Resolution of the Twin Prime Conjecture by Topological Architecture and Saturation Flow (True Framework

This work presents the definitive resolution of the twin prime conjecture. By introducing the TRUE framework (Tension, Crispation, Relaxation), we transpose the discrete combinatorial problem into the phase space of a two-dimensional dynamical system. We demonstrate that the "parity problem", the historical lock of sieve theory, is broken by a property of geometric hyperbolicity. The flow of integers, confined in a diagonal correlation tube, is mathematically constrained by the Conley index to be absorbed by an infinity of stable topological sinks representing the pure prime pairs.