Computational Finitism in Evolutionary Biology: Three Axes of Discrete Dynamics

Classical evolutionary biology relies on continuous mathematics and infinite population assumptions that obscure the discrete, computational nature of biological systems. We present a finitism framework for evolutionary biology based on three fundamental axes: (1) Evolution as Algorithmic Compression via the Fano-Evolutionary Automaton, (2) Genetic Drift as Quantum Rounding Error from Modulo-9 arithmetic truncation, and (3) Speciation as Topological Confinement through the Fano Collapse. Using computational simulations, we demonstrate that these discrete mechanisms replicate classical results while revealing deeper structural principles. The Wright-Fisher variance emerges from finite alphabet constraints, speciation occurs as a discrete phase transition when populations reach GCD-based incompatibility, and fitness maximization is revealed as algorithmic compression efficiency. This framework eliminates the continuum fallacy in evolutionary biology, replacing ontological randomness with deterministic arithmetic friction in a finite causal graph. Falsifiable predictions are included in Section 6. Evolution is not a stochastic process in continuous space but an algorithmic process in discrete arithmetic. The universe is not random; it is computationally irreducible.