AI 中文总结
该研究在例外约旦纲领框架下构建CKM扇区的有限狄拉克算符，给出CKM矩阵元的条件估计，构造阿尔伯特提升等结构，提出汤川块相关的九链接图候选，为解决标准模型的夸克质量与CKM矩阵问题提供纹理骨架方案。
AI 中文摘要
标准模型无法确定夸克质量或CKM矩阵。在例外约旦纲领中，平方根质量占据短的Sym³(3)链。将对称立方提升压缩到已占据节点上，得到一个根质量算符，其平方产生所提出的质量比，将该谱和相对左框架打包在一个有限狄拉克算符中，无需推导框架。在传输、虚节点振幅、实(2,3)和平衡正交积分选择的条件下，无拟合层在M_Z处给出|V_us|=0.2371（高5.3%）和|V_cb|=0.0422（高0.8%）。关系|V_ub|/|V_cb|=√(m_u/m_c)低了2倍；拟合一个复长边。两个平衡取向给出分支(ε,ω)=(0.002079,288.2°)和(0.005358,202.2°)，因此前者ε比率不稳健，原始ω依赖约定。对于采用的F₁-F₂家族嵌入，我们在𝔣₄(ℂ)中构造一个精确的皮尔斯变换阿尔伯特提升，再现共轭上/反下传输和φ₁₂=-2χ。对于采用的循环马约拉纳放置和实线性投影，其完备化具有实(e₄,e₃,e₆)支撑，而e₁正交积分消失；J_ℓ=0和δ^ℓ_CP=0或π是该类中的相容性结果。最小径向四次循环截断具有等大小满秩极值或平坦方向；混合阿尔伯特三次仅在所选三边缘子空间中给出稳定对齐。如果汤川块在投影桥中是线性的，六个对角质量链接加三个定向皮尔斯链接将形成一个连通单循环九链接图。这是Arkani-Hamed等人的纹理骨架候选，而非推导：家族真空选择、手征投影和右框架锁定仍未解决。
英文摘要
The Standard Model does not determine quark masses or the CKM matrix. In the exceptional-Jordan programme, square-root masses occupy short $\operatorname{Sym}^{3}(\mathbf{3})$ chains. Compressing the symmetric-cube lift onto occupied nodes gives a root-mass operator whose square yields the proposed mass ratios, packaging that spectrum and relative left frames in one finite Dirac operator without deriving the frames. Conditional on the transport, virtual-node-amplitude, real-$(2,3)$ and balanced-quadrature choices, the no-fit layer gives $|V_{us}|=0.2371$ ($5.3\%$ high) and $|V_{cb}|=0.0422$ ($0.8\%$ high) at $M_Z$. The relation $|V_{ub}|/|V_{cb}|=\sqrt{m_u/m_c}$ is a factor two low; one complex long edge is fitted. The two balanced orientations give branches $(\varepsilon,ω)=(0.002079,288.2^\circ)$ and $(0.005358,202.2^\circ)$, so the former $\varepsilon$ ratio is not robust and raw $ω$ is convention-dependent. For an adopted $F_1$--$F_2$ family embedding, we construct an exact Peirce-changing Albert lift in $\mathfrak f_4(\mathbb C)$, reproducing conjugate up/anti-down transport and $φ_{12}=-2χ$. For an adopted cyclic Majorana placement and real-linear projection, its completion has real $(e_4,e_3,e_6)$ support while the $e_1$ quadrature vanishes; $J_\ell=0$ and $δ^\ell_{CP}=0$ or $π$ are compatibility results in this class. The minimal radial-quartic cyclic truncation has equal-magnitude full-rank extrema or a flat direction; a mixed Albert cubic gives stable alignment only in a chosen three-edge subspace. Six diagonal mass links plus three directed Peirce links would form a connected one-cycle nine-link graph if the Yukawa block is linear in the projected bridge. This is a candidate Arkani-Hamed et al. texture skeleton, not a derivation: family-vacuum selection, chiral projection and right-frame locking remain open.
Comments33 pages, 2 tables; ancillary verification script included. Results v1-corrected relative to Zenodo record 10.5281/zenodo.21196380 (4 July 2026): sign error in the texture scan fixed, Layer-2 fit solved exactly on a coherent PDG 2024 target set; see footnote 1 for the change log
