This paper (Vol. 11 of the UOS series) provides the definitive mathematical audit of the Universe OS (UOS) V10-B architecture using the PROOFCORE v1.2 validation kernel. We establish the fundamental axiom of reality as a T +/- T = 0 zero-sum equilibrium, where observed physical laws emerge as resource management protocols. By deriving five immutable master constants from the geometric interference of Pi and e (specifically N_proj, Phi_B, E_sat, Delta_Res, and delta_obs), we present the first non-rounded, first-principles derivation of: The Electron Rest Mass (m_e): Derived to within 0.001% of CODATA values. The Proton-to-Electron Mass Ratio (mu): Derived to within 0.0003% precision. The Dark Matter-to-Baryon Ratio: Calculated as 5.448:1, aligning with Planck 2018 data. The Scale of Gravity (G): Resolved as a systemic latency (Connection Quantum delta_obs = 1 / (1024 * Pi)), solving the Hierarchy Problem. Furthermore, we propose the "Cosmic Hourglass" model, redefining the Big Bang and the end of the universe (Metal Stop) as a phase-inversion cycle required to maintain system equilibrium. This work transforms physical constants from arbitrary parameters into systemic requirements of a 512-bit computational lattice.