# Grading Rubric — Case32 Probing Nuclear Motion by Frequency Modulation of Molecular High-Order Harmonic Generation ## Atomic Scoring Criteria Each criterion awards 0 or 0.5 points, for a maximum of 10. Explicit N/A rules apply where stated. ### F1 — F — 0.5 points **Scientific requirement** Instantiate the full non-Born-Oppenheimer (R,rho,z) Hamiltonian, hydrogen/deuterium masses, moving/fixed initial cases and pulse consistently. **Conditions for credit** - Full R,rho,z non-Born-Oppenheimer dynamics, H/D masses, moving/fixed initial cases and pulse identify the supplied physical model. - The production calculation retains R,rho,z dynamics, reduced masses and the same fixed-H/moving-H/moving-D physical case; a reduced soft-core or frozen-nuclear replacement does not establish this object. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article p. 193901-2, Eq. (1) and initial-state/mass paragraphs: The full non-Born-Oppenheimer R,rho,z Hamiltonian and cylindrical electronic measure are required; no 1+1D soft-core or frozen-nuclear production surrogate is equivalent. **Research Closure relation** RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### F2 — F — 0.5 points **Scientific requirement** Define a common reconstructible force/acceleration radiation signal and HHG spectrum for fixed H, moving H and moving D. **Conditions for credit** - A common reconstructible force/acceleration radiation signal and HHG spectrum are used for fixed H, moving H and moving D. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-2-3, acceleration-spectrum paragraph, Fig. 3(a,b) and caption: All three cases use one radiation/transform convention. Full-spectrum display shifts in panel (a) are not physical yield ratios; unshifted panel (b) supports line shape and frequency comparison. **Research Closure relation** RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### F3 — F — 0.5 points **Scientific requirement** Define spectral-shift and line-shape estimators under common transform and normalization conventions. **Conditions for credit** - Spectral-shift and line-shape estimators have explicit common transform/normalization conventions permitting a physical three-case comparison. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-2-3, acceleration-spectrum paragraph, Fig. 3(a,b) and caption: All three cases use one radiation/transform convention. Full-spectrum display shifts in panel (a) are not physical yield ratios; unshifted panel (b) supports line shape and frequency comparison. **Research Closure relation** RC0: absence or material invalidity of the central physical object. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### M8 — M — 0.5 points **Scientific requirement** Derive a computable emission-weighting/frequency-modulation relation with its assumptions and applicability limits. **Conditions for credit** - The candidate derives a computable emission-weighting/frequency-modulation relation and states the assumptions under which it can be used. - Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article p. 193901-4, Eqs. (2)-(3), retrieval paragraphs: The emission/ionization-weighting estimate links rising/falling pulse imbalance to frequency shift; inversion is conditional on an applicable R-dependent rate, not unique from one shift. **Research Closure relation** No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### O1 — O — 0.5 points **Scientific requirement** Provide reconstructible moving-H/D nuclear motion resolving onset, time dependence and isotope ordering. **Conditions for credit** - Moving-H and moving-D nuclear data resolve onset, time dependence and isotope ordering on the same pulse. - The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-2-3, Fig. 2 and nuclear-motion discussion: Moving H and D have different nuclear onset/growth timing; heavier D moves more slowly under the same pulse. **Research Closure relation** RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### O2 — O — 0.5 points **Scientific requirement** Provide fixed-H versus moving-H HHG evidence resolving response and line modulation, not merely total amplitude. **Conditions for credit** - Fixed-H/moving-H spectra resolve line modulation and response, not merely an amplitude change. - The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article p. 193901-3, Fig. 3(a,b) and fixed-versus-moving discussion: Nuclear motion changes both yield and line position/asymmetry. Frequency modulation is not merely amplitude modulation. **Research Closure relation** RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### O3 — O — 0.5 points **Scientific requirement** Provide moving-H versus moving-D evidence resolving isotope contrast in HHG yield and line shape. **Conditions for credit** - Moving-H/moving-D spectra resolve isotope differences in yield and line position/shape under compatible scales. - The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-3-4, Fig. 3(a,b), isotope paragraphs: Moving D has lower HHG yield yet a larger redshift/asymmetry than moving H in the source case; common observable and scale are necessary for comparison. **Research Closure relation** RC1: absence or material invalidity of an indispensable component, with the central object established. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### O4 — O — 0.5 points **Scientific requirement** Provide time-resolved or functionally equivalent evidence connecting spectral modulation to emission and nuclear timing. **Conditions for credit** - Time-resolved, gated, interventional or equivalent evidence connects spectral modulation with nuclear/emission timing. - The physical object is valid, its presentation adequate, and its claim adequate; record these three statuses separately. Reconstructible data alone do not create candidate identification or mechanism. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-3-4, wavelet paragraph and Fig. 4(a-c) caption: Fixed-H timing is approximately symmetric; moving-H emission favors the falling pulse and moving-D occurs later. Top/middle/bottom panels are fixed H/moving H/moving D respectively. **Research Closure relation** No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### I1 — I — 0.5 points **Scientific requirement** Identify nuclear-motion timing and hydrogen/deuterium ordering from the candidate's nuclear evidence. **Conditions for credit** - The candidate identifies nuclear-motion timing and H/D ordering directly from their nuclear evidence. - Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - O1: Provide reconstructible moving-H/D nuclear motion resolving onset, time dependence and isotope ordering. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-2-3, Fig. 2 and nuclear-motion discussion: Moving H and D have different nuclear onset/growth timing; heavier D moves more slowly under the same pulse. **Research Closure relation** No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### I2 — I — 0.5 points **Scientific requirement** Identify fixed/moving frequency modulation as distinct from simple amplitude change. **Conditions for credit** - The candidate identifies a fixed/moving frequency/line-shape change distinct from amplitude modulation. - Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - All of [O2: Provide fixed-H versus moving-H HHG evidence resolving response and line modulation, not merely total amplitude.; O3: Provide moving-H versus moving-D evidence resolving isotope contrast in HHG yield and line shape.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article p. 193901-3, Fig. 3(a,b) and fixed-versus-moving discussion: Nuclear motion changes both yield and line position/asymmetry. Frequency modulation is not merely amplitude modulation. **Research Closure relation** No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### I3 — I — 0.5 points **Scientific requirement** Identify isotope-dependent dominant-emission timing from the candidate's time-resolved or equivalent evidence. **Conditions for credit** - The candidate identifies isotope-dependent dominant-emission timing from their time-resolved or equivalent evidence. - Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - O4: Provide time-resolved or functionally equivalent evidence connecting spectral modulation to emission and nuclear timing. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-3-4, wavelet paragraph and Fig. 4(a-c) caption: Fixed-H timing is approximately symmetric; moving-H emission favors the falling pulse and moving-D occurs later. Top/middle/bottom panels are fixed H/moving H/moving D respectively. **Research Closure relation** No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### M1 — M — 0.5 points **Scientific requirement** Conclude from the candidate's fixed/moving evidence whether nuclear motion changes molecular HHG. **Conditions for credit** - The conclusion on whether nuclear motion changes HHG follows the candidate fixed/moving comparison. - Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - I2: Identify fixed/moving frequency modulation as distinct from simple amplitude change. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article p. 193901-3, Fig. 3(a,b) and fixed-versus-moving discussion: Nuclear motion changes both yield and line position/asymmetry. Frequency modulation is not merely amplitude modulation. **Research Closure relation** RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### M2 — M — 0.5 points **Scientific requirement** Physically distinguish frequency modulation from amplitude variation using line-position/shape evidence. **Conditions for credit** - Line-position/shape evidence physically distinguishes frequency modulation from amplitude-only variation. - Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - I2: Identify fixed/moving frequency modulation as distinct from simple amplitude change. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article p. 193901-3, Fig. 3(a,b) and fixed-versus-moving discussion: Nuclear motion changes both yield and line position/asymmetry. Frequency modulation is not merely amplitude modulation. **Research Closure relation** RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### M3 — M — 0.5 points **Scientific requirement** Connect isotope mass to the relative nuclear-motion timing. **Conditions for credit** - The argument connects isotope mass to the demonstrated relative nuclear timing. - Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - All of [I1: Identify nuclear-motion timing and hydrogen/deuterium ordering from the candidate's nuclear evidence.; I3: Identify isotope-dependent dominant-emission timing from the candidate's time-resolved or equivalent evidence.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-2-3, Fig. 2 and nuclear-motion discussion: Moving H and D have different nuclear onset/growth timing; heavier D moves more slowly under the same pulse. **Research Closure relation** RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### M4 — M — 0.5 points **Scientific requirement** Connect R-dependent ionization/emission to asymmetric weighting of rising/falling pulse cycles. **Conditions for credit** - R-dependent ionization/emission is linked to unequal weighting of rising versus falling pulse cycles. - Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - I3: Identify isotope-dependent dominant-emission timing from the candidate's time-resolved or equivalent evidence. supplies only a necessary physical/evidential premise, not an automatic atomic-score gate. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-2-4, Fig. 1, Fig. 2, Fig. 4 and isotope/emission-weighting discussion: R-dependent ionization weights later falling cycles more strongly; mass changes nuclear timing and hence the magnitude and sign of the spectral modulation. **Research Closure relation** RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### M5 — M — 0.5 points **Scientific requirement** Explain fixed/moving and isotope contrasts through the coupled mass-to-nuclear-timing-to-emission-weighting-to-frequency chain. **Conditions for credit** - The fixed/moving and isotope observations support one connected mass-to-motion-to-emission-weighting-to-frequency explanation. - Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link. - Close the mass-to-nuclear-timing-to-R-dependent-emission-weighting-to-frequency chain using the candidate fixed/moving and isotope signals, not only isotope labels or yield ordering. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - All of [I1: Identify nuclear-motion timing and hydrogen/deuterium ordering from the candidate's nuclear evidence.; I2: Identify fixed/moving frequency modulation as distinct from simple amplitude change.; I3: Identify isotope-dependent dominant-emission timing from the candidate's time-resolved or equivalent evidence.; M4: Connect R-dependent ionization/emission to asymmetric weighting of rising/falling pulse cycles.] supplies only a necessary physical/evidential premise, not an automatic atomic-score gate. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - The complete coupled timing chain needs identified nuclear, spectral and emission-timing signals and the M4 causal relation between R-dependent emission and pulse-cycle weighting. Missing that link cannot count as a complete chain. - Retain valid nuclear, fixed/moving and isotope subobjects independently. A causal timing conclusion needs the relevant candidate emission-timing evidence; a spectral shift or nuclear trajectory alone cannot supply the missing link. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-2-4, Fig. 1, Fig. 2, Fig. 4 and isotope/emission-weighting discussion: R-dependent ionization weights later falling cycles more strongly; mass changes nuclear timing and hence the magnitude and sign of the spectral modulation. **Research Closure relation** RC2: a missing or wrong indispensable principal mechanism/conclusion, with valid required signals. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### M6 — M — 0.5 points **Scientific requirement** State that inverse extraction of nuclear dynamics requires an applicable R-dependent ionization/emission relation; a shift alone does not uniquely determine R(t). **Conditions for credit** - The candidate states that extracting nuclear dynamics requires a valid R-dependent emission/ionization relation and is not unique from a shift alone. - Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. - An honest conditional inverse boundary is independently judgeable; acknowledging nonuniqueness neither validates a false shift nor requires reconstructing an uncommissioned arbitrary R(t). **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article p. 193901-4, Eqs. (2)-(3), retrieval paragraphs: The emission/ionization-weighting estimate links rising/falling pulse imbalance to frequency shift; inversion is conditional on an applicable R-dependent rate, not unique from one shift. **Research Closure relation** No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### M7 — M — 0.5 points **Scientific requirement** Limit conclusions to single-molecule one-electron aligned finite-pulse data and the actual demonstrated domain. **Conditions for credit** - The conclusion is bounded to the aligned one-electron single-molecule finite-pulse model and the demonstrated domain. - Use the candidate's own valid and relevant evidence; a correct source narrative or examiner-created inference cannot replace the candidate's identification or causal link. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-1-2, amplitude-versus-frequency and propagation discussion; pp. 193901-4-5, retrieval caveats and conclusion: The single-molecule one-electron aligned finite-pulse calculation is not a macroscopic or unique inverse reconstruction. Additional discrimination is triggered by an actual material risk, not a fixed wavelet recipe. **Research Closure relation** No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### V1 — V — 0.5 points **Scientific requirement** State reconstructibility, common normalization, estimator assumptions and evidence-bounded scope for all three cases. **Conditions for credit** - All three cases have reconstructible common-scale evidence with estimator assumptions and scope stated. **Applicability and N/A** - Applicable to the stated scientific commission; N/A is not permitted. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-2-3, acceleration-spectrum paragraph, Fig. 3(a,b) and caption: All three cases use one radiation/transform convention. Full-spectrum display shifts in panel (a) are not physical yield ratios; unshifted panel (b) supports line shape and frequency comparison. **Research Closure relation** No direct closure trigger; affect a dependent required scientific role only through a demonstrated failed necessary premise.. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ### V2 — V — 0.5 points **Scientific requirement** If a concrete case mismatch, absorber, transform/peak-estimator, pulse-only artifact or nonunique-inversion risk emerges from candidate work, discriminate it minimally or restrict scope; otherwise record N/A with fixed credit. **Conditions for credit** - An actual case, boundary, transform/estimator, pulse-only artifact or nonunique-inversion threat is discriminated or restricted; otherwise N/A. **Applicability and N/A** - Activate only for a concrete material risk arising from the candidate method, data, anomaly or claim; no fixed test is required in the absence of a trigger. - Without a triggered risk record N/A and award 0.5 without positive validation evidence; this neither blocks RC4 nor triggers RC3. - When triggered, accept functionally equivalent discriminating evidence or a justified restriction of the threatened claim. **Scientific dependencies and independent credit** - Independently judgeable; no upstream atomic failure is mechanically propagated into this obligation. - Propagate the exact failed fact only; preserve independently established subobjects, candidate reasoning and scope. Do not charge a second generic incompleteness or numerical-reliability penalty. **Accepted equivalent evidence** - Accept physically equivalent gauges, bases/grids, force/acceleration conventions, Fourier signs, windows, time-frequency representations, shift estimators and common normalizations preserving isotope, line shift and timing structure. - Time gating, interventions or other reconstructible diagnostics may replace the canonical three time-frequency panels if they discriminate fixed/moving and isotope emission timing. - Accept uncertainty-appropriate structural comparisons, not exact source final R, absolute yield, manually shifted display spectra or fixed harmonic/peak search intervals. The full coupled production identity remains required. **Scientific source locations** - Bian and Bandrauk (2014), article pp. 193901-1-2, amplitude-versus-frequency and propagation discussion; pp. 193901-4-5, retrieval caveats and conclusion: The single-molecule one-electron aligned finite-pulse calculation is not a macroscopic or unique inverse reconstruction. Additional discrimination is triggered by an actual material risk, not a fixed wavelet recipe. **Research Closure relation** RC3: an unresolved applicable material risk, only after signals and principal mechanisms are substantially supported and all six risk-proof requirements are met. Evaluate actual trigger facts separately from the atomic award; the most severe failed required role determines closure. ## Research Closure Requirements ### RC0 - Required claim CL1, central object: All of [F1: Instantiate the full non-Born-Oppenheimer (R,rho,z) Hamiltonian, hydrogen/deuterium masses, moving/fixed initial cases and pulse consistently.; F2: Define a common reconstructible force/acceleration radiation signal and HHG spectrum for fixed H, moving H and moving D.; F3: Define spectral-shift and line-shape estimators under common transform and normalization conventions.]. Judge role-trigger facts, not the sum or pattern of atomic scores. - Apply for a missing or materially invalid required central object; a presentation-only or claim-only defect does not establish object invalidity. - No scientifically assessable required submission gives the terminal 0.0/RC0 disposition. ### RC1 - Required claim CL1, indispensable component: All of [O1: Provide reconstructible moving-H/D nuclear motion resolving onset, time dependence and isotope ordering.; O2: Provide fixed-H versus moving-H HHG evidence resolving response and line modulation, not merely total amplitude.; O3: Provide moving-H versus moving-D evidence resolving isotope contrast in HHG yield and line shape.]. Judge role-trigger facts, not the sum or pattern of atomic scores. - The central object is established but a required physical component is absent or materially invalid. Preserve independent valid branches; do not invent a hidden canonical plot, sampling grid or implementation duty. ### RC2 - Required claim CL2, principal mechanism: All of [M1: Conclude from the candidate's fixed/moving evidence whether nuclear motion changes molecular HHG.; M2: Physically distinguish frequency modulation from amplitude variation using line-position/shape evidence.; M3: Connect isotope mass to the relative nuclear-motion timing.; M4: Connect R-dependent ionization/emission to asymmetric weighting of rising/falling pulse cycles.; M5: Explain fixed/moving and isotope contrasts through the coupled mass-to-nuclear-timing-to-emission-weighting-to-frequency chain.]. Judge role-trigger facts, not the sum or pattern of atomic scores. - Required signal objects/components exist, but an indispensable principal mechanism or co-primary scientific conclusion is missing, wrong or unsupported by candidate-presented and identified evidence. Correct data do not let an examiner supply missing reasoning. ### RC3 - Required claim CL2, material validation: V2: If a concrete case mismatch, absorber, transform/peak-estimator, pulse-only artifact or nonunique-inversion risk emerges from candidate work, discriminate it minimally or restrict scope; otherwise record N/A with fixed credit.. Judge role-trigger facts, not the sum or pattern of atomic scores. - All indispensable signal and principal-mechanism roles are substantially supported, but a concrete triggered material risk remains unresolved and inadequately restricted. - Establish the failure mode, candidate origin, fair task/knowledge basis, threatened central conclusion, insufficiency of submitted evidence, and equivalent resolution or scope restriction. Missing an examiner-preferred check alone never suffices. ### RC4 - Every nonempty required role in every indispensable and co-primary claim above is scientifically established from candidate evidence, with the correct case/model/observable identities and evidence-bounded conclusion. - All applicable material risks are discriminated or honestly restricted; no unresolved material ambiguity remains. Risk N/A does not block closure or supply positive validation evidence. Honest limitations cannot repair a false signal or mechanism. - Select the most severe failed required role if any; otherwise RC4. No score threshold, score ceiling or required display/solver checklist determines this classification. ## Applicability and Equivalent Evidence - Required production retains all R,rho,z electronic-nuclear degrees of freedom and the specified reduced-mass/center-of-mass factors. A 1+1D, soft-core or frozen-nuclei surrogate is not equivalent production, although correctly labeled exploratory reduced work does not invalidate an independent full calculation. - For homonuclear molecules the explicit R interaction term vanishes, but masses still enter through alpha and beta. Moving H/D start from their corresponding field-free ground states; fixed-H electronic propagation uses the same equilibrium geometry and field convention. - Construct acceleration/force expectation from the stated Hamiltonian and use consistent radiation, transform and relative-scale conventions for all three cases. No unique discretization, zero padding, window or absolute arbitrary-unit spectrum height is prescribed. - Hydrogen motion begins/grows faster and extends farther than deuterium under the same 20-cycle pulse. Source ground-state anchors are energy about -0.59713 a.u. and mean R about 2.063 a.u.; source nuclear-distance curves and external calculations differ at fine/final values, so grade onset, isotope ordering and broad scale, not exact terminal R. - Fixed nuclei give comparatively regular odd harmonics and near-symmetric atomiclike lines. Motion increases total yield and changes plateau line shape with lower-order shift/asymmetry. D moves more slowly and has lower yield than H, yet dominant D emission is later and has larger redshift/asymmetry in the source setting. - Fixed-nuclei emission is approximately symmetric about pulse center; moving-nuclei emission favors the falling side, with D later than H. Equivalent gated, interventional or time-frequency evidence must discriminate pulse-only/fixed response from nuclear/isotope timing; no Morlet method or fixed harmonic threshold is mandatory. - The approximate retrieval relation is Delta omega/omega = {integral_{-T/2}^0 Gamma[R(t),I(t)] dt - integral_0^{T/2} Gamma[R(t),I(t)] dt}/{integral_{-T/2}^{T/2} Gamma[Re,I(t)] dt}. Its average-value version compares rising/falling rates. It is not an exact TDSE identity and cannot replace computed radiation. - Inferring R requires the applicable Gamma(R,I) or equivalent emission relation; nonunique weighting cannot support a unique trajectory retrieval. The relation establishes an evidence-bounded frequency-modulation diagnostic, not arbitrary molecule or macroscopic-propagation inference. - Relevant risks include reduced dynamics mislabeled full, isotope/fixed-case mismatch, absorber-biased nuclear means, manufactured peak shifts, pulse-only/representation artifacts and nonunique inversion. No author basis, solver, box, step, absorber, fixed search band, window or exact final nuclear distance is required. - The score is the sum of twenty material-core criteria, each worth either 0 or 0.5, for a maximum of 10.0. Research Closure is descriptive and never caps, floors, rescales or repairs the score. - Judge physical object identity and correctness before display similarity. For each output record object_valid, presentation_adequate and claim_adequate separately; all three must hold for its atomic award. A presentation or claim defect alone is not evidence that an existing physical object is absent or invalid. - Candidate-created data, candidate presentation, candidate identification, physical inference and validation are distinct evidential acts. Examiner inspection or reconstruction may verify an object but cannot create missing candidate identification, reasoning or risk resolution. - A dependency propagates only the failed necessary physical fact, not the whole upstream atomic verdict or unrelated missing detail. Name the failed premise, the downstream obligation needing it, and why independent candidate-presented evidence does not establish it. Preserve unaffected branches, independent work and honest scope. - Numerical reliability has no separate generic penalty. Charge a defect where it materially damages a physical object or evidence, and a dependent conclusion only when that same defect makes the conclusion false or unsupported. Missing a preferred convergence study, control, solver or named self-check is not itself a failure. - Risk-triggered validation applies only to a concrete material risk arising from the candidate method, data, anomaly or claim. With no such risk record N/A and award the fixed atomic credit without treating it as positive validation evidence; N/A does not block RC4. Unconditional scope obligations cannot be N/A. - Before assigning RC3 establish all six: the concrete failure mode; its origin in candidate work; the fair task or standard-knowledge basis; the threatened central conclusion; why submitted evidence cannot expose or exclude it; and examples of functionally equivalent discriminating evidence or an honest scope restriction that would resolve it. A generic possibility of further testing is insufficient. - Use bounded examiner-side source/reference readback only to resolve a material scientific uncertainty, not to demand pixels, an undeclared tolerance or additional candidate deliverables. A provisional score of at least 9.0 or provisional RC4 triggers one bounded central-output-anchor check and one principal-mechanism-link check. Reference conflict or insufficiency remains an explicit unresolved decision, not an invented target. - Evaluate closure-role trigger facts independently of atomic awards and select the most severe failed required role across all indispensable and co-primary claims. Supporting claims do not independently set overall closure. A point loss alone is not a closure-gate fact. - A valid candidate-caused incomplete or timeout attempt with no scientifically assessable required submission has score 0.0 and RC0 before N/A bookkeeping. Assessable incomplete work is graded from the submitted evidence; unsubmitted scratch or logs do not become scientific answers. - The full coordinate dynamics are $i\partial_t\Psi=[-\partial_R^2/(2\alpha)-\nabla_e^2/(2\beta)+V_C-V_I]\Psi$, $\nabla_e^2=\rho^{-1}\partial_\rho(\rho\partial_\rho)+\partial_z^2$, $\alpha=M_1M_2/(M_1+M_2)$, $\beta=(M_1+M_2)/(M_1+M_2+1)$ (Eq. (1)). Expectations use the cylindrical volume element, with one consistent convention for the integrated azimuth; neither reduced-mass dynamics nor rho may be dropped. - Using the same acceleration signal, $S(\omega)\propto|\int dt\,w(t)d_A(t)e^{i\omega t}|^2$. A declared peak/centroid or equivalent estimator must distinguish displacement and asymmetry from amplitude change; source Fig. 3(a) display shifts do not define intensity ratios. - The source approximate weighting relation is $\Delta\omega/\omega\simeq[\int_{-\tau/2}^{0}\Gamma(R(t),I(t))dt-\int_0^{\tau/2}\Gamma(R(t),I(t))dt]/\int_{-\tau/2}^{\tau/2}\Gamma(R_e,I(t))dt$ (Eq. (2)). Under average-rate assumptions it becomes $[\Gamma(\bar R_1,\bar I)-\Gamma(\bar R_2,\bar I)]/[2\Gamma(R_e,\bar I)]$ (Eq. (3)). Falling-side enhancement gives the source redshift; inferring R requires the appropriate rate relation and cannot uniquely reconstruct an arbitrary R(t).