Information Protection as a Fundamental Principle X: Observable Signatures of Modified Dynamics --- Complete Relativistic Equations, Radiation Corrections, Inertial Noise, and Finite-Temperature Effects

We derive the observable consequences of the information-response dynamics. The complete relativistic equation of motion, with the effective inertial mass mₑff (a, v) = m0 gamma (v) mu (a/a0), unifies Newtonian, relativistic, and deep-MOND dynamics. The modified Larmor formula is solved exactly in a closed form valid across the full acceleration range, predicting an enhancement of radiation in the deep-MOND regime. The inertial acceleration noise spectrum is derived from the fluctuation-dissipation theorem, yielding a white-noise floor and a low-frequency 1/f tail with a rigid 2/pi coefficient. This noise drives an analytic resolution of the cusp-core problem, with the core radius given by a dimensionally closed formula evaluating to approx 1. 3 kpc for typical dwarfs, using the topological glueball mass from Paper VIII. A precise, testable prediction for equivalence principle violation is given: the ratio of inertial to gravitational mass is exactly mu (a/a0), yielding an O (1) violation in a freely falling laboratory while remaining unobservable in Earth orbit, consistent with MICROSCOPE. Finite-temperature corrections explain why MOND effects are absent in the laboratory. All results are zero-parameter predictions of the framework.