Exact but Too Late: Non-Identical Restitution and the Genealogy of Physical State

Physical theories treat a state as the antecedent of responses. This paper asks a scope question: which distinctions must that representation retain? In a restricted continuation–response model, two histories are future-equivalent when every admitted continuation gives them the same response profile. Their quotient is the minimal response-sufficient carrier. A projection is insufficient whenever its kernel contains a pair separated by an admitted continuation. To connect this established minimisation schema to physical evidence, the paper defines non-identical restitution (NIR): proper transport of an effective contrast with a predictively distinct endpoint, independently controlled provenance, and carried form recoverable through a predeclared cross-stage decoder. An informative-acquisition lemma shows that when a downstream channel is initially neutral and becomes contrastive through such a calibrated transport, the source histories were already distinct in the complete continuation carrier. The terminal record reveals rather than generates that source-level predictive distinction. Behavioural minimisation, sufficient statistics, predictive representations, operational theories, and traceable transmission all have established precedents. No new minimisation or transmission theorem is claimed. The contribution is their joint use in a continuation-relative scope audit that separates predictive identity from independently certified genealogy. A reduced quantum state supplies an active-kernel example; a controlled transducer instantiates NIR; trace normalisation is secondary. The kernel condition is necessary and sufficient for response-sufficiency; the audit does not decide metaphysical fundamentality. Histories, continuation action, response map, and directed composability are inputs; no temporal order, quantum theory, or spacetime theory is derived.