Topological Natural Selection: A Paradigm Shift from Mathematical Necessity to Geometric Fitness in G₂ Manifolds Subtitle: Reinterpreting the Fine-Structure Constant and the 7/78 Dimension Ratio as Optimal Survivors

Abstract

We propose a fundamental paradigm shift in mathematical physics: Topological Natural Selection (TNS). Departing from the traditional doctrine of strict mathematical necessity, TNS posits that fundamental physical parameters—such as the fine-structure constant α and the 7/78 dimensional ratio in the E₆ → G₂ cascade—are not uniquely enforced mathematical singularities, but rather the optimal survivors selected by topological stability and phase coherence. By introducing a topological fitness function _topo defined over the embedding space, we demonstrate how the TUT coherence window (|ΔΦ| < √α ≈ 0.085424) acts as a geometric selective pressure. TNS unifies particle physics, cosmic strata, and biological phase-locking under a single evolutionary framework, offering testable predictions for vacuum stability and biological functional collapse.