The Persistence Criterion:Distinguishing Epistemic Obscuration from OntologicalElimination in Physical Theories

This preprint introduces the Persistence Criterion (PC), a conceptual and mathematical framework for distinguishing epistemic obscuration from ontological elimination in physical theories. The central claim is that uncertainty, noise, decoherence, or coarse-graining reduce empirical distinguishability of states or observables without implying that the underlying theoretical structures cease to exist. The framework is developed across classical estimation theory, stochastic dynamical systems, and quantum theory. In the classical domain, noisy observation models and information-theoretic metrics are used to show how distinguishability contracts while state variables persist, consistent with standard treatments in estimation theory and statistical physics (e.g., Fisher information and Bayesian filtering). For dynamical systems, stochastic differential equations and Fokker–Planck dynamics illustrate how deterministic generators remain structurally present despite diffusion-dominated behavior, aligning with established results in open-system dynamics and control theory. In the quantum domain, the Persistence Criterion is formulated using density operators, completely positive trace-preserving (CPTP) maps, and the algebraic (C*-algebraic) formulation of quantum mechanics. Decoherence is treated as an obscuring process acting on states via CPTP channels, while the underlying observable algebra remains invariant. This formulation draws on standard results from quantum information theory and algebraic quantum mechanics, emphasizing that loss of coherence or distinguishability does not entail annihilation of observables or dynamical structure (Holevo, 2011; Nielsen Breuer Wallace, 2012; Ruetsche, 2018). No new physical dynamics or empirical predictions are proposed. The contribution is conceptual and formal: clarifying how existing mathematical frameworks already encode persistence under uncertainty, and providing a principled interpretational constraint applicable across classical and quantum theories.