π: The Braid Closure Invariant

We formalize braid class as a geometric invariant governing coherent survival in Unified Vibrational Field Theory (UVFT). Coherence persists when modal strain remains within the admissible closure class of a braid embedding. Collapse occurs not through force imbalance, but through loss of spectral admissibility. We show that braid closure, strain–coherence balance, and spectral positivity of an associated stability operator are mathematically equivalent conditions. This establishes π as a geometric closure threshold whose preservation defines topological survival.