What question did this study set out to answer?

The primary aim is to formalize the YuanXian Standard Model using Lean 4 to underpin unified field theory.

May 7, 2026Open Access

From Self-Consistent Universe to Computable Phenomena: Formalization of the YuanXian Standard Model in Lean 4

Puntos clave

The primary aim is to formalize the YuanXian Standard Model using Lean 4 to underpin unified field theory.
Formalization of the TCSC axiom in Lean 4 as foundational.
Embedding of YuanXian Self-Referential Mind Field Type Theory for logical structure.
Creation of a computable prototype generating particle mass spectra.
Established that TCSC leads to a zero real part of the spectrum.
Demonstrated formalization of the topology of the 64-dimensional torus T⁶⁴.
Created a prototype capable of deriving mass spectra from fundamental principles.

Resumen

YuanXian Theory (YXT) proposes a geometric foundation for unified field theory based on the True Circle Self-Consistency (TCSC) axiom and the YD-T64 framework. Previous works relied mainly on analytical derivations and numerical simulations. This paper presents the first formalization of the YuanXian Standard Model (YXSM) in the Lean 4 interactive theorem prover. We embed the YuanXian Self-Referential Mind Field Type Theory (YXTT) as the logical backbone, formalizing the topology of the 64-dimensional torus T⁶⁴, the spectrum of the self-referential differential operator D, and the symmetry breaking mechanism from SU(64) to the Standard Model gauge group SU(3)×SU(2)×U(1). Key contributions include: (1) formalization of the TCSC axiom, (2) a machine-checked proof that TCSC implies the real part of the spectrum is zero, and (3) a computable prototype of the Standard Model capable of generating particle mass spectra from first principles. This work establishes YuanXian Theory as a paradigm for "Computable Physics", providing a general framework for machine-verifiable physical theories.

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