Special Relativity as an Entropy-Flat Limit Law

This preprint derives the kinematic structure of Special Relativity as a limit law of persistence geometry. The central object is a resolution metric that quantifies distinguishability across one temporal and three spatial resolution directions. An entropy-flat regime is defined operationally by three conditions: negligible path dependence (to the required order), trivial holonomy on admissible loops, and global integrability of local loss rules. These conditions are regime delimiters, not new postulates. In this regime the transport connection is curvature-free at the regime order, which forces the resolution line element to be constant. Demanding a finite invariant normalization together with bounded admissible spatial rates excludes positive-definite quadratic forms and fixes an indefinite (Lorentzian) signature. The resulting constant quadratic form contains a single conversion scale σσ, interpreted here as the maximal entropy-resolved rate compatible with persistence-stable evolution in the flat regime (empirically identified with cc). The invariance group of the constant metric is then derived directly as the set of linear frame transformations preserving the line element, yielding Lorentz-type symmetry without invoking a light postulate or presupposing spacetime ontology. Time dilation and length contraction follow from the invariant normalization and resolution scaling. Mass–energy equivalence arises in the flat regime as a Noether charge associated with time-translation symmetry of an entropy-weighted effective action; only the flat-regime quadratic structure of that action is imported from prior work. The paper is falsifiable: it specifies validity boundaries (when curvature becomes leading-order) and derives weak-curvature correction scalings parameterized by an invariant curvature measure εε, alongside explicit falsification criteria.