A Hierarchical Meta-Formal Architecture for Long-Horizon Semantic Continuity and Recursive Fixed-Point Closure in Intelligent Systems

This paper presents Self-Preserving Flow (SPF), a meta-formal architecture for modeling long-horizon semantic continuity in recursively adaptive intelligent systems. SPF addresses the problem that systems may preserve local operational validity while gradually losing historical semantic reconstructibility across extended recursive evolution. The framework introduces a layered continuity architecture consisting of Dynamic Pattern Adaptation (DPA), the Semantic Consistency Layer (SCL), Meta-SCL governance, and recursive fixed-point closure constraints. SPF defines intelligent stability not as static behavioral invariance, but as the preservation of historically recoverable semantic lineage across recursive adaptation. We formalize weak and strong identity continuity, propose a recoverability-centered notion of semantic persistence, and provide a hierarchy of continuity conditions governing recursive intelligent systems. We further discuss how SPF differs from existing approaches in model collapse mitigation, scalable oversight, and recursive self-improvement. This paper is intended primarily as a theoretical architecture and continuity-framework paper. The mathematical sections should be interpreted as an initial formalization scaffold for continuity structures rather than as a complete closed mathematical system.