Epistemic Phase Transitions: A Universal Theory of Descriptive Validity Across Observation Scalesed Item

We identify and formalize a universal class of phase transitions that occur not in physical systems, but in the descriptive validity of theoretical frameworks. These Epistemic Phase Transitions (EPTs) emerge when observational parameters (integration horizon H, measurement resolution ∆x, epistemic distance d) cross critical thresholds Ωc. Below Ωc, theoretical descriptions exhibit catastrophic fail- ure (numerical instability, interpretability collapse); above Ωc, the same descrip- tions achieve robust validity. We establish: (i) a unified mathematical framework characterizing EPTs across computational physics (CFL stability), symbolic re- gression (weak-form integration), and decision theory (degeneracy resolution); (ii) universal scaling laws predicting transition widths; (iii) an epistemic uncertainty principle relating integration horizon to noise tolerance; (iv) empirical validation demonstrating 1000× error discontinuities at critical thresholds. Applications span the replication crisis in psychology (failures occur in Regionsub), AI reliability (LLM validity windows), and financial crisis detection. This framework provides the first mathematical theory of when scientific descriptions are valid, distinct from physical phase transitions, emergent phenomena, quantum observer effects, and renormal- ization group flows.