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

This paper situates identity persistence under transformation in relation to Hilbertian formal admissibility, Brouwerian constructive witness, homotopy type-theoretic transport, and formal verification. It argues that these frameworks answer adjacent but distinct questions: whether a symbolic move is lawful, whether an object or proposition is witnessed, what follows from an available identification, and whether a specified property is verified. Identity persistence asks a prior question for persistence claims: what declared admissibility regime licenses treating a transformation as preserving the same identity-bearing unit? The paper develops this distinction through counterfactual tests and frames identity persistence as regime-bound invariant continuity rather than a replacement for existing foundations.