Selection as Universal Geometry: Darwin, Turing, and the Quantum Bridge

We show that the replicator equation — the mathematical statement of natural selection — is the unique continuous-time limit of a general discrete update kernel, the Darwin kernel, defined on the probability simplex. This kernel is formally identical, up to choice of fitness function, to the Feller kernel of Track U in the Configured Observation Planes framework of Spencer (2026a). The identification implies that selection, in every domain where it operates, is a geometric phenomenon: the flow of a vector field on a probability simplex, governed by the same topological constraints whether the variants are organisms, strategies, memes, or quantum states. We establish, in sequence: the derivation of the Price…