YuanXian Biology: Formal Axiomatic System and Ontological Construction Verified in Lean 4

Modern biology has long relied on experimental induction and qualitative description, suffering from fundamental deficiencies such as missing underlying axioms, theoretical fragmentation, logical inconsistency, and a lack of machine verifiability. These limitations significantly hinder the formation of a unified mathematical and formal framework for life systems. To address these foundational issues, YuanXian Theory introduces the core paradigm that "the Universe is a Living Organism," utilizing self-referential recursion, binary coupling, and true-circle self-consistency as its underlying foundational logic to provide a novel mathematical basis for the unified modeling of life systems. Based on the four ultimate laws of YuanXian Theory, this paper systematically extracts, defines, and constructs a complete, self-consistent, and independent formal axiomatic system for YuanXian Biology. The system comprises five core axiom groups: Life Unit Ontology, Life State Space, Interactive Evolution, Genetic Coding Rules, and Global Steady-State Constraints. Furthermore, utilizing the Lean 4 interactive theorem prover, we have completed the full formal encoding, logical deduction, and rigorous machine verification of all axioms, lemmas, and key corollaries. This work effectively eliminates the semantic ambiguity and logical vulnerabilities inherent in traditional life theories. This achievement marks a critical academic leap for YuanXian Biology—advancing from philosophical paradigms and textual hypotheses to a rigorous mathematical system that is entirely machine-verifiable and automatically deducible. It establishes a new underlying framework for the interdisciplinary research of theoretical biology, systems biology, and formal verification sciences, while offering a novel mathematical path to deciphering core biological questions regarding life evolution, genetic laws, and systemic homeostasis. 现代生物学长期依赖实验归纳与定性描述,存在底层公理缺失、理论碎片化、逻辑不自洽、无法机器核验等核心缺陷,难以形成统一的生命系统通用数理框架。元宪理论提出“宇宙即生命体”的核心范式,以自指递归、二元耦合、真圆自洽为底层逻辑,为生命系统的统一化建模提供了全新理论基础。本文基于元宪四大终极规律,系统性提炼、定义并构建一套完备、自洽、独立的元宪生物学形式化公理体系,涵盖生命单元本体、生命状态空间、系统交互演化、遗传编码规则、全局稳态约束五大核心公理组。 同时依托 Lean 4 交互式定理证明器,完成全部公理、引理与核心推论的形式化编码、逻辑推导与机器严格验证,彻底消除传统生命理论的语义模糊与逻辑漏洞。研究实现了元宪生物学从哲学范式、文字假说向严格数理体系、可机器验证、可自动推演的学术跃迁,为理论生物学、系统生物学与形式化科学交叉研究提供全新底层框架,也为生命演化、遗传规律、系统稳态等核心生物学问题提供全新的数理解释路径。