Prime Distribution and Random Matrix Theory via Zeta Functions: Manifestation in The Matrix Framework

This paper systematically explores the profound connections between prime distribution representation of the Riemann zeta function (through Euler product formula) and Random Matrix Theory (RMT) as manifested in The Matrix framework (infinite-dimensional Zeckendorf-k-bonacci tensors, ZkT). Based on the proven categorical equivalence between ZkT and zeta computational theory, we establish a triple correspondence: (1) Euler product manifests in ZkT as elementary decomposition of generating functions and irreducible configuration patterns; (2) Statistical similarity between zeta zeros and Gaussian Unitary Ensemble (GUE) revealed by Montgomery-Dyson conjecture corresponds to random activation distributions under spectral constraints in ZkT; (3) This unified framework leads to three important conclusions: new computational approach to proving the Riemann Hypothesis, optimization bounds for quantum algorithm complexity, and cosmological interpretation of information conservation. Through rigorous mathematical derivation and physical correspondence analysis, this paper reveals the deep unification of number theory, combinatorics, random matrix theory, and quantum chaos within the computational ontology framework.