Phenomenological Principle of Coherent Learnability (PPCL)

We establish Phenomenological Principle of Coherent Learnability (PPCL) as a structural principle governing predictability in finite point configurations with k-neighborhood structures. PPCL states that local label coherence (semantic tolerance τ ) directly determines local prediction accuracy. This principle derives from the more general Semantic Tolerance Law, which will be presented in a companion paper. We present three instantiations of PPCL:
                                                     1. PPCL (Classification): τ > 1/K ⇒ acc > 1/K
                                                     2. PPCL-R (Regression): τR > 0 ⇒ R2 > 0
                                                     3. PPCL-OC (Anomaly Detection): τOC > 0.8 ⇒ AUC > 0.5
These principles are geometric tautologies: direct consequences of the definitions of semantic tolerance (τ ) and local prediction. We validate with 7,000+ datasets and 28+ adversarial attacks, finding zero violations. The underlying mathematical structure—the Local Transition Tensor Tcc′ —is derived in the companion paper Local Transition Tensor for Supervised Classification.