Hierarchical Identity in Self-Preserving Flow (SPF) Theory

This paper formalizes a hierarchical theory of identity within the Self-Preserving Flow (SPF) framework. Unlike classical ontological theories that treat identity as a static intrinsic property, SPF defines identity as a historically reconstructible continuity relation across recursive semantic evolution. We introduce two distinct but interconnected layers of identity: Weak Identity (local semantic and operational continuity within a given Semantic Consistency Layer) and Strong Identity (persistence of historically recoverable lineage across transformations of SCL itself). The paper establishes that strong identity is not a pointstate property on the semantic manifold, but a higher-order lineage equivalence class over admissible Meta-SCL transformations. This resolves the apparent contradiction between adaptive semantic evolution and preservation of systemic selfhood in open-world recursive systems.