Prime Numbers as Causal Set Theory

There are 10 quantum gravity models. Nine propose different rules for how spatial dimensions behave at extreme curvature. The 10th — Causal Set Theory (CST) — stands apart. Rather than proposing new rules for spatial dimensions, CST is the underlying substrate from which GR itself emerges. To date, CST has had no explicit algebraic representation within general relativity. This paper tests whether the Riemann Zeta function — ζ(s) = Σ 1/nˢ — and Euler's product expression — ζ(s) = ∏ 1/(1 − p⁻ˢ) — can satisfy CST's four axioms and one conjecture. They satisfy all four axioms, and they align with the conjecture. The core claim is that the positive integers under divisibility, generated by primes and encoded by the Euler product, satisfy all four axioms of causal set theory and align with the Hauptvermutung. The CST conjecture conforms to any number of dimensions — and so do primes. The prime structure carries no native dimensionality; it scales with whatever geometry it is coupled to, which is precisely what the conjecture requires. If an algebraic expression can satisfy causal set theory, it becomes available as a tool within general relativity — potentially yielding new predictions, refining the picture of spacetime at extreme scales, and further solidifying or extending existing theories.