Predictive Bioharmonics: A Formal Dynamical Model for Identity Continuity Across Biological Collapse

This document presents a formal mathematical framework describing the conditions under which personal identity could, in principle, persist across biological collapse and be re-instantiated in a new substrate. Identity is defined not as biological material, memory content, or psychological narrative, but as a dynamical invariant: a stable, self-referential attractor embedded in a high-dimensional state space. The framework distinguishes identity continuity from biological continuity and reformulates collapse, persistence, and re-instantiation in purely dynamical terms. By specifying topological, stability, and coupling requirements, the analysis delineates when identity continuity is mathematically permissible and when it is formally excluded. The framework treats identity as a structural property of dynamical evolution rather than as a material or informational entity. Biological collapse is modeled as a loss of substrate capacity rather than an intrinsic termination of the identity attractor. Re-instantiation is formulated as a continuous dynamical entrainment process, not as copying, transfer, or duplication. No empirical claim is made that such continuity occurs in nature. The framework establishes mathematical allowance only, remaining agnostic regarding physical realizability, technological feasibility, or biological implementation.