Theorem 4: Recursive Fixed-Point Closure Theorem in Self-Preserving Flow (SPF)

This theorem establishes the final recursive closure condition of the Self-Preserving Flow (SPF) hierarchy. Theorem 1 stabilized state evolution, Theorem 2 stabilized semantic constraint evolution, and Theorem 3 stabilized governance evolution. However, unrestricted recursive self-modification introduces the fundamental threat of infinite meta-regression (St → SCLt → Φt → Ψt → . . .). Without a recursively irreducible fixed structure, semantic systems lose dimensional coherence and collapse into unrestricted relativistic drift. This theorem proves that long-horizon recursive stability requires the existence of a canonical fixed-point invariant under arbitrary admissible recursive governance transformations. SPF identifies this invariant not as semantic content, ontology, or governance logic, but as the canonical traceability topology (A) preserving historical reconstructibility itself.