Black Holes as Terminal Resonance Geometry in USP Field Theory Operational Model, Finite Compression, and Observational Diagnostics

This work presents a quantitative USP Field Theory description of black holes as terminal resonance geometries arising from elastic field compression and frequency saturation. A working radial frequency profile is introduced: f(r) = (f_max · κ) / (f_max r + κ) where κ is a geometry constant (Hz·m) and f_max is a finite saturation ceiling frequency. This formulation prevents singular divergence and produces a maximally compressed, finite-density core. Atomic structure becomes unstable when the local frequency mismatch exceeds a binding tolerance: Δf_bind = E_bind / h For hydrogen, Δf_bind ≈ 3.3 × 10^15 Hz. In a 10^6 solar-mass example, the radius at which Δf reaches this threshold is approximately r_bind ≈ 2.9 × 10^9 m, comparable to the Schwarzschild radius. A minimal nonlinear elastic toy model is provided with boundary conditions and parameter anchoring. Finite saturation emerges naturally from nonlinear stiffening. Opacity is modeled via resonance locking using a Lorentzian cross section: σ(f) = σ_0 Γ^2 / [ (f_γ,local − f(r))^2 + Γ^2 ] Order-of-magnitude estimates suggest that mm-band observations (e.g., EHT at 230 GHz) may constrain the effective linewidth Γ, absorber density n_abs, and saturation behavior. Additional diagnostics include: • Frequency-selective shadow attenuation • Polarization scaling with shear index n • Jet opening angle scaling θ_j ~ 1/n • Potential small-impact-parameter lensing deviations from pure 1/r behavior Agreement with General Relativity is expected at large radii. Deviations are restricted to deep-interior saturation scales or extremely small impact parameters. This document provides a parameterized, testable framework suitable for comparison with horizon-scale imaging, polarimetry, and VLBI jet data.