Datasets:

Tauben
/

PhysClosureBench

Establish the source-equivalent direct length-gauge nondipole SFA amplitude with the same light-cone Volkov phase, leading-1/c momentum shift/prefactor and state-specific orbital-gradient matrix element.

Conditions for credit

Establish the source-equivalent direct length-gauge nondipole SFA amplitude with the same light-cone Volkov phase, leading-1/c momentum shift/prefactor and state-specific orbital-gradient matrix element.

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, F4; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

He, Lao and He (2017), article pp. 163203-1–2, Eqs. (1)–(5), especially Eq. (5). Direct length-gauge light-cone SFA amplitude and leading nondipole shift/prefactor. Velocity-gauge Table I is not the commissioned branch.

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

Bind 1s,2s,2p_0,2p_+1 and 2p_−1, their individual binding energies and momentum orbitals, right-circular polarization and propagation axis into a matched family.

Conditions for credit

Bind 1s,2s,2p_0,2p_+1 and 2p_−1, their individual binding energies and momentum orbitals, right-circular polarization and propagation axis into a matched family.

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, F4; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article pp. 163203-3–4, Fig. 2(a,b), caption and magnetic-sublevel paragraph. Five hydrogenic state identities, circular handedness and angular-momentum dependence. State-specific binding energies/orbitals follow standard hydrogenic quantum mechanics, not a fitted source ordering.

Research Closure relation

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

F4 — F — 0.5 points

Scientific requirement

Define normalized mean longitudinal momentum, paired mean kinetic energy, photon-order identity, a transparent comparison metric and reconstructible case-to-data mapping.

Conditions for credit

Normalized mean longitudinal momentum and kinetic energy are paired from the same direct-branch distribution with the declared measure and units.
Photon-order, comparison metric and underlying-data mapping permit independent reconstruction without substituting the asymptotic law for either computed moment.

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, 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Fig. 2(a), Eq. (7); Eq. (5), p. 163203-2. Normalized longitudinal mean and reconstructible one-member/full-five-state response roles. At-least-one valid member and five-of-five family completeness are separate task obligations.

Research Closure relation

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

O1 — O — 0.5 points

Scientific requirement

Present at least one physically valid, reconstructible and adequately displayed normalized- intensity-response member among the five specified states, with correct local state/case mapping.

Conditions for credit

At least one specified-state intensity-response member is valid, reconstructible and locally adequate; state identity is checked for that member.
Full five-state completeness is not a prerequisite to this local milestone.
Record object_valid, presentation_adequate and claim_adequate separately; all must hold for the applicable full or explicitly bounded local award.

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 F4). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for O2, O3, O4; 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.
Full five-state F3 credit is not a hard prerequisite for valid partial coverage; verify each member's physical identity locally.

Accepted equivalent evidence

Accept algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Fig. 2(a), Eq. (7); Eq. (5), p. 163203-2. Normalized longitudinal mean and reconstructible one-member/full-five-state response roles. At-least-one valid member and five-of-five family completeness are separate task obligations.

Research Closure relation

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

O2 — O — 0.5 points

Scientific requirement

Present a reconstructible same-direct-branch sequence of paired and from few-photon to substantially larger absorbed-photon order.

Conditions for credit

Present a reconstructible same-direct-branch sequence of paired and from few-photon to substantially larger absorbed-photon order.
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 F4). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for O1, O3, O4; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Eq. (7), Fig. 1(a–c) and adjoining photon-order paragraph. Finite-to-large-order partition structure. The task tests it with independently computed paired means and a transparent discrepancy; fitted coefficient panels are source evidence, not compulsory 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

Construct and present a transparent discrepancy or equivalent comparison from the paired sequence sufficient to discriminate finite-order and asymptotic behaviour and identify its domain.

Conditions for credit

Construct and present a transparent discrepancy or equivalent comparison from the paired sequence sufficient to discriminate finite-order and asymptotic behaviour and identify its domain.
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: O2. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for O1, O4; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Eq. (7), Fig. 1(a–c) and adjoining photon-order paragraph. Finite-to-large-order partition structure. The task tests it with independently computed paired means and a transparent discrepancy; fitted coefficient panels are source evidence, not compulsory 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.

O4 — O — 0.5 points

Scientific requirement

Present the full five-of-five homogeneous response family: every 1s,2s,2p_0,2p_+1,2p_−1 member is physically valid, reconstructible, adequately presented and mutually comparable under matched cases, normalization and coordinates.

Conditions for credit

All five specified state members are physically valid, reconstructible and adequately presented.
They form one mutually comparable family under matched cases, normalization and coordinates; fewer than five does not satisfy this full-coverage milestone.
Record object_valid, presentation_adequate and claim_adequate separately; all must hold for the applicable full or explicitly bounded local award.

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 F4). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for O1, O2, 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Fig. 2(a), Eq. (7); Eq. (5), p. 163203-2. Normalized longitudinal mean and reconstructible one-member/full-five-state response roles. At-least-one valid member and five-of-five family completeness are separate task obligations.

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 sign, scale, intensity response and distinguishable relative l,m structure from the complete five-state comparable family.

Conditions for credit

Identify sign, scale, intensity response and distinguishable relative l,m structure from the complete five-state comparable family.

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: O4. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Fig. 2(a), Eq. (7); Eq. (5), p. 163203-2. Normalized longitudinal mean and reconstructible one-member/full-five-state response roles. At-least-one valid member and five-of-five family completeness are separate task obligations.

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 finite-to-larger-order discrepancy evolution from the candidate's paired sequence and comparison rather than taking the asymptotic relation as input.

Conditions for credit

Identify finite-to-larger-order discrepancy evolution from the candidate's paired sequence and comparison rather than taking the asymptotic relation as input.

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 AND O3). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for I1, 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Eq. (7), Fig. 1(a–c) and adjoining photon-order paragraph. Finite-to-large-order partition structure. The task tests it with independently computed paired means and a transparent discrepancy; fitted coefficient panels are source evidence, not compulsory 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

Distinguish an evidence-supported asymptotic domain from still-finite-order samples, with comparison scope and uncertainty.

Conditions for credit

Distinguish an evidence-supported asymptotic domain from still-finite-order samples, with comparison scope and uncertainty.

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; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Eq. (7), Fig. 1(a–c) and adjoining photon-order paragraph. Finite-to-large-order partition structure. The task tests it with independently computed paired means and a transparent discrepancy; fitted coefficient panels are source evidence, not compulsory outputs.

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

Explain initial-angular-momentum dependence of longitudinal partition from the candidate's multistate evidence.

Conditions for credit

Explain initial-angular-momentum dependence of longitudinal partition from the candidate's multistate 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: I1. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M2, M3, M4, M5, M6, M7, M8; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article pp. 163203-3–4, Fig. 2(a,b), state-dependent partition paragraphs; Eq. (5), p. 163203-2. Orbital-gradient momentum structure and initial angular momentum explain state dependence; opposite magnetic substates need not have identical longitudinal means.

Research Closure relation

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

M2 — M — 0.5 points

Scientific requirement

Connect that dependence to bound-state momentum structure without treating source ordering as an imposed prior.

Conditions for credit

Connect that dependence to bound-state momentum structure without treating source ordering as an imposed prior.

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. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M1, M3, M4, M5, M6, M7, M8; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article pp. 163203-3–4, Fig. 2(a,b), state-dependent partition paragraphs; Eq. (5), p. 163203-2. Orbital-gradient momentum structure and initial angular momentum explain state dependence; opposite magnetic substates need not have identical longitudinal means.

Research Closure relation

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

M3 — M — 0.5 points

Scientific requirement

Explain the under-barrier contribution to the observed finite-intensity state dependence.

Conditions for credit

Explain the under-barrier contribution to the observed finite-intensity state dependence.

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. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M1, M2, M4, M5, M6, M7, M8; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Eq. (6), tunnelling/under-barrier paragraph, Eq. (7), Fig. 2(b). Continuum energy and under-barrier/bound-state contributions are distinct. The velocity-gauge limiting Eq. (6) does not replace the length-gauge result.

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

Distinguish and connect continuum-energy and bound/under-barrier contributions to longitudinal partition.

Conditions for credit

Distinguish and connect continuum-energy and bound/under-barrier contributions to longitudinal partition.

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. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M1, M2, M3, M5, M6, M7, M8; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Eq. (6), tunnelling/under-barrier paragraph, Eq. (7), Fig. 2(b). Continuum energy and under-barrier/bound-state contributions are distinct. The velocity-gauge limiting Eq. (6) does not replace the length-gauge result.

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

Infer the large-order partition relation from the candidate's paired moments, not mere repetition of a known formula.

Conditions for credit

Infer the large-order partition relation from the candidate's paired moments, not mere repetition of a known formula.

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. This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M1, M2, M3, M4, M6, M7, M8; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Eq. (7), Fig. 1(a–c) and large-order limit paragraph; length-gauge qualification on p. 163203-2. Source limits alpha→1, beta→1/3, gamma→0 motivate the tested relation. A same-direct-branch paired-moment discrepancy is the task-defined numerical test, not a printed separate source figure.

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 explicit discrepancy to test →(+Ip/3)/c and explain finite-order deviations and the chosen metric.

Conditions for credit

Use the explicit discrepancy to test →(+Ip/3)/c and explain finite-order deviations and the chosen metric.

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 AND I2). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M1, M2, M3, M4, M5, M7, M8; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Eq. (7), Fig. 1(a–c) and large-order limit paragraph; length-gauge qualification on p. 163203-2. Source limits alpha→1, beta→1/3, gamma→0 motivate the tested relation. A same-direct-branch paired-moment discrepancy is the task-defined numerical test, not a printed separate source figure.

Research Closure relation

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

M7 — M — 0.5 points

Scientific requirement

Establish that the relation follows from independently computed same-direct-branch observables, not separate fitted coefficient panels or formula substitution.

Conditions for credit

Establish that the relation follows from independently computed same-direct-branch observables, not separate fitted coefficient panels or formula substitution.

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 AND O3). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M1, M2, M3, M4, M5, M6, M8; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Eq. (7), Fig. 1(a–c) and large-order limit paragraph; length-gauge qualification on p. 163203-2. Source limits alpha→1, beta→1/3, gamma→0 motivate the tested relation. A same-direct-branch paired-moment discrepancy is the task-defined numerical test, not a printed separate source figure.

Research Closure relation

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

M8 — M — 0.5 points

Scientific requirement

State evidence-supported direct circular-polarization asymptotic scope and its finite-to-asymptotic mechanism without extrapolation to rescattering, linear polarization, spin or absolute yield.

Conditions for credit

State evidence-supported direct circular-polarization asymptotic scope and its finite-to-asymptotic mechanism without extrapolation to rescattering, linear polarization, spin or absolute yield.

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). This identifies facts, not prerequisite half-point awards.
Preserve independently valid evidence for M1, M2, M3, M4, M5, 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-2, length-gauge paragraph; pp. 163203-3–4, circular versus linear/rescattering branch discussion. Direct circular asymptotic scope and separation from rescattering, spin and absolute-yield claims.

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

Limit conclusions to the calculated direct length-gauge-equivalent right-circular branch, specified states and supported order/intensity domain.

Conditions for credit

Limit conclusions to the calculated direct length-gauge-equivalent right-circular branch, specified states and supported order/intensity domain.

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.

Accepted equivalent evidence

Accept algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-2, length-gauge paragraph; pp. 163203-3–4, circular versus linear/rescattering branch discussion. Direct circular asymptotic scope and separation from rescattering, spin and absolute-yield claims.

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

If actual ATI resolution, subtractive-moment cancellation, pulse convention, order sampling, state/case binding or claims trigger a concrete threat to a central conclusion, provide discriminating evidence or proportionate restriction; otherwise record N/A.

Conditions for credit

If actual ATI resolution, subtractive-moment cancellation, pulse convention, order sampling, state/case binding or claims trigger a concrete threat to a central conclusion, provide discriminating evidence or proportionate restriction; 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 V1; 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 algebraically equivalent leading-1/c direct length-gauge amplitudes with the same light-cone phase, momentum shift and orbital-gradient matrix element; consistent Cartesian/cylindrical integration and analytic hydrogenic or independently validated numerical Fourier orbitals are allowed. Dipole-only, velocity-gauge table targets and rescattering-only calculations are not equivalent.
Accept transparent alternative discrepancy metrics, photon-order sequences and pulse conventions that discriminate finite from asymptotic behaviour and state their domain. No fixed intensity/frequency grid, N=4/8/16 sequence, coefficient fit, delta-pz curve, source panel or absolute yield is required.
Presented energy-resolved probabilities or an absorbed-energy ledger that uniquely reconstruct paired mean kinetic energy are equivalent to separately listed , provided direct branch, pulse convention, normalization and finite-order domain agree. Nominal order/frequency labels, substitution of the asymptotic formula or examiner reconstruction from unpresented data are not equivalent. The comparison/residual must still be candidate-presented.

Scientific source locations

Article p. 163203-3, Eq. (7) and paragraph on unreliable extraction of the small ponderomotive coefficient; Eq. (5), p. 163203-2. Concrete moment-resolution and finite-order inference threats. Conditional validation is task-defined and imposes no particular ATI mesh or residual metric.

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.

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 F3 AND F4): Establish the source-equivalent direct length-gauge nondipole SFA amplitude with the same light-cone Volkov phase, leading-1/c momentum shift/prefactor and state-specific orbital-gradient matrix element. Bind 1s,2s,2p_0,2p_+1 and 2p_−1, their individual binding energies and momentum orbitals, right-circular polarization and propagation axis into a matched family. Define normalized mean longitudinal momentum, paired mean kinetic energy, photon-order identity, a transparent comparison metric and reconstructible case-to-data mapping.

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.
O4: Present the full five-of-five homogeneous response family: every 1s,2s,2p_0,2p_+1,2p_−1 member is physically valid, reconstructible, adequately presented and mutually comparable under matched cases, normalization and coordinates.
(O2 AND O3): Present a reconstructible same-direct-branch sequence of paired and from few-photon to substantially larger absorbed-photon order. Construct and present a transparent discrepancy or equivalent comparison from the paired sequence sufficient to discriminate finite-order and asymptotic behaviour and identify its domain.

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.
M3: Explain the under-barrier contribution to the observed finite-intensity state dependence.
M8: State evidence-supported direct circular-polarization asymptotic scope and its finite-to-asymptotic mechanism without extrapolation to rescattering, linear polarization, spin or absolute yield.

RC3

Required objects and principal mechanisms are established, but a concrete material validation or scope threat to a central conclusion remains unresolved.
V2: If actual ATI resolution, subtractive-moment cancellation, pulse convention, order sampling, state/case binding or claims trigger a concrete threat to a central conclusion, provide discriminating evidence or proportionate restriction; 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

The direct amplitude is W_L^(1)(p)=−i integral d eta exp{i[S_p(eta)+Ip eta]}(1−pz/c) E(eta)·i grad_k phi_tilde_0(k), evaluated at k=(p_perp+A(eta),pz−[Ep+Ip]/c), with Ep=p²/2 and the corresponding nondipole light-cone Volkov phase.
Set P(p)=|W_L^(1)(p)|² and form =integral pz P d³p/integral P d³p and =integral Ep P d³p/integral P d³p from the same distribution. Overall orbital normalization cancels; peak displacement, standard deviation or an unnormalized integral is not the required mean.
The matched 1400-nm right-circular family contains 1s,2s,2p_0,2p_+1,2p_−1 with their correct Ip and momentum orbitals, propagation along z and consistent helicity. Judge positive source-scale means, systematic intensity response and distinguishable angular-momentum-dependent relative structure, not exact source samples.
The large-order direct relation is →(+Ip/3)/c. It must be tested with independently computed paired observables and a transparent discrepancy; imposing the relation or separate alpha/beta/gamma fits does not verify it. Finite-order deviations and actual asymptotic domain must be distinguished.
O1 is an at-least-one-valid-member milestone; O4 is the five-of-five physically valid, reconstructible, adequately presented and mutually comparable milestone. Preserve O1 when full coverage fails. Cross-state identification I1 requires five comparable members, not a lone member.
Independent coefficient panels, Table-I velocity-gauge values, rescattering, spin, absolute yield and a complete momentum-distribution display are outside required scope. ATI under-resolution, cancellation of close moments, pulse conventions and finite-order-as-asymptotic claims matter only when actually material.
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.
In atomic units, $W_L^{(1)}(\mathbf p)=-i\int d\eta,e^{i[S_{\mathbf p}(\eta)+I_p\eta]}(1-p_z/c)\mathbf E(\eta)\cdot i\nabla_{\mathbf k}\widetilde\phi_0(\mathbf k)|{\mathbf k=(\mathbf p_\perp+\mathbf A,,p_z-[p^2/2+I_p]/c)}$ (Eq. (5)). Here $\eta=t-z/c$, $\mathbf E=-\partial_\eta\mathbf A$ and $S{\mathbf p}=\int^\eta[p^2/2+(\mathbf A\cdot\mathbf p+A^2/2)/(1-p_z/c)]d\eta\prime$. Algebraically equivalent leading-$1/c$ forms are accepted in the nonrelativistic nondipole domain; an arbitrary gauge swap in SFA is not automatically equivalent.
For $P(\mathbf p)=|W_L^{(1)}|^2$, $\langle p_z\rangle=\int p_zP,d^3p/\int P,d^3p$ and $\langle E_p\rangle=\int(p^2/2)P,d^3p/\int P,d^3p$. Both moments must use the same direct-branch state, case, measure and distribution. A peak shift or unnormalized numerator is not the longitudinal mean; overall orbital normalization cancels.
The independently tested asymptotic relation is $\langle p_z\rangle\to[\langle E_p\rangle+I_p/3]/c$. An admissible residual is $D=c\langle p_z\rangle-\langle E_p\rangle-I_p/3$ or a transparently scaled equivalent; it is computed from paired moments rather than used to generate either moment. $N=\lfloor I_p/\omega\rfloor+1$ is the source threshold-order convention, with pulse/channel conventions declared. The five hydrogenic states have $I_p=1/(2n^2)$, so $1s$ and $n=2$ states cannot share an incorrectly fixed binding energy.
O1 requires at least one locally valid specified-state member; O4 requires all five mutually comparable members. A missing member damages the complete family and conclusions genuinely requiring it, but cannot erase valid local-member output or independently valid foundations. The large-order paired family is independently assessable; neither a missing Delta-pz curve nor unsubmitted coefficient-fit panels creates another component failure.