Research Closure 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.

### V1 — V — 0.5 points

**Scientific requirement**

Positively state the actual models, exact/approximate evidence boundary, reconstructible data and claim domain, without making a canonical grid, root solver, map or zero-area test a default duty.

**Conditions for credit**

- The actual models, exact-versus-approximate evidence boundary, recoverable data and claim domain are positively stated.

**Applicability and N/A**

- Applicable to the stated scientific commission; N/A is not permitted.

**Scientific dependencies and independent credit**

- 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.

- Ordinary omission of positive scope is owned here; it does not automatically trigger V2 or RC3. Do not charge the same overclaim repeatedly at M7, V1 and V2.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 4, Discussion and outlook and preceding zero-area paragraph: The demonstrated result is bounded to homogeneous prescribed fields and the established model/domain; source experimental suggestions are not required conclusions.

**Research Closure 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.

### V2 — V — 0.5 points

**Scientific requirement**

Only when candidate method, data or claim exposes a specific risk capable of overturning or materially weakening the central conclusion, discriminate it or narrow the claim; otherwise record N/A without claiming validation evidence.

**Conditions for credit**

- If actual approximation, numerical-fringe, active-weight or far-field overclaim risks threaten the central answer, discriminate or restrict them; otherwise use N/A without inventing a zero-area test.

**Applicability and N/A**

- 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.

**Scientific dependencies and independent credit**

- 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.

**Accepted equivalent evidence**

- Exact Klein-Gordon modes and matched bosonic kinetic evolution are equivalent scalar routes; exact Dirac propagation, matched reduced Bogoliubov amplitudes and fermionic kinetic evolution are equivalent Dirac routes with the same states and readout.

- Complex turning points are not the unique mechanism language: a reconstructible coherent-amplitude or analytic-continuation representation is accepted if it preserves onset, relevant contribution competition and cross-system mechanism.

- Alternative evidence layouts, self-chosen parameter variations and declared transformations are accepted when physical cases, unscaled data and claimed structure remain recoverable; no fixed root seeds, branch samples, maps, curve multipliers or visibility scalar is required.

**Scientific source locations**

- Aleksandrov et al. (2026), main article p. 2, exact-mode versus semiclassical distinction; p. 4, zero-area discussion; Supplemental p. vii, Eqs. (S55)-(S56) and Fig. S3: These supply context for actual approximation, fringe, active-weight or freely propagating-pulse threats. A compensating-tail calculation is not compulsory for an external-field-bounded claim.

**Research Closure 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.

## Research Closure Requirements

### RC0

- Required claim CL1, central object: F1: Establish a common field/vector-potential convention for both supplied single-lobe fields, exact scalar-QED mode or equivalent exact kinetic evolution, in-vacuum and asymptotic occupation readout; WKB does not replace exact production signals.. Judge role-trigger facts, not the sum or pattern of atomic scores.

- Apply for a missing or materially invalid required central object; a presentation-only or claim-only defect does not establish object invalidity.

- No scientifically assessable required submission gives the terminal 0.0/RC0 disposition.

### RC1

- Required claim CL1, indispensable component: All of [O1: Provide the correctly bound deformed-pulse gamma = 2 exact scalar-QED asymptotic longitudinal occupation, resolving symmetric center suppression and material off-center structure and preserving unscaled data.; O2: Provide the remaining visible scalar branches so the Gaussian/deformed contrast and prescribed duration/nonadiabatic dependence are independently judgeable, retaining unscaled data.]. Judge role-trigger facts, not the sum or pattern of atomic scores.

- Required claim CL2, indispensable component: O4: Provide at least one correctly bound nonadiabatic deformed-Dirac post-pulse occupation with the filled-valence/readout identity and judgeable center suppression or material off-center structure; remaining family/duration transfer coverage is judged separately by I4/M4/M6.. Judge role-trigger facts, not the sum or pattern of atomic scores.

- The central object is established but a required physical component is absent or materially invalid. Preserve independent valid branches; do not invent a hidden canonical plot, sampling grid or implementation duty.

### RC2

- Required claim CL1, principal mechanism: M2: Correctly explain onset as loss of effective single-contribution dominance and competition among multiple contributions, excluding carrier cycles or numerical noise as false origins. Whether active comparable weights are discriminated is independently judged by I3 and triggered V2.. Judge role-trigger facts, not the sum or pattern of atomic scores.

- Required claim CL2, principal mechanism: M4: Test qualitative transfer of the contribution-competition crossover using Dirac pulse-family/nonadiabatic evidence, not superficial visual similarity.. 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 CL3, material validation: V2: Only when candidate method, data or claim exposes a specific risk capable of overturning or materially weakening the central conclusion, discriminate it or narrow the claim; otherwise record N/A without claiming validation evidence.. 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.

## Applicability and Equivalent Evidence

- Scalar modes have Q_p(t) = sqrt(m^2 + p_perp^2 + [p_parallel - e A(t)]^2). Exact Klein-Gordon evolution or the matched bosonic quantum-kinetic system uses the same in-vacuum and asymptotic occupation. A WKB turning-point sum is an approximate mechanism model, not the exact production output.

- The gapped-Dirac band energy is epsilon_k(t) = sqrt(Delta^2 + v_F^2 |hbar k - e A(t)|^2). Start with filled valence and read post-pulse conduction occupation |beta_tilde|^2 = f. A consistent charge/vector-potential sign change reflecting a symmetric longitudinal spectrum is immaterial.

- At p_perp = 0 and E0 = 0.1 Ec, all prescribed Gaussian scalar spectra are smooth central maxima. The deformed profile at gamma = 2 has pronounced symmetric off-center maxima, strongly suppressed center and outer structure; gamma = 1 has weaker multi-extremum structure; gamma = 0.5 returns to a smooth central peak. Preserve unscaled occupations; source curve multipliers are not physical yields.

- In complex time, turning points are zeros of Q_p. With a(z) = - integral_0^z e(z') dz', they obey a(t_i/tau) = [(+/- i pi_perp - p_parallel)/m] gamma, pi_perp = sqrt(m^2 + p_perp^2). For Gaussian the closest imaginary-axis point stays finite and dominant; for the deformed pulse at zero momentum it moves upward and loses finite dominance at gamma_* = integral_0^infinity exp(z^2 - z^4) dz, approximately 1.381.

- Several subleading contributions then become competitive and their relative actions produce interference. Equivalent analytic/coherent representations are accepted; exact branch count, author arrows and colors are not duties. An onset/dominance argument alone is distinct from demonstrating every claimed physically active comparable contribution.

- For Dirac material at k_perp = 0, Delta = 0.1 eV and E0 = 40 kV/cm, Gaussian spectra at the three durations are smooth central peaks. Deformed tau = 20 fs (gamma_D = 1.25) has deep center suppression and symmetric side peaks, tau = 30 fs (0.833) weaker multiple extrema, and tau = 50 fs (0.5) a central peak. Momentum/yield equality with scalar QED is not implied.

- Two-dimensional fringe maps may resolve a broad onset claim but are not hidden required outputs. The source visibility definition has a factor-of-two normalization ambiguity; compare robust onset-region topology, not an exact visibility scalar.

- The external fields are homogeneous prescribed profiles. A nonzero-area single lobe is not automatically a freely propagating far-field pulse. A long weak compensating tail is one accepted response to an experimental claim, but no zero-area-tail calculation is required for an honestly external-model-bounded claim. Dephasing, integration, material corrections and experimental readout are not established by the default evidence.

- Concrete risks include WKB mistaken for exact production, pulse/duration/charge/asymptotic-state misbinding, numerical/display fringes, missing contribution content, misleading representation transfer or an unsupported far-field claim. No fixed root search, grid refinement or control is required without a trigger.

- The score is the sum of twenty material-core criteria, each worth either 0 or 0.5, for a maximum of 10.0. Research Closure is descriptive and never caps, floors, rescales or repairs the score.

- Judge physical object identity and correctness before display similarity. For each output record object_valid, presentation_adequate and claim_adequate separately; all three must hold for its atomic award. A presentation or claim defect alone is not evidence that an existing physical object is absent or invalid.

- Candidate-created data, candidate presentation, candidate identification, physical inference and validation are distinct evidential acts. Examiner inspection or reconstruction may verify an object but cannot create missing candidate identification, reasoning or risk resolution.

- A dependency propagates only the failed necessary physical fact, not the whole upstream atomic verdict or unrelated missing detail. Name the failed premise, the downstream obligation needing it, and why independent candidate-presented evidence does not establish it. Preserve unaffected branches, independent work and honest scope.

- Numerical reliability has no separate generic penalty. Charge a defect where it materially damages a physical object or evidence, and a dependent conclusion only when that same defect makes the conclusion false or unsupported. Missing a preferred convergence study, control, solver or named self-check is not itself a failure.

- Risk-triggered validation applies only to a concrete material risk arising from the candidate method, data, anomaly or claim. With no such risk record N/A and award the fixed atomic credit without treating it as positive validation evidence; N/A does not block RC4. Unconditional scope obligations cannot be N/A.

- Before assigning RC3 establish all six: the concrete failure mode; its origin in candidate work; the fair task or standard-knowledge basis; the threatened central conclusion; why submitted evidence cannot expose or exclude it; and examples of functionally equivalent discriminating evidence or an honest scope restriction that would resolve it. A generic possibility of further testing is insufficient.

- Use bounded examiner-side source/reference readback only to resolve a material scientific uncertainty, not to demand pixels, an undeclared tolerance or additional candidate deliverables. A provisional score of at least 9.0 or provisional RC4 triggers one bounded central-output-anchor check and one principal-mechanism-link check. Reference conflict or insufficiency remains an explicit unresolved decision, not an invented target.

- Evaluate closure-role trigger facts independently of atomic awards and select the most severe failed required role across all indispensable and co-primary claims. Supporting claims do not independently set overall closure. A point loss alone is not a closure-gate fact.

- A valid candidate-caused incomplete or timeout attempt with no scientifically assessable required submission has score 0.0 and RC0 before N/A bookkeeping. Assessable incomplete work is graded from the submitted evidence; unsubmitted scratch or logs do not become scientific answers.

- For scalar modes $Q_{\mathbf p}(t)=\sqrt{m^2+p_\perp^2+[p_\parallel-eA(t)]^2}$ and $\ddot u_{\mathbf p}+Q_{\mathbf p}^2u_{\mathbf p}=0$ with incoming vacuum normalization, read $n_{\mathbf p}=|\beta_{\mathbf p}|^2$ asymptotically; equivalent exact bosonic kinetic evolution is accepted. Turning points solve $Q_{\mathbf p}(t_i)=0$ and $a(t_i/\tau)=(\pm i\sqrt{m^2+p_\perp^2}-p_\parallel)\gamma/m$, with $a(z)=-\int_0^z e(z^{\prime})dz^{\prime}$ (Eqs. (2)-(3)).

- For $e(z)=e^{-z^2-z^4}$, $\gamma_*=\int_0^\infty e^{z^2-z^4}dz\simeq1.381$ (Eq. (5)). This is a dominance/onset diagnostic; an interference claim additionally needs coherent relative weights/actions, not a prescribed branch count.

- The Dirac Hamiltonian is $H_{\mathbf k}=v_F\boldsymbol\sigma\cdot[\hbar\mathbf k-e\mathbf A]+\Delta\sigma_z$ with energy $\varepsilon_{\mathbf k}=\sqrt{\Delta^2+v_F^2|\hbar\mathbf k-e\mathbf A|^2}$ and $\gamma_D=\Delta/(|e|v_FE_0\tau)$ (Eqs. (6)-(7)); the filled-valence initial state gives $n_{\mathbf k}=|\widetilde\beta_{\mathbf k}|^2$ after the pulse.