Axioms and Observable Invariance for Sigma-Time Models

Sigma Transform Calculus uses bounded-variation clocks to describe systems whose effective evolution may include continuous clock mass, atomic updates, and physical-time intervals with no clock advance. A calculus of this kind requires more than a clock measure: it also requires an explicit distinction between representation and observable content, a fixed model identity, and a rule preventing later analytic papers from upgrading calibration choices into theorems. This paper supplies that axiomatic interface. We define a sigma-time model as declared data consisting of a clock, state and trajectory classes, gauge action, canonical representatives, admissible observables, units, model-identity ledger, calibration protocol, claim classes, and propagation duties. The main results show that gauge-invariant observables factor through canonical representatives, that deterministic canonicalization is required for meaningful comparison away from degeneracy, and that later papers may cite this interface only for observable invariance, model identity, prediction admissibility, and citation boundaries. We do not prove existence, uniqueness, transform theorems, numerical convergence, or PDE well-posedness here; those results belong to later papers whose hypotheses must satisfy this interface.