Finite Realism: Epistemology, Metaphysics, and Physics Under Finite Resources

Finite Realism is an operational framework for epistemology, metaphysics, and physics that makes finite resource constraints explicit. Ontological commitment is licensed only within a declared window W, and only when a structure passes a joint earning criterion: it must (i) compress sequential predictions beyond a predeclared baseline (prequential/MDL or PAC-Bayes gains) and (ii) remain stable under admissible interventions, as measured by a window integral probability metric DW built from implementable tests and guarded by data-processing closures. Objectivity is not assumed but derived: it is the communication fixed point at which capacity-limited agents converge when exchanging bounded messages honestly within W. The formalism develops a window semantics using presheaves over measurement contexts and DPI-guarded IPMs, with all optimizations carried out on finite partitions induced by the admissible test class. A standing contract fixes three metrics — the licensing metric DW, a hybrid compute/report norm dₕyb, and a product total-variation norm dPi used for LP projections — together with explicit transfer bounds between them. An output-level budget inequality aggregates decoherence residuals, detector mismatch, intervention sensitivity, ND-projection error, and sampling error into a single auditable certification bound. Two case studies anchor the framework in physics. In general relativity, a finite-sample latency diagnostic tests whether a noisy beacon network earns a conformal structure: the classic theorem that causal order determines the conformal class serves as a consistency target, with Hoeffding-based concentration controlling mis-order probability. In quantum theory, pointer outcomes are certified as ε-facts — budgeted claims that a measurement result is operationally definite at resolution ε — using explicit Lipschitz witnesses for robust contextuality (worked out for CHSH) and visibility-based decoherence surrogates with declared scope conditions. Together, these components replace informal appeals to explanatory virtue with quantitative compression-under-control, and make the scope and limits of every ontological claim auditable within its declared window.