Theorem 1: Local Admissibility Does Not Imply Long-Horizon Historical Continuity

This theorem establishes the foundational mathematical result underlying Self-Preserving Flow (SPF): Local admissibility of recursive transitions is insufficient to guarantee longhorizon historical continuity. We provide a rigorous proof using nonlinear semantic manifolds, admissibility neighborhoods, and recoverability mappings. The theorem formally demonstrates that systems may remain locally valid at every recursive step while still undergoing cumulative semantic deviation sufficient to produce eventual historical irrecoverability. This result provides the mathematical basis for introducing the Semantic Consistency Layer (SCL) and Meta-SCL within the SPF architecture.