AI 中文总结
本研究提出夸克-轻子互补性的最小三代实现，通过三双最大混合的刚性形变构建轻子混合矩阵，无新增连续参数，预测值与实验符合度高，具备明确的可证伪性。
AI 中文摘要
我们提出了一种夸克-轻子互补性（QLC）的最小三代实现方案，其中非平凡关联矩阵是三双最大混合（TBM）的严格幺正刚性形变。在标准TBM约定下，该形变是绕归一化轴$n_{gg}=(2,1,2)^T/3$的转动，转动角由卡比博角确定，即$α_{gg}=-3θ_C/4$。由此得到的假设式$\text{U}_\text{PMNS}=\text{V}_\text{CKM}^\text{†}\text{U}_\text{TBM} R_{n_{gg}}(-3θ_C/4)$，在结构选择固定后，狄拉克轻子混合扇区没有新的连续参数。结合2025年粒子数据组的CKM拟合结果，该方案预测$θ_{12}=33.29^\text{°}$、$θ_{13}=8.46^\text{°}$、$θ_{23}=49.19^\text{°}$以及$\text{δ}_\text{CP}=180.79^\text{°}$，且CKM诱导的不确定性远小于当前的振荡实验误差。我们推导了领头阶的Wolfenstein求和规则；特别地，实形变保持了CKM诱导的压制效应$\text{J}_\text{CP}=-Aηλ^3/6+\text{O}(λ^4)$，因此相位接近CP守恒。回溯性简洁度扫描显示，在匹配2016年和2018年振荡数据的测试中，$(2,1,2),3/4$这一组合在5510个有向本原整数/有理数候选中排名第一。在包含49622个候选的2018年扩大扫描中，它的原始得分排名第二，但在多种独立简洁度度量下，在复杂度不超过自身的候选中仍保持第一；对固定$(2,1,2)$轴的转动强度进行轮廓分析得到$r_\text{BF}=0.74941$。我们通过约定协变的味空间生成元构造了该形变，并给出了精确的有效本征架实现$M_ν=A I+B S_{gg}+C S_{gg}^2$。该构造目前在正序情况下是允许的，大气中微子扇区对其约束最强；其大气角处于上八分圆以及狄拉克相位接近$π$的特性，为证伪该理论提供了明确的观测目标。
英文摘要
We propose a minimal three-family realization of quark--lepton complementarity (QLC) in which the non-trivial correlation matrix is an exactly unitary, rigid deformation of tri-bimaximal mixing. In a canonical TBM convention the deformation is a rotation about the normalized axis $n_{gg}=(2,1,2)^T/3$, with rotation angle fixed by the Cabibbo angle, $α_{gg}=-3θ_C/4$. The resulting ansatz, $\UPMNS=\VCKM^\dagger\UTBM R_{n_{gg}}(-3θ_C/4)$, contains no new continuous parameter in the Dirac lepton-mixing sector once the structural choice is fixed. With the 2025 Particle Data Group CKM fit it predicts $θ_{12}=33.29^\circ$, $θ_{13}=8.46^\circ$, $θ_{23}=49.19^\circ$, and $\dcp=180.79^\circ$, with CKM-induced uncertainties much smaller than present oscillation errors. We derive leading Wolfenstein sum rules; in particular, the real deformation preserves the CKM-induced suppression $\Jcp=-Aηλ^3/6+\mathcal O(λ^4)$ and hence a near-CP-conserving phase. A retrospective simplicity scan shows that the pair $(2,1,2),3/4$ ranks first among 5510 oriented primitive-integer/rational candidates when tested on epoch-matched 2016 and 2018 oscillation data. In an enlarged 49,622-candidate 2018 scan it is second in raw score but remains first among candidates no more complex than itself under several independent simplicity measures; profiling the rotation strength for the fixed $(2,1,2)$ axis gives $r_{\rm BF}=0.74941$. We formulate the deformation by a convention-covariant flavor-space generator and give an exact effective eigenframe realization $M_ν=A I+B\Sgg+C\Sgg^2$. The construction is presently allowed in normal ordering, with the atmospheric sector providing its strongest pressure; its upper-octant atmospheric angle and near-$π$ Dirac phase provide sharp falsifiability targets.
