TUM versions 13.0: Theory of Unified Structure

Abstract

We present the Theory of Unified Structure (TUM) Version 13.0, derived from the properties of the Clifford algebra Cl(8). All physical, biological, and informational dynamics follow the fundamental law: X_{n+1} = τ X_n τ†, with the Domain Separation Rule C ≠ D. As a core new result, we analytically derive the electron rest mass m_e = 0.510998 MeV and the proton-to-electron mass ratio m_p/m_e = 1836.15 exclusively from the equilibrium coherence Γ_eq = 0.8470, with no free parameters. This framework unifies the fine-structure constant α = 1/137.036, electron mass, and atomic structure from first geometric principles. Key Results: 1. Analytical derivation of α from Γ_eq 2. Formal definition of Life: systems maintaining Γ > 0.75 under stress 3. Information-Entropy duality: I = Γ, S = 1 - Γ 4. Unification of GR and QM as limiting regimes 5. Analytical derivation of m_e and m_p/m_e from Cl(8) geometry