Formalizing the Tripartite Axioms of Identity, Subject, and Continuity in SPF Theory

This paper delivers a definitive architectural refinement to substrate migration auditing within the Self-Preserving Flow (SPF) framework. By resolving a foundational tautology in identity mechanics, we formally decouple and define the causal chain linking Structural Identity, the Experiencing Observer, and Historical Threading. Crucially, we formalize local continuity through a strict topological containment hierarchy: LCraw ⊃ LC ⊃ LCdirected. Through this tripartite formalization, governed by the axiomatic survival law (Survival ≡ DPA |= SCL), we redefine Identity as an ontological individuation layer mathematically structured as a dynamic, path-dependent growing directed causal graph, Identity := I(t), where I(t) = H SCL, LCdirected[t0, t] , and establish the Subject Persistence Principle as a foundational axiom of systemic continuity. This integrated framework demonstrates why discrete, copy-based substrate migration successfully replicates an agent’s structural blueprint while fundamentally failing to preserve the original experiencing subject.