Core Distinguishability Relativity (CDR) introduces a minimum-divergence intervention framework for testing whether observed transitions in a dynamical system exhibit an information-driven selection bias relative to a pre-registered reference Markov kernel. Given a decomposition of system states into interacting components and a fixed baseline transition kernel, CDR defines a non-circular, kernel-local integration gain that quantifies how strongly the reference dynamics couple components beyond conditional independence. The CDR hypothesis class is nested: the null hypothesis corresponds to no reweighting relative to the baseline kernel, whereas the alternative hypothesis assumes strictly positive reweighting derived from a relative-entropy (minimum Kullback–Leibler divergence) principle. Under this construction, transitions follow an exponential-family reweighted kernel that minimally departs from the reference dynamics while incorporating integration gain. This framework yields formal distinguishability under mild variance conditions while preserving continuity in the limit where reweighting vanishes. CDR further specifies an operational inference program based on Bayesian evidence (Bayes factors) with parsimonious priors, practical model-selection surrogates such as BIC/MDL, explicit identifiability diagnostics (including Fisher information and conditioning checks), and adversarial safeguards against degeneracy when flexible baselines absorb effects. Canonical validation domains (controlled reference models) and mandatory negative controls, including time-shuffle and surrogate constructions, are incorporated to enforce falsifiability and replication-ready reporting. Clarification Note In CDR, the term “Relativity” denotes kernel-relativity: distinguishability is defined epistemically relative to a pre-registered reference transition kernel. The framework is unrelated to Einsteinian spacetime relativity and instead invokes the methodological principle that meaningful distinctions emerge only relative to a fixed observational baseline.
Thiago Siqueira da Luz e Silva (Mon,) studied this question.