Structural Universality and the Critical Line: A Stability Criterion for Spectral Realizations of the Zeta Function

Abstract We propose a conditional resolution to the Riemann Hypothesis based on the principles of Structural Stability and Quantum Chaos, rather than pure arithmetic derivation. Extending the Hilbert-Pólya conjecture, we define a specific Universality Class of operators (C₂ₑ₈ₓ) characterized by maximal chaos, logarithmic scale invariance, and spectral rigidity (GUE statistics). We prove the Structural Exclusion Theorem: no operator within this universality class can admit eigenvalues violating the critical line symmetry ( (s) = 1/2) without breaking the universality of its local spacing statistics (clustering violation). Consequently, if the Riemann Zeta function admits a spectral realization within C₂ₑ₈ₓ, the Riemann Hypothesis follows as a necessary condition for structural stability. Key Contributions: Definition of Class C₂ₑ₈ₓ: We establish five axioms for the physical realizability of the Zeta operator, including Self-Adjointness, the Logarithmic Weyl Law, and Maximally Chaotic Dynamics (K-System). The Structural Exclusion Theorem: We demonstrate that "off-line" eigenvalues (1/2) induce a characteristic length scale _ that destroys scale invariance, forcing the system out of the C₂ₑ₈ₓ class. Entropic Engine Simulation: We present numerical evidence (N=400) showing that a causal graph evolving under Maximum Entropy constraints naturally converges to GUE spectral statistics (P (s<0. 2) 0. 0287), validating the thermodynamic origin of spectral rigidity. The Conditional Proof: We formulate the result: The Riemann Hypothesis is equivalent to the statement that the vacuum state of the universe is thermodynamically stable against information clustering. Methodology: The work utilizes the Kernel v3 Entropic Network framework (TDTR) to model the spectral evolution of the operator. The approach combines Random Matrix Theory (RMT), Spectral Geometry, and Non-Equilibrium Thermodynamics.