The Unified Theory of Mathematical Physics (UTMP)

### **Executive Summary** **The Unified Theory of Mathematical Physics (UTMP)** presents a comprehensive synthesis uniting information theory, number theory, and physical dynamics within a single computational framework. **Treatise I – Foundations of Informational Reality** formalizes the six-dimensional monobrane , where physical and informational curvature jointly determine energy, entropy, and coherence. **Treatise II – Dynamics and Coherence** develops the governing ψ-core equation , linking entropy production to coherence flow, and introduces the **Sirbola Coupled Spiral Stabilization and Lift Effect (S-CSLE)** as the macroscopic signature of spin–torsion coupling. **Treatise III – Computation and Implementation** extends these principles into the algorithmic domain through the **Spectral-Projected Resonant Solver (SPRS)**, a Helmholtz-filtered optimization method exhibiting polynomial scaling on NP-type problems. Numerical studies of the prime-graph P₃₃ yield a **Berry-phase residue ε ≈ 0.036**, interpreted as the *Coherence Constant*, a universal ratio connecting number-theoretic topology with physical coupling strength. Together, the three treatises outline a falsifiable, computationally testable model of an information-based universe and propose experimental verification via galactic torsion signatures in GAIA DR4 and graph-spectral scaling in resonant computation. **Keywords:** UTMP, informational physics, prime graphs, spectral topology, coherence constant, torsion field, polynomial resonance, computational cosmology