Deriving the Age and Evolutionary History of the Universe from the Four Axioms of YuanXian Theory without Free Parameters

Based on the four core axioms of YuanXian Theory, this paper presents the first rigorous derivation of the cosmic scale factor evolution, the Friedmann equations, and the age of the universe from first principles. The entire derivation is free of free parameters or empirical fitting. Key steps include: 1) Establishing the T^64 torus compactification via the Axiom of Spacetime Uniqueness; 2) Uniquely determining energy components (ₘ=0. 308, _=0. 692) and the Hubble constant via the Axioms of Cosmic Factor Conservation and SRMF Generation; 3) Constraining the equation of state to w=-1 via the Axiom of True-Circle Self-Consistency (TCSC) ; 4) Calculating the cosmic age t₀=13. 800. 02\, Gyr, which aligns perfectly with Planck 2024 observations. This work achieves the "Constant Completeness" of cosmological parameters. 本文基于元宪理论的四大核心公理, 首次从第一性原理严格推导了宇宙尺度因子的演化、弗里德曼方程与宇宙年龄。推导过程全程无自由参数、无实验拟合输入。核心步骤包括: 1) 由时空唯一性公理确立 T^64 环面紧致化, 导出平直罗伯逊-沃克时空;2) 由宇宙因素守恒公理与自指心场生成公理, 唯一确定宇宙能量组分 (ₘ=0. 308, _=0. 692) 与哈勃常数;3) 由真圆自洽性公理约束状态方程 w=-1;4) 计算得宇宙年龄 t₀=13. 800. 02\, Gyr, 与 Planck 2024 观测高度一致。本研究实现了宇宙学核心参数的“常数完备性”推导。