Substrate Ontology: A Unified Framework from Discrete Substrate to Physical Reality Philosophical Foundations, Physical Interpretation, and Humanistic Significance

This paper presents Substrate Ontology, a unified philosophical and physical framework built upon two irrefutable observations—matter can move and things can be distinguished—and three axioms: finite information, minimal scale, and intrinsic symmetry breaking. From these axioms, we derive that entropy increase is the inevitable accumulation of closure deficits in discrete geometry; singularities are pseudo-problems arising from the misuse of continuous models; the effective number of digits of π grows stepwise with the age of the universe as ; and all transcendental numbers share this truncation source, collectively contributing to entropy increase. We further argue that irrational numbers do not exist in the physical world, and that the real number line is replaced by discrete lattice points. The framework provides a unified ontological foundation for general relativity, quantum field theory, thermodynamics, and cosmology, while offering testable predictions including gravitational wave echoes, stepwise drift of fundamental constants, and discretization of high-frequency gravitational waves. Finally, we explore the humanistic significance of stochastic deficits as the ontological foundation of freedom, life, and creativity. Keywords: Discrete substrate; finite information; dynamic precision horizon; transcendental number truncation; entropy increase; irreality of irrational numbers; arrow of time; epistemological boundary; testable predictions; unification of fundamental forces