Definitive Verification of YuanXian Theory: Independence, Minimal Completeness of the Four Laws, and the Establishment of Cosmic Living Organism Ontology

The core thesis of YuanXian Theory (YXT) --- that the universe is an autopoietic, self-referential, and self-consistent living organism --- fundamentally relies on the foundational status of its four core laws. This paper accomplishes three definitive tasks: 1. Independence: The four laws are pairwise independent, containing zero logical redundancy, and cannot be derived from one another; 2. Minimal Completeness: The four laws constitute a minimal complete set; removing any single law leads to systemic incapacitation; 3. Ontological Status: YuanXian Theory is established as the unique, self-consistent, self-referential, and autopoietic axiomatic framework for describing the universe. The formal verification is executed via a Lean 4 and Rocq dual-engine architecture. Lean 4 serves as the industrial-grade verification foundation, while Rocq provides the foundational Calculus of Inductive Constructions kernel responsible for proving the non-contradiction of the axiomatic laws. The rigorous verification of law independence employs the model-theoretic counter-model method, constructing four dedicated mathematical models (M1, M2, M3, M4) to explicitly isolate each law. Any YuanXian corollary verified by this dual-engine framework is declared a definitive conclusion --- no longer a "debatable academic opinion," but a machine-verifiable objective truth. All formal code has been permanently archived in the official repository. 元宪理论(YXT)的核心命题——宇宙是一个自指、自洽、自生的生命体——其合法性完全依赖于四大核心规律的基础地位。本文完成三项判决性工作: 1. 独立性:四大规律两两独立,无逻辑冗余,不可互推; 2. 最小完备性:四大规律构成最小完备集,缺一则系统失能; 3.