Chapter 16: TOV Phase Boundary and Forced Topology Relaxation

Chapter 17 constructed the TOV star builder: a family of equilibrium configurations parameterized by central density, each a self-consistent solution of the τ-Einstein equation within a ball topology. But every ball-topology solution has a finite domain of validity. As mass accumulates—through accretion or core collapse—the gravitational character G_ω(x) grows without bound while the matter character T^mat_ω(x) saturates. The mismatch produces a GR tension that the ball topology cannot absorb. This chapter proves that when the tension exceeds a structural threshold, the configuration must undergo a topology change from the ball (geometric, deformable) to the torus (topological, stabilized). This is the forced topology relaxation theorem: the phase boundary between neutron star and black hole is not a dynamical process happening in time, but a structural property of the τ³ fibration—a boundary in the space of admissible configurations that no refinement-coherent trajectory can avoid.