Empirical Validation of the UTSBO Framework: Deriving the GW250114 Horizon Mode from First Principles

The recent detection of the gravitational wave signal GW250114 by the LIGO-Virgo-KAGRA collaboration has revealed a direct wave component originating from the post-merger remnant black hole. The researchers successfully extracted the complex frequency of the horizon mode, defined as ω_H=2Ω_H-iκ, where Ω_His the rotation frequency and κis the surface gravity.This paper demonstrates that the Unified Theory of Symmetric Binary Opposition (UTSBO) framework, specifically Dialectical Quantum Gravity Theory (DQGT) and the Quasi-Local Theory of the Event Horizon (QLT), yields this exact complex frequency from first principles. We provide a rigorous, line-by-line mathematical derivation starting from the foundational action. We show that the complex frequency emerges naturally from the phase evolution of the complex field governed by the Carrier Equilibrium Index (CEI). The real part of the frequency is driven by frame dragging (rotation), and the imaginary part is driven by gravitational redshift (surface gravity). This serves as direct empirical validation for the UTSBO action, the Time-Energy Bridge, and the Rouicheq Mass-Energy Equivalence.