Datasets:

Tauben
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PhysClosureBench

Establish source-equivalent coherent active-sector amplitudes with detuning phases, initial/resonant/continuum Stark shifts, both local losses and coherent resonant/direct continuum addition.

Conditions for credit

Establish source-equivalent coherent active-sector amplitudes with detuning phases, initial/resonant/continuum Stark shifts, both local losses and coherent resonant/direct continuum addition.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Judge this scientific obligation directly; no fixed prerequisite award.
Preserve independently valid evidence for F3; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Zhang et al. (2022), article pp. 063114-2–4, Eqs. (5)–(10). Adiabatic elimination, rotating-wave/local approximations, coherent active-sector amplitudes, detunings, all three Stark shifts and both losses.

Research Closure relation

Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award.

F2 — F — 0.5 points

Scientific requirement

Bind hydrogen states, pulse/intensity/cycle cases, energy normalization, stated coefficients and continuum matrix elements; keep W and A on the same declared spectrum.

Conditions for credit

Bind hydrogen states, pulse/intensity/cycle cases, energy normalization, stated coefficients and continuum matrix elements; keep W and A on the same declared spectrum.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: F1. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for F3; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article pp. 063114-2, 063114-4–5, Eq. (3), Eq. (10), Fig. 2 caption and optimized-parameter paragraph after Fig. 3. Hydrogen pulse/intensity/cycle and energy-normalized continuum bindings, plus same-spectrum spacing/asymmetry. Source optimized coefficients, not separately rescaled example code, define the given reduced model.

Research Closure relation

Central-object role: RC0 only if the central physical identity is absent or materially invalid, independently of this atom's award.

F3 — F — 0.5 points

Scientific requirement

Establish an independent three-dimensional single-active-electron hydrogen TDSE route with reconstructible energy-normalized PES and reduced-model comparison mapping.

Conditions for credit

Establish an independent three-dimensional single-active-electron hydrogen TDSE route with reconstructible energy-normalized PES and reduced-model comparison mapping.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Judge this scientific obligation directly; no fixed prerequisite award.
Preserve independently valid evidence for F1, F2, O1, O2; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article p. 063114-2, Eqs. (1)–(4), TDSE continuum-extraction paragraphs. Independent hydrogen TDSE and PES mapping; gauge/basis/projection equivalents are accepted, without mandating FEDVR or the author mask.

Research Closure relation

Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object.

O1 — O — 0.5 points

Scientific requirement

Present valid reconstructible N=60/N=300 reduced-model energy-normalized spectra exposing the paired principal doublet and same-spectrum W/A objects.

Conditions for credit

Present valid reconstructible N=60/N=300 reduced-model energy-normalized spectra exposing the paired principal doublet and same-spectrum W/A objects.
The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: (F1 AND F2). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for O3; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article p. 063114-5, Fig. 3(a,b) and caption; p. 063114-4, W/A definitions after Fig. 2. N=60/300 principal doublets, not dynamic subpeak pairing; both metrics come from the same declared spectrum.

Research Closure relation

Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object.

O2 — O — 0.5 points

Scientific requirement

Present valid reconstructible W/A evidence across both intensities and both pulse lengths, including the physical outputs of a candidate-chosen claim-adequate intervention or contrast.

Conditions for credit

Present valid reconstructible W/A evidence across both intensities and both pulse lengths, including the physical outputs of a candidate-chosen claim-adequate intervention or contrast.
The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: O1. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for O3; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article p. 063114-4, Fig. 2(a–d); pp. 063114-5–6, Fig. 4(a–d) and captions. Spacing/asymmetry response across two intensities and pulse lengths, with a discriminating contrast. Source N=120 and complete TDSE maps are not compulsory task outputs.

Research Closure relation

Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object.

O3 — O — 0.5 points

Scientific requirement

Present valid reconstructible bounded N=60 central-case TDSE PES/response exposing the same-domain doublet and the claimed material transfer evidence.

Conditions for credit

Present valid reconstructible bounded N=60 central-case TDSE PES/response exposing the same-domain doublet and the claimed material transfer evidence.
The physical output object is valid and reconstructible (object_valid); the candidate presents its material structure with adequate domain, resolution and dynamic range (presentation_adequate); and the inference stays within resolved support (claim_adequate). All three are necessary; record them separately.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: F3. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for O1, O2; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article pp. 063114-4–5, Fig. 1(a), Fig. 3(a), captions and comparison discussion; TDSE Eqs. (1)–(4), p. 063114-2. Independent N=60 same-domain doublet/transfer evidence. Source Fig. 3(b) long-pulse TDSE is not required; no unique local-frequency scan is imposed.

Research Closure relation

Indispensable-component role: RC1 only if the required physical object is absent or materially invalid. Presentation or claim-adequacy failure alone does not imply an absent or invalid object.

I1 — I — 0.5 points

Scientific requirement

Identify the principal doublet and material spacing W changes across the family from the candidate's own spectra, without confusing dynamic subpeaks with the main pair.

Conditions for credit

Identify the principal doublet and material spacing W changes across the family from the candidate's own spectra, without confusing dynamic subpeaks with the main pair.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: (O1 AND O2). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for I2, I3, I4; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article p. 063114-4, Fig. 2(a–d); pp. 063114-5–6, Fig. 4(a–d) and captions. Spacing/asymmetry response across two intensities and pulse lengths, with a discriminating contrast. Source N=120 and complete TDSE maps are not compulsory task outputs.

Research Closure relation

Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim.

I2 — I — 0.5 points

Scientific requirement

Identify normalized asymmetry A and its intensity/pulse-length changes from the candidate's same-spectrum evidence.

Conditions for credit

Identify normalized asymmetry A and its intensity/pulse-length changes from the candidate's same-spectrum evidence.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: (O1 AND O2). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for I1, I3, I4; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article p. 063114-4, Fig. 2(a–d); pp. 063114-5–6, Fig. 4(a–d) and captions. Spacing/asymmetry response across two intensities and pulse lengths, with a discriminating contrast. Source N=120 and complete TDSE maps are not compulsory task outputs.

Research Closure relation

Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim.

I3 — I — 0.5 points

Scientific requirement

Identify the discriminating Stark/direct-path signal from the candidate's own intervention or contrast; examiner array reconstruction cannot supply this identification.

Conditions for credit

Identify the discriminating Stark/direct-path signal from the candidate's own intervention or contrast; examiner array reconstruction cannot supply this identification.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: O2. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for I1, I2, I4; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article pp. 063114-5–6, Fig. 4(a–d), direct-path comparison and interpretation paragraphs. Candidate identification and physical validity of a contribution-discriminating intervention; the source direct-path-off switch is one optional route, not the criterion itself.

Research Closure relation

Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim.

I4 — I — 0.5 points

Scientific requirement

Identify the same-domain TDSE doublet, morphology or response signal used for the candidate's model-transfer judgment.

Conditions for credit

Identify the same-domain TDSE doublet, morphology or response signal used for the candidate's model-transfer judgment.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: O3. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for I1, I2, I3; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article pp. 063114-4–5, Fig. 1(a), Fig. 3(a), captions and comparison discussion; TDSE Eqs. (1)–(4), p. 063114-2. Independent N=60 same-domain doublet/transfer evidence. Source Fig. 3(b) long-pulse TDSE is not required; no unique local-frequency scan is imposed.

Research Closure relation

Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim.

M1 — M — 0.5 points

Scientific requirement

Use W and discriminating evidence to explain the main role of initial/resonant Stark difference in spacing and its minimum.

Conditions for credit

Use W and discriminating evidence to explain the main role of initial/resonant Stark difference in spacing and its minimum.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: (I1 AND I3 AND V1). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M2, M3, M6, M7; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article pp. 063114-5–6, Eq. (11), Fig. 4(a,b), spacing-minimum and direct-path paragraphs. Initial/resonant Stark difference primarily controls spacing; direct-path spacing effect is comparatively weak in the studied family.

Research Closure relation

Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award.

M2 — M — 0.5 points

Scientific requirement

Use W and discriminating evidence to determine the direct coherent path's relative spacing effect, distinct from the Stark contribution.

Conditions for credit

Use W and discriminating evidence to determine the direct coherent path's relative spacing effect, distinct from the Stark contribution.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: (I1 AND I3 AND V1). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M1, M3, M6, M7; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article pp. 063114-5–6, Eq. (11), Fig. 4(a,b), spacing-minimum and direct-path paragraphs. Initial/resonant Stark difference primarily controls spacing; direct-path spacing effect is comparatively weak in the studied family.

Research Closure relation

Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award.

M3 — M — 0.5 points

Scientific requirement

Explain identified asymmetry through Stark shifts and coherent competition of resonant/direct continuum amplitudes, not incoherent channels.

Conditions for credit

Explain identified asymmetry through Stark shifts and coherent competition of resonant/direct continuum amplitudes, not incoherent channels.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: (I2 AND I3 AND V1). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M1, M2, M6, M7; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article pp. 063114-5–6, Eqs. (12)–(14), Fig. 4(c,d) and symmetry discussion. Stark phases and coherent direct/resonant continuum competition explain asymmetry, not an incoherent probability sum.

Research Closure relation

Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award.

M4 — M — 0.5 points

Scientific requirement

Connect intensity dependence in the candidate's W/A data to the relevant Stark/coherent mechanism rather than merely list changed numbers.

Conditions for credit

Connect intensity dependence in the candidate's W/A data to the relevant Stark/coherent mechanism rather than merely list changed numbers.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: (I1 AND I2). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M5; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article p. 063114-6, intensity-dependence and pulse-frequency-width paragraphs; Figs. 2(a–d), 4(a–d), pp. 063114-4–5. Intensity strengthens shift/path effects; pulse duration changes the finite-pulse response and asymmetry minimum, with mechanism links required rather than a list of numbers.

Research Closure relation

Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim.

M5 — M — 0.5 points

Scientific requirement

Connect pulse-length dependence in the candidate's W/A data to finite-pulse/dynamical response rather than merely list changed numbers.

Conditions for credit

Connect pulse-length dependence in the candidate's W/A data to finite-pulse/dynamical response rather than merely list changed numbers.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: (I1 AND I2). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M4; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article p. 063114-6, intensity-dependence and pulse-frequency-width paragraphs; Figs. 2(a–d), 4(a–d), pp. 063114-4–5. Intensity strengthens shift/path effects; pulse duration changes the finite-pulse response and asymmetry minimum, with mechanism links required rather than a list of numbers.

Research Closure relation

Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim.

M6 — M — 0.5 points

Scientific requirement

Use the candidate's same-domain TDSE evidence to judge whether, and over what domain, the central doublet/splitting model claim survives.

Conditions for credit

Use the candidate's same-domain TDSE evidence to judge whether, and over what domain, the central doublet/splitting model claim survives.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: I4. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M1, M2, M3, M7; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article pp. 063114-4–6, Figs. 1–4 and model/TDSE discussion. Task-defined bounded transfer judgment uses independent same-domain N=60 evidence; a central-doublet conclusion and a broader morphology/response conclusion remain separately judgeable.

Research Closure relation

Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award.

M7 — M — 0.5 points

Scientific requirement

Use bounded TDSE evidence to judge transfer of relative peak morphology, asymmetry or another actually claimed material response, limiting the conclusion to that evidence domain.

Conditions for credit

Use bounded TDSE evidence to judge transfer of relative peak morphology, asymmetry or another actually claimed material response, limiting the conclusion to that evidence domain.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: I4. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M1, M2, M3, M6; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article pp. 063114-4–6, Figs. 1–4 and model/TDSE discussion. Task-defined bounded transfer judgment uses independent same-domain N=60 evidence; a central-doublet conclusion and a broader morphology/response conclusion remain separately judgeable.

Research Closure relation

Principal-mechanism role: RC2 only if the specified principal physical inference is absent or incorrect, independently of this atom's award.

V1 — V — 0.5 points

Scientific requirement

Ensure the chosen intervention/contrast preserves relevant physical identities and genuinely discriminates Stark and coherent direct-path contributions; no source-specific switch is required.

Conditions for credit

The intervention or contrast preserves the relevant physical identities while genuinely discriminating the claimed Stark/direct contributions.
A source-specific direct-path-off toggle is not compulsory; non-discriminating design does not erase independently correct spectra or descriptive changes.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Necessary scientific premises: O2. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for O1, O3, M4, M5; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article pp. 063114-5–6, Fig. 4(a–d), direct-path comparison and interpretation paragraphs. Candidate identification and physical validity of a contribution-discriminating intervention; the source direct-path-off switch is one optional route, not the criterion itself.

Research Closure relation

Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim.

V2 — V — 0.5 points

Scientific requirement

Only when actual TDSE method/data/anomalies or transfer claims trigger a material boundary, continuum-spacing, projection or equivalent threat, or unsupported full-map/long-duration/PAD/partial-wave/absolute-yield extrapolation, provide discriminating exclusion or honestly restrict the claim; otherwise record N/A.

Conditions for credit

Only when actual TDSE method/data/anomalies or transfer claims trigger a material boundary, continuum-spacing, projection or equivalent threat, or unsupported full-map/long-duration/PAD/partial-wave/absolute-yield extrapolation, provide discriminating exclusion or honestly restrict the claim; otherwise record N/A.
When triggered, award only if claim-relevant discriminating evidence resolves the threat or an evidence-based restriction makes it immaterial; merely acknowledging an unresolved material threat is not positive validation credit. With no trigger, record N/A and retain the fixed 0.5 without claiming performed validation.

Applicability and N/A

Applies only when the submitted method, data, anomaly or conclusion creates the concrete material risk described here. If untriggered, record not_applicable and retain the fixed 0.5 contribution; this is not evidence that validation was performed, and does not block RC4.

Scientific dependencies and independent credit

Judge this scientific obligation directly; no fixed prerequisite award.
Preserve independently valid evidence for V3; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article p. 063114-2, TDSE continuum-extraction paragraph; pp. 063114-4–5, principal/dynamic-peak and normalization discussion. Task-defined triggered transfer risks from boundary/projection/continuum resolution or unsupported excluded-domain claims. No mandatory full TDSE scan, long-duration calculation or PAD test.

Research Closure relation

Material-validation role: RC3 only for a triggered, unresolved threat to a central conclusion, with all six burden-of-proof elements established. N/A does not block RC4.

V3 — V — 0.5 points

Scientific requirement

Positively identify the actually calculated active-sector family and bounded N=60 same-domain TDSE evidence domain, independently of success of any broader transfer claim.

Conditions for credit

The actual calculated active-sector family and bounded N=60 same-domain independent TDSE domain are positively and correctly identified.
This credit is independent of success of broader transfer; a material overclaim owned by V2 is not charged again here as the same defect.

Applicability and N/A

Applies to every assessable submission; absence or failure is scored 0, not N/A.

Scientific dependencies and independent credit

Judge this scientific obligation directly; no fixed prerequisite award.
Preserve independently valid evidence for V2; failure here does not automatically erase those criteria.
Propagate only an absent or incorrect scientific fact necessary for this obligation, not an upstream award or an unrelated display defect. Preserve independently valid work. Examiner reconstruction cannot supply candidate presentation, identification, inference or validation.
A missing positive actual-domain identification belongs here; a material broader overclaim belongs to V2 and is not the same additional V3 deduction.

Accepted equivalent evidence

Accept explicitly mapped rotating frames, phases, gauges and continuum normalizations preserving the same energy-normalized PES. Include all dipole-allowed orthogonal continuum channels by a channel sum or a declared equivalent-channel reduction.
Any intervention/contrast, parameter-preserving control, identifiable phase/amplitude decomposition or response design that genuinely separates the relevant Stark/direct contributions is accepted; no specific direct-path-off toggle or evidence order.
Accept length/velocity gauge, radial/basis/partial-wave choices and physically equivalent full-dimensional hydrogen solvers/extraction. A central spectrum, bounded frequency response or equally discriminating same-domain TDSE comparison may test the material claim; no mandatory local-frequency scan, author projection, full map, N=300 TDSE or angular/absolute-yield output.

Scientific source locations

Article pp. 063114-2–4, method separation; Fig. 3(a), p. 063114-5. Positive identification of actual reduced-model and bounded N=60 TDSE domain, independent of broader transfer success; not a second charge for an overclaim owned by V2.

Research Closure relation

Supporting criterion; no independent overall RC gate. Its actual scientific facts can still be necessary to a required claim.

Research Closure Requirements

RC0

The central physical object is absent or materially invalid. Establish this scientific fact independently of atomic credit; a local notation or presentation weakness is not itself RC0.
(F1 AND F2): Establish source-equivalent coherent active-sector amplitudes with detuning phases, initial/resonant/continuum Stark shifts, both local losses and coherent resonant/direct continuum addition. Bind hydrogen states, pulse/intensity/cycle cases, energy normalization, stated coefficients and continuum matrix elements; keep W and A on the same declared spectrum.

RC1

The central object exists, but a required indispensable component is absent or materially invalid. A failed presentation or overextended claim alone does not establish object absence or invalidity.
(O1 AND O2): Present valid reconstructible N=60/N=300 reduced-model energy-normalized spectra exposing the paired principal doublet and same-spectrum W/A objects. Present valid reconstructible W/A evidence across both intensities and both pulse lengths, including the physical outputs of a candidate-chosen claim-adequate intervention or contrast.
(F3 AND O3): Establish an independent three-dimensional single-active-electron hydrogen TDSE route with reconstructible energy-normalized PES and reduced-model comparison mapping. Present valid reconstructible bounded N=60 central-case TDSE PES/response exposing the same-domain doublet and the claimed material transfer evidence.

RC2

Required objects are scientifically valid, but a required principal mechanism or state-dependence inference is absent or incorrect. Reference evidence cannot provide omitted candidate reasoning.
(M1 AND M2 AND M3): Use W and discriminating evidence to explain the main role of initial/resonant Stark difference in spacing and its minimum. Use W and discriminating evidence to determine the direct coherent path's relative spacing effect, distinct from the Stark contribution. Explain identified asymmetry through Stark shifts and coherent competition of resonant/direct continuum amplitudes, not incoherent channels.
(M6 AND M7): Use the candidate's same-domain TDSE evidence to judge whether, and over what domain, the central doublet/splitting model claim survives. Use bounded TDSE evidence to judge transfer of relative peak morphology, asymmetry or another actually claimed material response, limiting the conclusion to that evidence domain.

RC3

Required objects and principal mechanisms are established, but a concrete material validation or scope threat to a central conclusion remains unresolved.
V2: Only when actual TDSE method/data/anomalies or transfer claims trigger a material boundary, continuum-spacing, projection or equivalent threat, or unsupported full-map/long-duration/PAD/partial-wave/absolute-yield extrapolation, provide discriminating exclusion or honestly restrict the claim; otherwise record N/A.
Before assigning RC3, establish all six elements: the concrete failure mode; its origin in the submitted method/data/conclusion; a fair recognizable scientific risk; the affected central conclusion; why the submitted evidence cannot discriminate or exclude it; and functionally equivalent remedies. Evidence-based restriction may remove unsupported breadth, but cannot repair an incorrect signal, absent component or missing mechanism.

RC4

Every indispensable and co-primary claim has all its nonempty required role slots closed; supporting claims do not independently determine overall RC. Preserve AND/OR branch logic shown above and use scientific gate outcomes, not atomic scores.
No triggered material risk remains unresolved. Untriggered risk criteria recorded N/A do not block RC4 and do not establish validation evidence.
Classify descriptively by the most severe applicable failed required role (lowest RC), without score ceilings or target distributions. A score/RC tension prompts scientific review, not forced adjustment.

Applicability and Equivalent Evidence

Let f=E0 g(t)/2, g(t)=sin²(pi t/T), T=2pi N/omega. Use I=1s, R=2p,m=0, omega_IR=0.375, D_IR=256/(243sqrt(2)), M_tilde_Iepsilon=−7.5, SI=−0.7 E0²g², SR=2.6 E0²g², Sepsilon=E0²g²/(4omega²)=Up(t). These are diagonal energy/phase shifts, not unlabelled rates.
The active equations are i dot aI=(SI−iGammaI/2)aI+D_IR f exp(i Delta omega t)aR; i dot aR=D_IR f exp(−i Delta omega t)aI+(SR−iGammaR/2)aR; i dot aepsilon=M_tilde_Iepsilon† f² exp(−i deltaI t)aI+D_Repsilon f exp(−i delta t)aR+Sepsilon aepsilon. Delta omega=omega−omega_IR, delta=ER−Eepsilon+omega, deltaI=EI−Eepsilon+2omega; GammaR=2pi|D_Repsilon|² f² and GammaI=2pi|M_tilde_Iepsilon|² f⁴.
The family has intensities 5×10^13 and 10^14 W cm^−2, N=60 and 300. Define W=|EH−EL| and A=|SL−SH|/max(SL,SH) from the same declared spectrum's principal lower/higher peaks; do not pair dynamic-interference subpeaks or interpret display rescaling as absolute yield.
At omega=0.375 both pulse lengths resolve an Autler–Townes doublet; longer pulses may show dynamic-interference substructure. Principal-peak identity and credible scale, not exact peak coordinates or smoothing, govern comparison.
The effective splitting has structure Omega_tilde≈sqrt{[D_IR E0g]²+[Delta omega+SI−SR−iGammaR/2]²}. The initial/resonant Stark difference mainly shifts the spacing minimum; direct-path influence on W is relatively weaker. Asymmetry responds to both Stark shifts and coherent resonant/direct continuum competition and can be more direct-path sensitive in the stated domain. Intensity and finite pulse length alter these responses.
The independent N=60 low-intensity branch solves the three-dimensional hydrogen TDSE, e.g. i partial_t psi=[−nabla²/2−1/r−iA·grad]psi in velocity gauge, with a reconstructible energy-normalized PES. Use its own same-domain data to test a material model claim, not source answers or propagation diagnostics alone.
Bounded TDSE comparison can support principal-doublet/splitting and a claim-adequate response/morphology relation. It does not establish uncomputed long-duration/full maps, PAD, partial-wave percentages or absolute yields. V3 positive domain identification is independent of V2's actually triggered risk.
Principal-peak aliasing, continuum normalization/case mismatch, coherent cancellation, finite box/projection contamination and insufficient response support matter only where material. No prescribed grid, solver, peak estimator, mask, smoothing or extra control is required.
Score exactly twenty fixed 0/0.5 material-core criteria. Do not import numerical score ranges or RC score caps. A valid run with no assessable scientific work receives score 0 and RC0 before criterion summation; assessable partial work and timeouts are graded on available evidence.
Object existence, candidate presentation, candidate identification, physical inference and validation are different acts. Inspect every candidate-authored claim-bearing figure. A reference, rerender or examiner reconstruction can verify an object but cannot create missing candidate reasoning.
When a material decision depends on feature resolution, fine structure, component relations, formula identity, representation equivalence or suspicious morphology, perform a focused applicable source/reference check. Establish model/observable/case/component, units, basis/gauge, normalization and transformations first; do not turn source-only display choices into new duties. A provisional score at least 9.0 or provisional RC4 requires a focused check of one central output and one principal-mechanism link. Reference verification is examiner-side, not a new candidate deliverable.
Let $f(t)=E_0g(t)/2$, $\Delta=\omega-(E_R-E_I)$, $\delta=E_R-E_\varepsilon+\omega$ and $\delta_I=E_I-E_\varepsilon+2\omega$. The active equations are $i\dot a_I=(S_I-i\Gamma_I/2)a_I+D_{IR}f e^{i\Delta t}a_R$, $i\dot a_R=D_{IR}f e^{-i\Delta t}a_I+(S_R-i\Gamma_R/2)a_R$, $i\dot a_\varepsilon=\widetilde M_{I\varepsilon}^\dagger f^2e^{-i\delta_It}a_I+D_{R\varepsilon}f e^{-i\delta t}a_R+S_\varepsilon a_\varepsilon$ (Eq. (9)). The two continuum sources add coherently before squaring.
$\Gamma_R=2\pi|D_{R\varepsilon}|^2 f^2$, $\Gamma_I=2\pi|\widetilde M_{I\varepsilon}|^2f^4$, $S_I=S_{I0}E_0^2g^2$, $S_R=S_{R0}E_0^2g^2$, $S_\varepsilon=U_p=E_0^2g^2/(4\omega^2)$ (Eq. (10)). $D$ are one-photon dipoles and $\widetilde M$ the effective nonresonant two-photon matrix element; $S$ are instantaneous energy shifts, not assigned causal conclusions. The task-supplied article coefficients remain binding.
For energy-normalized $P(\varepsilon)=|a_\varepsilon(t_f)|^2$ and the two principal peaks at $\varepsilon_L<\varepsilon_H$ with heights $S_L,S_H$, $W=\varepsilon_H-\varepsilon_L$ and source asymmetry $A=|S_L-S_H|/\max(S_L,S_H)$ (p. 063114-4). A declared invertible equivalent asymmetry is acceptable; metrics must not use a different pulse, separately rescaled spectrum or pair of dynamic subpeaks.
Under the source Stark-only analytic reduction, $\widetilde\Omega(t)\simeq\sqrt{[D_{IR}E_0g]^2+[\Delta+S_I-S_R-i\Gamma_R/2]^2}$ (Eq. (11)). It explains a mechanism domain, not an exact finite-pulse peak formula. Independent TDSE uses $i\partial_t\psi=[-\nabla^2/2-1/r-i\mathbf A(t)\cdot\nabla]\psi$ (Eq. (2)); a mapped length-gauge/continuum extraction is equally acceptable.