PRE-REGISTRATION Membrane-Governance in Quasi-Elastic Proton Knockout:A Cross-Nuclear Test of Parameter-Sensitivity Hierarchyin Polarization Observables

Membrane_Governance_PreRegistration_Gaconnet_2026.pdf

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Don L. Gaconnet

LifePillar Institute for Recursive Sciences

ORCID: 0009-0001-6174-8384

Zenodo DOI: 10.5281/zenodo.19634071

OSF DOI: 10.17605/OSF.IO/MVYZT

Registration date: [to be filled at OSF submission]

Registered venue: Open Science Framework (osf.io)

Status: Pre-analysis. No data examination has commenced at time of registration.

1. Purpose and Scope

This document pre-registers an empirical test of a specific prediction about the relative sensitivity of polarization observables to different classes of theoretical input in quasi-elastic proton knockout reactions. The prediction is that optical-potential parameters govern polarization-observable predictions more strongly than non-optical-potential parameters (bound-state wavefunction choice, nuclear current operator prescription, electromagnetic form factor parametrization) across eligible datasets.

The test is pre-registered to establish methodological discipline and priority. Analysis will proceed only after this document is time-stamped at a public registry.

2. Generating Framework

The prediction is derived from the Law of Recursion (Gaconnet, 2026a), which claims that in active exchange processes, boundary/interface structures govern exchange outcomes more strongly than bulk or interior structures. Applied to nuclear knockout, the Law identifies the optical potential as the membrane node of the seven-node topology. Membrane governance, as a feature of the framework, predicts that parameters describing the optical potential should dominate the sensitivity of observables that measure the exchange outcome.

This pre-registration tests the empirical prediction. It does not test the Law of Recursion as a first principle, nor does it establish structural unification across domains. Those claims require separate work. The present test is successful or unsuccessful on its own terms.

3. Primary Prediction

Statement: For each eligible quasi-elastic proton knockout dataset measuring polarization observables, the parameter whose variation produces the largest change in the observable (under the sensitivity metrics defined in §5) will be an optical-potential parameter.

Formal expression: Let P = {p₁, p₂, …, pₙ} be the set of theoretical input parameters examined in an eligible dataset’s sensitivity analysis, partitioned into POP (optical-potential parameters) and PNOP (non-optical-potential parameters). Let S(pᵢ) denote the sensitivity of the polarization observable to parameter pᵢ under a specified metric. The prediction is:

max{S(p) : p ∈ POP} > max{S(p) : p ∈ PNOP}

for every eligible dataset.

Critical constraint: Within each dataset, all parameters must be evaluated with the same metric for the ranking comparison. The metric hierarchy (A > B > model-spread, defined in §5) determines which metric is used for the dataset as a whole, not per-parameter. If Metric A is available for all parameters in a dataset, Metric A is used for all. If Metric A is available for some but not all parameters, all parameters fall back to Metric B or model-spread so the comparison is on a common footing. Metric A results for individual parameters are reported as supplementary detail but do not enter the ranking that determines confirmation or falsification.

4. Eligible Datasets

Inclusion Criteria

Published quasi-elastic proton knockout measurement of a polarization observable (r′LT, ALT′, ATL, or analogous helicity-dependent observable).

Accompanying RDWIA or equivalent theoretical analysis.

Published sensitivity analysis including at least one optical-potential parameter variation and at least one non-optical-potential parameter variation in the same paper or in directly citable companion work.

Sufficient methodological detail to identify the magnitude of parameter variations applied.

Exclusion Criteria

Datasets with sensitivity analyses covering only one parameter class are excluded to preserve the cross-class comparison. If the eligible pool is small as a result, this restriction is retained and the paper is reframed as a limited-scope test rather than a cross-nuclear aggregate.

Analyses where parameter variation magnitudes cannot be determined from published material are excluded.

Non-quasi-elastic reactions, inclusive measurements without polarization, or unpolarized cross sections are out of scope for this test.

Candidate Datasets Identified Prior to Registration

Nucleus	Source	Status
⁴⁰Ca(ē, ē′p)³⁹K	Kolar et al. 2025, Physics Letters B 871, 139977, Mainz Microtron	Motivating case
¹⁶O(ē, ē′p)¹⁵N	Candidate papers from NIKHEF and Jefferson Lab Hall A; to be confirmed in Phase 1	To be confirmed
¹²C(ē, ē′p)¹¹B	Candidate papers from Saclay and Jefferson Lab; to be confirmed in Phase 1	To be confirmed
Additional	⁹Be, ²⁰⁸Pb, ²H, ³He, ⁴He if inclusion criteria are satisfied	To be confirmed

The eligible-dataset list will be frozen at the end of Phase 1 and published as a supplement to this registration before Phase 2 analysis begins.

5. Sensitivity Metric

Three metrics are defined, in order of rigor. All three will be reported where the underlying data permit. The primary result is rank ordering (Metric C), which survives all known methodological confounds identified in pre-registration discussion.

Foundational constraint: Within any single dataset, all parameters entering the ranking comparison must be evaluated with the same metric. Mixed-metric rankings are prohibited because the metrics are not on the same numerical scale. Metric A values are approximately five times larger than Metric B values for equivalent intrinsic sensitivity (by Taylor expansion, SB ≈ 0.20 × SA). Ranking parameters evaluated under different metrics against each other would introduce systematic bias toward whichever parameter received the higher-tier metric. The hierarchy A > B > model-spread determines the metric used for the dataset as a whole: use the highest-tier metric for which data are available for all parameters in the dataset.

Metric A — Normalized Partial Derivatives

(Primary where data permit for all parameters in the dataset.)

For each parameter pᵢ with nominal value p⁰ᵢ and a published sensitivity curve O(pᵢ) showing observable O as a function of pᵢ over a range including p⁰ᵢ:

SA(pᵢ) = |∂O/∂pᵢ|p⁰ᵢ × p⁰ᵢ / |O(p⁰ᵢ)|

This is the dimensionless logarithmic sensitivity, isolating intrinsic parameter-dependence from the accuracy of current best estimates. Metric A requires continuous sensitivity curves in the published material. The absolute value in the denominator ensures S is non-negative regardless of the sign of the observable.

Metric B — Matched Fractional Variation

(Primary when Metric A is unavailable for all parameters in the dataset.)

For each continuous parameter pᵢ, compute the observable change resulting from a ±10% variation about the nominal value:

SB(pᵢ) = |O(1.10 × p⁰ᵢ) − O(0.90 × p⁰ᵢ)| / |O(p⁰ᵢ)|

The 10% fraction is specified in advance, matched across all continuous parameters, to eliminate the confound between intrinsic sensitivity and the accuracy of the current parametrization. The absolute value in the denominator ensures S is non-negative regardless of observable sign.

For discrete parameters (bound-state model choice, current operator prescription, form factor parametrization) where ±10% is not defined, Metric B is replaced by model-spread:

SB(pdiscrete) = [max{O} − min{O}] / |O(pref)|

where pref (the reference model) is defined as the model used as the baseline in the published sensitivity analysis being examined. If the published analysis does not designate a baseline, the model that appears most frequently in the published literature for that nucleus and observable is used. This rule is specified in advance to prevent post-hoc selection of a favorable reference.

The asymmetry between continuous and discrete comparisons is noted as a methodological limitation; results relying on this comparison are flagged in per-dataset reporting.

Metric C — Rank Ordering

(Primary reported result.)

For each dataset, all eligible parameters are ranked by their sensitivity score under a single metric applied uniformly to all parameters in that dataset (determined by the hierarchy: use the highest-tier metric available for all parameters). The prediction is confirmed for the dataset if the top-ranked parameter is in POP.

Rank ordering is robust to the continuous-vs-discrete comparability problem, to the “how wrong is the current parametrization” confound, and to the specific numerical choice of matched fraction. It is the primary reported metric. Metrics A and B are reported as supporting evidence where available and as cross-checks on rank stability.

6. Falsification Conditions

Per-Dataset

Confirmed: The prediction is confirmed for a given dataset if, under Metric C (with uniform metric application), the top-ranked parameter is an optical-potential parameter.

Falsified: The prediction is falsified for a given dataset if, under Metric C (with uniform metric application), the top-ranked parameter is a non-optical-potential parameter.

Aggregate

The membrane-governance prediction as stated requires confirmation in every eligible dataset. Partial holding is reported as a scope restriction on the claim, not as overall confirmation. Specifically:

If the prediction holds in all eligible datasets, the cross-nuclear membrane-governance claim is supported.

If the prediction holds in some but not all datasets, the claim is restricted to the subset of nuclei/observables where it holds, and the pattern of failure is reported as a constraint on the claim’s domain.

If the prediction fails in a majority of datasets or in the most methodologically rigorous datasets, the claim is considered falsified as stated.

No averaging across datasets. No weighted aggregation. Per-dataset results are reported in full.

Robustness Checks

Metrics A and B, where computable for all parameters in a dataset, must produce rank orderings consistent with Metric C. Disagreement between metrics within a dataset is reported and discussed.

If Metric C confirmation depends on the choice between Metric A, Metric B, or model-spread comparison for specific parameters, this dependency is explicitly flagged.

The 10% matched-fraction choice in Metric B is varied to 5% and 20% as a sensitivity check. Rank stability across these variations is reported.

7. Operational Definitions

Optical-Potential Parameters (P_OP)

Central real (V), central imaginary (W), spin-orbit real (V_LS), spin-orbit imaginary (W_LS), surface (V_S), and geometric parameters (radii, diffusenesses) of the nuclear optical potential. Variation ranges anchored to the uncertainty bands in the Cooper-Hama-Clark global Dirac optical potential parametrization (Cooper et al., 1993; 2009) or equivalent local parametrizations as specified in the original analysis.

Non-Optical-Potential Parameters (P_NOP)

Bound-state wavefunctions: Variation across Woods-Saxon, Hartree-Fock (Skyrme and Gogny), and relativistic mean-field descriptions as used in published analyses.

Nuclear current operator: cc1 vs. cc2 vs. cc3 prescriptions (de Forest, 1983).

Electromagnetic form factor parametrization: Variation across standard parametrizations (Galster, Kelly, Ye et al.).

Off-shell extrapolation procedure: Where applicable.

8. Analysis Plan

Phase 1 — Literature search and dataset qualification. Identify published quasi-elastic knockout polarization-observable measurements with accompanying sensitivity analyses. Apply inclusion and exclusion criteria. Produce the final eligible-dataset list. Publish the list as a registration supplement before Phase 2 begins. No sensitivity data are extracted or examined in Phase 1; only bibliographic information and verification of inclusion criteria.

Phase 2 — Sensitivity extraction. For each eligible dataset, extract published sensitivity data (curves, variation magnitudes, χ²/DoF tables, parameter-variation plots). Determine the highest-tier metric available for all parameters in each dataset. Compute sensitivity scores under the uniform metric for each dataset. No analysis of the rank ordering is performed in Phase 2; only metric computation.

Phase 3 — Prediction evaluation. For each eligible dataset, apply the falsification conditions in §6. Record per-dataset confirmation or falsification under Metric C with uniform metric application, with Metrics A and B reported as supporting detail where available. Tabulate aggregate results per §6.

Phase 4 — Reporting. Full per-dataset results published with no selection or filtering. Methodological limitations, metric disagreements, and scope restrictions reported explicitly. If the eligible-dataset pool is small (e.g., only Kolar 2025 and one other dataset satisfy inclusion criteria), the paper is framed as a limited-scope test with motivation for broader future work, not as a cross-nuclear aggregate confirmation.

9. Stated Limitations

Selection effects in the published literature. The published nuclear knockout literature may systematically report optical-potential sensitivities more thoroughly than non-optical-potential sensitivities, biasing the eligible-dataset pool toward confirmation. Datasets where non-optical-potential sensitivities are underreported relative to optical-potential ones will be flagged in per-dataset discussion.

Continuous-vs-discrete comparability. Optical-potential parameters have continuous uncertainty bands; bound-state wavefunctions and current operators are discrete model choices. The model-spread substitute defined in Metric B is methodologically asymmetric with respect to the continuous-variation metric. The uniform-metric-per-dataset constraint and rank ordering (Metric C) mitigate but do not eliminate this asymmetry.

Cross-metric scale incompatibility. Metric A and Metric B are not on the same numerical scale (SB ≈ 0.20 × SA by Taylor expansion). Rankings that mix metrics across parameters within a single dataset are prohibited to prevent systematic bias. This constraint may force datasets with rich sensitivity data for some parameters but not others to fall back to a lower-tier metric.

Scope. This test addresses polarization observables in quasi-elastic proton knockout. Extension to unpolarized cross sections, non-quasi-elastic reactions, or other reaction channels is not entailed by the result of this test.

Dependence on published sensitivity analyses. The test does not involve re-computation from source codes. Any errors, limitations, or methodological choices in the underlying published analyses propagate into this test’s results. Where multiple published analyses of the same dataset disagree on sensitivity magnitudes, all are reported and the disagreement is discussed.

Framework-level implications. Confirmation of the prediction supports the empirical claim that membrane-locus parameters dominate polarization-observable sensitivity in nuclear knockout. It does not establish the Law of Recursion as a first principle, nor does it demonstrate cross-domain structural invariance. Those claims require the separately pre-registered secondary predictions (§10) and additional theoretical work outside this test’s scope.

10. Secondary Predictions (Registered for Priority)

The membrane-governance pattern — boundary/interface parameters dominating exchange-outcome sensitivity more than bulk or interior parameters — is predicted to extend to two further domains. These predictions are registered here to establish priority. They are not tested in the present paper.

Secondary prediction 1 — QGP medium response. In hydrodynamic calculations of quark-gluon plasma wake structure, the sensitivity of wake-observables (amplitude, asymmetry, cone angle) to boundary-condition parameters (freezeout-surface treatment, confinement/deconfinement interface parametrization) will exceed the sensitivity to bulk-transport parameters (η/s, ζ/s, speed of sound cs) under matched fractional variation or rank-ordering.

Secondary prediction 2 — Biological membrane transport. In models of selective transport across biological membranes, the sensitivity of transport-observables to selectivity-filter parameters (pore geometry, selectivity-filter composition, protein conformational state) will exceed the sensitivity to bulk cytoplasmic or extracellular conditions (ionic strength, osmotic pressure, temperature within physiological range) under matched fractional variation or rank-ordering.

Scope note: Failure of either secondary prediction while the primary nuclear prediction holds indicates that membrane-governance is domain-restricted to nuclear knockout rather than being a cross-domain structural invariant. Confirmation of all three supports the cross-domain claim empirically, without establishing the generating framework formally.

11. Pre-Registration Integrity

No analysis of any eligible dataset has been performed at the time of registration. The author has read the Kolar et al. (2025) paper and is aware of its reported V_LS sensitivity (χ²/DoF reduction from 2.16 to 0.49 with 1.55× V_LS enhancement), which motivated the prediction but is not counted as independent confirmation for the purposes of this test — it is the motivating case. The cross-nuclear aspect of the test (¹²C, ¹⁶O, additional nuclei if eligible) involves datasets the author has not examined through this specific lens prior to registration.

Any modifications to this pre-registration made after initial submission will be version-tracked at OSF with explicit change logs. Modifications made after any eligible dataset has been analyzed will be flagged as post-hoc and will not carry pre-registration weight.

12. Authorship, Attribution, and Drafting Disclosure

Don L. Gaconnet is the sole scientific author. The framework generating the prediction (Law of Recursion; Gaconnet, 2026a), the methodological design, and the scientific responsibility for the test are his.

The pre-registration document was drafted with assistance from Anthropic’s Claude (Opus 4.6) during an extended methodological discussion. The AI assistant contributed to iterative refinement of the metric structure, identification of confounds (including the intrinsic-sensitivity-vs-parametrization-accuracy confound and the cross-metric scale incompatibility), and drafting of language. The scientific content — prediction, framework, falsification conditions — originates with the author. Claude’s role is disclosed here in the interest of transparency; it does not constitute authorship.

. References

Cooper, E. D., Hama, S., & Clark, B. C. (1993). Global Dirac phenomenology for proton-nucleus elastic scattering. Physical Review C, 47(1), 297–311.

Cooper, E. D., Hama, S., & Clark, B. C. (2009). Global Dirac optical potential from helium to lead. Physical Review C, 80, 034605.

de Forest, T. (1983). Off-shell electron-nucleon cross sections: The impulse approximation. Nuclear Physics A, 392(2), 232–248.

Gaconnet, D. L. (2026a). The Law of Recursion: A First Principle of Systemic Exchange. LifePillar Institute for Recursive Sciences. DOI: 10.17605/OSF.IO/MVYZT.

Kolar, T., Sabo-Napadensky, I., Achenbach, P., et al. (2025). Measurement of the helicity-dependent response in quasi-elastic proton knockout from ⁴⁰Ca. Physics Letters B, 871, 139977. DOI: 10.1016/j.physletb.2025.139977.

Meucci, A., Giusti, C., & Pacati, F. D. (2001). Relativistic corrections in (e,e′p) knockout reactions. Physical Review C, 64, 014604.

Picklesimer, A., Van Orden, J. W., & Wallace, S. J. (1985). Electromagnetic interactions and the (e,e′p) reaction. Physical Review C, 32, 1312.

— End of Pre-Registration Document —

© 2026 Don L. Gaconnet. All Rights Reserved. LifePillar Institute for Recursive Sciences.