Rei: A Four-Axiom Foundation for Computational Existence Theory

Preprint. We present Rei, a computational system founded on exactly four axioms: Center-Periphery (A1), Extension-Reduction (A2), Sigma Accumulation (A3), and Genesis Phase Transition (A4). We prove mutual independence by constructing counter-models, derive fifteen core theorems, and validate the system with 1,689 passing tests. Open-source implementation: https://github.com/fc0web/rei-lang