The Recursive Continuity Framework: An Axiomatic Ontological Model of Identity, Continuity, and Collapse

Version 2.0 — Revised preprint. This version refines core definitions, clarifies recursive dependency and incorporation, and formalizes the criterion for collapse to improve precision and prevent misinterpretation.This paper presents a minimal ontological framework for understanding identity, continuity, and collapse. Rather than treating identity as dependent on memory, structure, or physical substrate, it is defined as the persistence of telic recursive self-reference across temporally continuous transformation. The framework is constructed from a small set of interdependent primitives—coherence, continuity, recursion, telos, identity, collapse, and being—each defined without reliance on external assumptions or prior definitions. This framework engages longstanding problems in the philosophy of identity, including persistence through change, duplication, and reconstruction, by providing a structurally consistent criterion for evaluating continuity without reliance on memory, physical substrate, or representational equivalence criteria. Within this model, persistence is determined solely by the maintenance of recursive continuity under the constraint of coherence, while termination occurs only upon irreversible break in that continuity. This allows questions of identity to be evaluated consistently across scenarios involving transformation, duplication, and reconstruction without contradiction. The framework is substrate-independent and non-hierarchical, describing identity as a process rather than a fixed entity. Its purpose is not to provide exhaustive answers, but to establish a structurally consistent foundation from which such questions can be evaluated.