Black Holes as Substrate Sinks: Hawking Temperature and Acoustic Horizon from the U-Cell Model

UCM Paper 37 (Theoretical). In the UCM, the substrate flow vflow = c√ (Rₛ/r) reaches the speed of light exactly at the Schwarzschild radius (Theorem 1, from Paper 35). This makes every black hole an acoustic black hole for sub-threshold modes: no cell mode escapes for r < Rₛ (Theorem 2). The surface gravity κ = c⁴/ (4GM) follows from the flow gradient, and the Hawking temperature TH = ℏc³/ (8πGMkB) follows from the Unruh effect applied to the substrate (Theorem 3) — reproducing the known result (6. 2×10⁻⁸ K for a solar-mass BH) without postulates. Two physical layers at the horizon: cell modes trapped, membrane phase free (→ Paper 38). UCM preprint series on Zenodo, ORCID 0009-0005-5088-4339.