Computational Ontology and Zeta Function Foundations: Pure Mathematical Reasoning and Physical Correspondence

We construct a unified computational ontology framework based on the Riemann zeta function $\zeta(s)$. Through pure mathematical tools including analytic continuation, information geometry, and spectral theory, we reveal the dialectical unity of divergence and convergence, the mathematical essence of entanglement, and the mechanisms of information conservation. The core of this framework lies in: complex numbers $s$ serving as carriers for algorithmic encoding, generating convergent geometric representations through analytic continuation while maintaining global conservation. We first reason about the self-consistency of these structures from a purely mathematical perspective, then indicate their correspondence with physical phenomena. This theory not only explains the mathematical meaning of $\zeta(-1) = -1/12$ but also provides foundations for the unification of algorithms, quantum mechanics, and geometry.