Emergent Randomness and the Anatomy of Deterministic Decay in Computational Finitism

Abstract

Standard Quantum Mechanics posits that randomness is ontological, a fundamental feature of reality where outcomes (such as radioactive decay or wave function collapse) are governed by irreducible probabilities (the Born rule). In this paper, we challenge this paradigm through the lens of Computational Finitism. We demonstrate that "quantum randomness" is an emergent property of Computational Irreducibility within a strictly deterministic, finite-alphabet substrate. Using a 1D Modulo-9 Cellular Automaton with non-linear update rules, we generate sequences that pass rigorous statistical tests for randomness (Shannon Entropy > 99.4%, flat autocorrelation) without a single random number generator. Furthermore, we apply this framework to particle physics, modeling gamma emission not as a probabilistic event, but as a deterministic "sawtooth" clock ticking until it hits the Topological Resonance Boundary (TRB = 9), triggering a state reset and photon emission. We conclude that the universe does not roll dice; it computes them.