Geometric Renormalization and Phase Space Quantization of the Riemann Zeta Function

We present a non-perturbative derivation of the Hamiltonian operator associated with the non-trivial zeros of the Riemann Zeta function. We postulate that the system dynamics do not occur in the classical coordinate $t$, but on a curved manifold parameterized by the invariant proper time $\tau = \sqrt{t^2 + 1/4}$. This transformation reveals a non-trivial vacuum structure with an event horizon at $\tau_0 \approx 6.289$ and a \textbf{Magna Metric of Density} $\mathcal{M}(\tau) \equiv \dot{\theta}$ derived analytically. We demonstrate that the system obeys a strict phase quantization governed by the universal resolution limit $\Delta\tau \ge \pi/(24\mathcal{M})$, identifying $\zeta(2)$ as the fundamental quantum of action. High-precision numerical verifications confirm the validity of the theory, reproducing the spectrum from the ground state up to the $n=10^{13}$ level with an absolute error lower than $10^{-153}$, establishing the Riemann Hypothesis as a necessary consequence of information conservation in a unitary geometry.