Identity Persistence after Brouwer and Hilbert_ Formal Admissibility, Constructive Witness, and Invariant Continuity

This paper positions identity persistence under transformation within the Brouwer-Hilbert-HoTT-verification landscape. It argues that Hilbertian formal admissibility, Brouwerian constructive witness, homotopy type-theoretic transport, and formal verification each answer different questions, but none alone determines when a changing object, process, proof, or decision remains the same through transformation. The paper introduces identity persistence as a prior admissibility frame for persistence claims: the declared regime under which transformations may be treated as preserving the same identity-bearing unit. It develops the argument through counterfactual tests showing formal legality without invariant preservation, construction without persistence, verification without replay-stable identity, and probability without stable objects of measurement. The paper is a philosophical companion to the Universal Identity and Persistence forcing theorem. It does not prove or extend the formal stack.