Background to the Identity-Persistence Theorem_ An Orientation Note on Lens, Reduction, and Scope

This note is a developmental orientation to the identity-persistence program. It is not part of the formal proof stack and does not introduce additional ontological, physical, biological, computational, or metaphysical claims. Its purpose is to explain how an earlier coherence-oriented lens was narrowed into the current formal problem: what must remain invariant for something to persist as the same through transformation within explicit admissibility constraints. The note distinguishes the generative lens from the canonical theorem: the lens motivated the search, while the theorem carries the claim. The note also clarifies what has been cut from the current canonical surface. Earlier materials that frame the work in terms of probability replacement, physics or cosmology, consciousness, free will, AGI, primes, chirality, or universal substrate language are treated as exploratory context and are superseded wherever they exceed the current formal stack. The positive claim is limited: many systems depend on persistence through transformation; persistence requires some basis for distinguishing continuation from replacement; invariants reduce arbitrary degrees of freedom; and the identity-persistence theorem is the disciplined formal extraction of that broader intuition. This document should be read as a scope-boundary and reader-orientation note for the identity-persistence theorem, not as a standalone proof or extension of the theorem.