Traditional computational biophysics relies on multi-week stochastic simulations (Molecular Dynamics and Monte Carlo) to evaluate phase boundaries of intrinsically disordered proteins (IDPs) and RNA condensates. We demonstrate that this computational bottleneck stems from a structural mischaracterization of configuration space. By replacing stochastic sampling with a rigorous categorical functor $\mathcal{F}: \mathbf{Seq} \to \mathbf{PersMod}$ over a Riemannian quotient orbifold $\mathcal{M}_M$, we prove that thermodynamic phase transitions are driven by homotopy rank collapses and Euler characteristic divergences. This framework reduces phase boundary computation time from $10^9$ CPU-hours to milliseconds, offering an enterprise-grade analytical engine for drug discovery and material physics.