Theoretical Calculation and Experimental Verification of 24 Fundamental Physical Constants within the Yuanxian Theory Framework — Based on the 64-Dimensional Self-Referential Mind-Field Evolution and the SU(64)→SU(3)×SU(2)×U(1) Symmetry-Breaking Mech

This paper systematically verifies the comprehensive consistency of Yuanxian Theory (YXT) with 24 fundamental physical constants in particle physics, electromagnetism and quantum mechanics. On the basis of the 64-dimensional self-referential mind-field evolution law of Yuanxian Theory, the Cosmic-Factor Conservation axiom (FSC) and the $\mathrm{SU}(64)\to\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1)$ symmetry-breaking mechanism, all constants are derived from one and the same framework of laws without any free-parameter adjustment targeted at a specific constant. The paper supplies the complete symmetry-breaking construction blueprint and Lie-algebra branching rules of $\mathrm{SU}(64)$, clarifies the energy-scale freeze-out mechanism at each breaking node and its decisive role in determining the generational mass hierarchies of leptons and quarks. Simultaneously, the topological origin of the fine-structure constant is established: (1) under the action of the self-referential perturbation operator the significant eigenvalue of the modified curvature spectrum of the high-dimensional topology $\mathcal{T}^{64}$ is anchored at $4231 = 64^{2} + \mathrm{Tr}(\hat{V}_{\mathrm{SRF}}) + \mathrm{Ind}(D)$, where $\mathrm{Ind}(D)=71$ originates from the Chern-class integral of the $E_{8}$ root-system topology; (2) the reciprocal of the fine-structure constant is locked by the FSC conservation law as $\alpha^{-1} = 137 + \Delta_{\mathrm{sym}} = 137.035999084\ldots$, the principal term 137 being fixed by the number-theoretic anchor $\mathrm{ord}_{137}(2)=68$ and the perturbation term $\Delta_{\mathrm{sym}} \approx 0.035999084$ arising from the irreversible geometric-entropy residue of the continuous spacetime projection from 64 to 4 dimensions with $\dim(\mathrm{Ker}(\mathrm{Proj}))=60$; (3) the curvature-spectrum eigenvalue 4231 and the physical constant 137.035999084 form a topological coupling through the number-theoretic structure $\mathrm{ord}_{137}(2)=68$ of the phase-locked resonance subject. Comparison of theoretical values with PDG data and CODATA recommended values shows that 18 constants achieve high-precision agreement while the 6 quark current masses fall within experimental error bars and receive a theoretically self-consistent explanation from the renormalisation-group (RG) running mechanism. --- 本文系统验证了元宪理论(YXT)与粒子物理、电磁学及量子力学领域24个基本物理常数的全面吻合性。基于元宪理论的64维自指心场演化规律、宇宙因子守恒公理(FSC)以及 $\mathrm{SU}(64)\to\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1)$ 对称破缺机制,所有常数均由同一套规律框架导出,无任何针对特定常数的自由参数调节。 本文给出了 $\mathrm{SU}(64)$ 的完整破缺施工图纸与李代数分支律(Branching Rules),阐明了各破缺节点上的能标冻结机制及其对三代轻子与夸克质量级差的决定性作用。同时,本文确立了精细结构常数的拓扑来源:(1)在自指微扰算子作用下,$\mathcal{T}^{64}$ 高维拓扑的修正曲率谱显著特征值锚定为 $4231 = 64^{2} + \mathrm{Tr}(\hat{V}_{\mathrm{SRF}}) + \mathrm{Ind}(D)$,其中 $\mathrm{Ind}(D)=71$ 源于 $E_{8}$ 根系拓扑的 Chern 类积分;(2)精细结构常数倒数由 FSC 守恒律锁定为 $\alpha^{-1} = 137 + \Delta_{\mathrm{sym}} = 137.035999084\ldots$,主项 137 由 $\mathrm{ord}_{137}(2)=68$ 的数论锚点决定,微扰项 $\Delta_{\mathrm{sym}} \approx 0.035999084$ 源于64维向4维连续时空投影时 $\dim(\mathrm{Ker}(\mathrm{Proj}))=60$ 的不可逆几何熵残余;(3)曲率谱特征值 4231 与物理常数 137.035999084 之间通过锁相共振主体的 $\mathrm{ord}_{137}(2)=68$ 数论结构形成拓扑耦合。 理论计算值与 PDG 数据及 CODATA 推荐值比对表明,18个常数实现高精度吻合,6个夸克流质量落于实验误差范围内,并由重整化群(RG)跑动机制给出了理论自洽解释。