The Theory of Regime Incompatibility and Thermodynamic Time Reversal: A Unified Framework for Emergent Physics

We present a comprehensive framework that resolves the conflict between Quantum Mechanics and General Relativity by proving their fundamental incompatibility. The Theory of Regime Incompatibility (TRI) establishes that no single continuous manifold can support both unitary evolution and diff-invariance. We introduce the Thermodynamic Time Reversal (TDTR) mechanism, which describes the irreversible transitions between these incompatible regimes as entropic operations. Finally, we uncover the Tamesis System: the underlying number-theoretic spectral geometry (Universality Class U1/2) that governs these transitions. Key Results: TRI (No-Go Theorems): Proof that a vacuum state cannot simultaneously optimize for Locality (GR) and Unitarity (QM). TDTR (Entropic Gravity): Validated against SPARC galaxy data (175 galaxies), reproducing flat rotation curves without Dark Matter by accounting for the elastic entropy of the vacuum memory. TAMESIS (Spectral Geometry): Derivation of the physical constants (Fine Structure) from the eigenvalues of the Prime Number Operator. This archive constitutes the final report of the Tamesis Research Program.