Redundancy and conditional dependence in per-history radiolytic counts

Abstract

A preregistration, deposited before any confirmatory production run under the protocol it specifies, for an information-theoretic analysis of per-history fluctuations in Monte Carlo water radiolysis (OpenTOPAS / TOPAS-nBio, Geant4-DNA IRT chemistry). The data matrix has one row per particle history and one column per chemical species, holding integer molecule counts rather than ensemble-averaged yields G(t). Counts rather than yields, because a yield is already divided by deposited energy and would inject that variable into every column at once. The ensemble is that of a track segment truncated after approximately 10 keV of primary energy loss. Three statistical estimands are defined and kept strictly apart: what the chemical record carries about a history-level source variable (the ionisation count), what it carries beyond deposited energy, and the residual dependence between species conditional on both. From the first a redundancy curve is built, formally analogous to the partial information plot of quantum Darwinism. From the third a pairwise conditional-dependence matrix and a conditional total correlation, motivated by — but not identified with — the factorisation condition of Spectrum Broadcast Structure, the pairwise form alone being known to be insufficient for it. Stoichiometric conservation is handled by exact coordinate reduction rather than by conditioning: the balance coordinate is a deterministic function of the analysed vector, so conditioning on it generates dependence instead of removing it. The primary falsifiable hypothesis is that residual dependence is enriched on the edges of a frozen reaction-network adjacency, tested against an exhaustive node-label permutation null. Enrichment, not recovery of the network — snapshot dependence can arise from a direct reaction, a shared precursor, a shared product, a chain of intermediates, or a conservation law. Frozen here: the simulation protocol and the exact build, the data contract, the definition of every quantity, the estimator family and its finite-sample acceptance criterion, four separate null hypotheses and their calibration, the mandatory diagnostics and fail-closed rules, the degeneracy branches, the directional predictions and the explicit non-claims. Quantities that can only be measured are deferred to two dated amendments, each with its decision rule already fixed: one after the capability checks and before the pilot, one after the pilot and before the confirmatory run. No claim is made that the classical diagnostics computed here demonstrate quantum Darwinism, Spectrum Broadcast Structure, or quantum coherence. Every quantity reported is a classical Shannon quantity on a classical ensemble. Results are statements about the model: TOPAS-nBio and Geant4-DNA IRT are validated against experiment for ensemble-mean time-dependent yields, not at the level of per-history fluctuation statistics, for which no experimental data exists.