Homology-Weighted Stochastic Dynamics on Simplicial Complexes: A Topology-Driven Ensemble with Ablation Controls

Computational study demonstrating that Betti-number feedback in Metropolis dynamics on simplicial complexes produces qualitatively different behavior from non-topological feedback. Ablation against triangle-count energy confirms the mechanism is genuinely topological: topological energy sustains loops and scales with ambient topology, while triangle-count energy destroys loops and shows no topology dependence. Normalized persistence (controlling for acceptance-rate artifacts) reaches 4–6x at high coupling on 13-column hexagonal lattices with cylindrical and toroidal boundary conditions. Includes complete Rust and Python implementations, raw JSON data for all experiments, and a static null test killing the Euler characteristic invariance claim. All code compiles and all results are independently reproducible. ryan.j.cardwell1@gmail.com <---In need of a peer review. Badly. Help!