A Hydrodynamic Saturation Model for Black Holes: Integrated Dark Medium (IDM) Framework — A Process‑Based Reinterpretation including Two Fragmentation Regimes, Transformational Coherence Length and Bubble Phase Separation

The Event Horizon Telescope (EHT) images of M87* and Sagittarius A* stand as landmark confirmations of compact gravitational object physics, widely interpreted within General Relativity (GR) as dark shadows cast by event horizons surrounding singularities. This work develops the Integrated Dark Medium (IDM) Framework: an alternative yet complementary physical interpretation based on process philosophy and medium physics, fully acknowledging the empirical success of GR while proposing different underlying mechanisms. We postulate that “spacetime curvature” is the geometric approximation of the macroscopic behavior of a continuous physical medium whose internal state is described by a scalar Transformational Index S —a measure of local organizational density. Where energy concentration grows, the medium progressively saturates: its refractive index n(S) rises, slowing effective light propagation ceff=c/n(S), until outward transport becomes negligible —forming a finite, three‑dimensional optical trapping region instead of an infinitely thin causal boundary or mathematical singularity. This complete formulation introduces two physical response regimes (Dry Brittle / Cooked Ductile), the Transformational Coherence Length C_L as critical order parameter, and a discrete bubble‑release mechanism via phase separation. This unifies tidal fragmentation, accretion‑disk states (SANE/MAD, Thin/ADAF), and AGN bubbles under a single principle. We yield distinct, falsifiable predictions: notably, chromatic dispersion Δ R/R is not constant —systems in the disordered Cooked/MAD regime show systematically larger frequency dependence (2.2%–3.5%) than ordered Dry/SANE systems (1.0%–1.8%), while purely geometric lensing predicts no correlation whatsoever. If supported, black holes become finite saturated phases of matter‑energy; if falsified, the framework will be revised accordingly.