Identity Persistence after Brouwer and Hilbert: Formal Admissibility, Constructive Witness, and the Licensing Layer for Persistence Claims

This paper positions identity persistence under transformation within the Brouwer-Hilbert-HoTT-verification landscape. Hilbertian formalism asks whether symbolic moves are admissible; Brouwerian intuitionism asks whether objects or propositions are constructively witnessed; HoTT studies transport once an identification, path, or equivalence is available; formal verification proves properties of specified systems. Identity persistence asks a prior question for persistence claims: under what admissibility conditions may a transformation be treated as preserving the same identity-bearing unit? The paper develops this distinction through counterfactual tests: formal legality without invariant preservation, construction without persistence criteria, verification without replay-stable identity, and probability without stable objects of measurement. It frames identity persistence as a regime-bound account of invariant continuity, not as a replacement for existing foundations. This paper is a philosophical companion to the Universal Identity and Persistence forcing theorem and does not prove or extend the formal stack.