Black Hole Evolution in the Absolute Medium: Terminal Identity Transition, Axiomatic Closure, and Post-Saturation Dynamics

We present a self-contained formulation of black hole evolution within the Absolute Medium (AM) framework. In AM, spacetime is modeled as an elastic substrate where gravitational phenomena arise from strain and dissociative pressure gradients. Black holes are defined as saturated regions where the scalar dissociative pressure reaches ε = 1, producing a dynamical freeze-out. The apparent conflict between eternal stability and long-term dissipation is resolved by the Terminal Identity Transition Principle (TITP): a discrete mapping from the saturated system S to a new dissipative system S′ with ε′ < 1. We derive the pure AM trigger condition, critical mass threshold, and post-transition dynamics directly from AM stress equations. The resulting S′ phase is a damped elastic strain field radiating ultra-low-frequency modes. Predictions include a SMBH mass cutoff at 10^6–10^8M⊙, a nHz stochastic background with spectral index γ ≈ 3–5, and a scalar-elastic angular correlation distinct from the Hellings–Downs curve.