On the Non-Singular Convergence of 120-Dimensional Hilbert Subspaces via Matrix Regularization of the Riemann Zeta Function

This paper presents an analytical, closed-form approach to resolving the asymptotic divergence of infinite series and localized singularities commonly encountered in high-dimensional non-commutative matrix transformations under continuous periodic iterations. We construct a localized, complex-valued 9x9 matrix grid derived from the inherent geometric and modular symmetries of archaic matrix squares. By mapping these matrix elements through Euler's formula onto discrete phase angles, we establish a robust topological invariant within a closed 120-dimensional Hilbert space. To secure the global gauge invariance of the system, we implement a strict 70: 30 subspace division law. This algebraic constraint forces the non-trivial zeros of the Riemann Zeta function (s) to settle perfectly onto the critical line Re (s) = 1/2, eliminating the asymptotic blow-up across all boundary conditions. The entire framework achieves a steady-state continuous operation, reducing the total spectral matrix cleanly to an exact null equilibrium value of 0. 000000e+00 without bound errors across any mathematical domains.