Persistence Locking Mechanism (PLM): A Structural Continuation Framework for Unresolved Micro-Scale Persistence Regions

The Persistence Locking Mechanism (PLM) is a structural continuation framework developed within Persistence Fingerprint Analysis (PFA) and the broader Paton System. PLM investigates whether unresolved or weakly resolved systems may still preserve coherent persistence topology beneath regions of descriptive instability, probabilistic fragmentation, confinement, or reduced observational clarity. Rather than replacing existing scientific theories, the framework functions as a persistence-overlay methodology that tests whether structurally compatible continuation pathways remain detectable across unresolved micro-scale terrain. The framework operates by extracting known persistence nodes from existing systems, overlaying pre-existing Paton persistence topology, identifying weighted structural lock regions, and evaluating whether logically admissible continuation corridors emerge. PLM treats mathematics as a scale-independent structural overlay capable of comparing persistence behaviour across quantum systems, confinement systems, probabilistic transition regions, recursive cognitive systems, dynamical systems, and unresolved micro-scale persistence domains. The framework does not propose ontological equivalence or replacement of quantum mechanics, QFT, QCD, string theory, or future quantum gravity frameworks. Instead, PLM functions as a constrained persistence-continuation framework for investigating whether fragmented or weakly resolved systems still preserve coherent continuation topology beneath regions of reduced descriptive visibility.