A Statistical Information–Geometric Framework Linking Number Theory, Quantum Information, and Spacetime Curvature

This project documents the conceptual development and formal mathematical formulation of a speculative information–geometric framework linking statistical number theory, quantum information, and spacetime geometry. The work explores whether statistical invariants derived from arithmetic structures—specifically those inspired by the Goldbach problem and the spectral properties of the Riemann zeta function—can be lifted into bounded, well-defined functionals suitable for covariant coupling in general relativity. Discrete number-theoretic quantities are treated via statistical limits and spectral damping, ensuring mathematical admissibility and dimensional consistency. The project is organized into two components: Conceptual Draft (GRTS.pdf) An early exploratory manuscript outlining the original ideas, motivations, and heuristic connections between arithmetic parity, information, and spacetime structure. Formal Preprint (LaTeX-based PDF and source files) A fully formalized mathematical framework adhering to international standards in mathematical physics. This version introduces precise definitions, propositions, lemmas, and conditional theorems, provides internal proofs, derives covariant field equations, incorporates existing experimental constraints from gravitational-wave observations, black-hole imaging, and cosmology, and presents an analytic–numerical illustration in homogeneous cosmology. No claims are made regarding proofs of the Riemann Hypothesis or the Goldbach Conjecture. Instead, both are reformulated as stability and positivity conditions on explicitly defined functionals. All physical predictions are stated in a falsifiable manner and are constrained to remain consistent with current observational data. The formal preprint supersedes the conceptual draft in mathematical rigor while preserving the original intellectual trajectory of the framework.