Restoration of Spectral Hermiticity and Noise Integration via Coupled MERA-Fluctuation Flow Equations: Towards a Resolution of the Riemann

Building upon the universal flow equations and infrared attractor dynamics established in the PROMETEO-PRIME framework, this paper addresses the role of high-frequency residual noise—traditionally filtered out by finite bond dimension truncation (χ = 16) in Multiscale Entanglement Renormalization Ansatz (MERA) networks. By constructing a coupled differential system that reintegrates the orthogonal fluctuation sector with the macroscopic Gaussian Unitary Ensemble (GUE) bulk, we formulate an expanded block-matrix effective Hamiltonian. We regularize the extended Hilbert space via a non-separable Hermitian cross-coupling term, forcing the Schmidt spectrum to decay as an anomalous power law governed by a non-ergodic extended (NEE) fractal dimension D₂ ≈ 0.8132, shielding the system from chaotic thermalization while preserving strict self-adjointness (Hₜₒₜₐₗ = Hₜₒₜₐₗ^). Empirical validation shows that the adjacent gap ratio stabilizes at the universal fixed point r ≈ 0.4678, verifying a topologically protected quantum phase that underpins the Hilbert-Pólya program and advances the spectral resolution of the Riemann Hypothesis.