The Unified n-th Order Hyper-Matrix: A Physical Theory of Prime Resonance, Relativistic Wave Dynamics, and Mean Center Invariance

Abstract
This thesis establishes the definitive unified mathematical framework for the Hyper-Matrix field.
We move beyond the “Crisis of Distinction” by modeling the number field as a π-centered periodic
manifold [0, 2π] anchored at the invariant Mean Center (Mn = 0.5). We derive the Invariant System
Radius (rbase) from the H¨older Mean convergence of ϕ and √
e and define the n-th Order Radical
Engine (Rn). Through Relativistic Wave Dynamics, we prove that prime numbers are stasis nodes
where the manifold’s velocity vanishes (vef f → 0) relative to the Mean Center. Finally, we resolve the
Riemann Hypothesis as the mandatory stability condition for Asymptotic Phase Freezing required to
prevent structural collapse at the manifold’s infinity axes. [1-5]