From Philosophical Program to Formal Science: The Complete Axiomatization, Dual Realization and Machine Verification of YuanXian Theory (YXT)

This paper presents the complete transition of YuanXian Theory (YXT) from a philosophical-physical program aimed at unifying physics, mathematics, consciousness and life, into a fully formalized, computable, and machine-verifiable scientific theory. Grounded in four core axioms — True-Circle Self-Consistency (TCSC), Spacetime Manifold Uniqueness (STM), Factor Conservation (FSC), and Self-Referential Mind-field Generation (SRM) — the theory is rigorously realized in two foundational systems: Self-Referential Mind-Field Type Theory (YXTT) based on Homotopy Type Theory, and an ontological extension of ZFC set theory.We prove the equivalence of both realizations and derive numerous testable consequences, including the theoretical computation of 24 fundamental physical constants with high precision, a conditional proof of the Riemann Hypothesis, the rigorous theorem that the total energy of the universe is zero, and the prediction of the True-Circle Self-Referon (TCSR) particle. All formalizations and proofs have been machine-verified in Lean 4 and Coq and are fully open-sourced.