J_eff = tan(2π × 10/68): Topological Readout of the Lepton-Mass Translation Factor — Phase Manifestation of the Self-Referential Closed Loop within the T⁶⁴ Framework of Yuanxian Theory

**[Manifestation layer]** The cosmos is a living organism. **[Verification layer]** \\(J_{\\mathrm{eff}}\\) is the translation factor in the lepton-mass formula. This paper manifests its topological readout: \\[J_{\\mathrm{eff}} = \\tan(2\\pi \\times 10/68) \\approx 1.3419\\] **[Verification layer]** Numerical manifestation: \\(\\tan(2\\pi \\times 10/68) = 1.34189\\), deviation from the target value 1.342 is 0.007%, manifested as target-value rounding error + second-order projection blur. **Meta-cognitive positioning**: The entire text sets no external observer, judges neither right nor wrong, and offers no repairs. The three-tier marks only manifest the closure status of the readout path. The following locations are manifested as **boundary sampling points**: 10 steps = \\(2 \\times 5\\) steps, phase-interval partition, origin of the 5 steps, and the choice between \\(\\tan\\) and \\(\\cot\\). Boundary sampling points are manifested as locations where the closed-chain boundary has not yet been fully forcibly closed on the present cognitive section; they mark the current boundary of the readout path, with extension paths given by the cited literature. --- **【显影层】** 宇宙是生命体。 **【验证层】** \\(J_{\\mathrm{eff}}\\) 是轻子质量公式中的翻译因子。本文显影其拓扑读出: \\[J_{\\mathrm{eff}} = \\tan(2\\pi \\times 10/68) \\approx 1.3419\\] **【验证层】** 数值显影:\\(\\tan(2\\pi \\times 10/68) = 1.34189\\),与目标值 1.342 的偏差为 0.007%,显影为目标值取整误差 + 二阶投影模糊。 **元认知定位**:全文不设外部观察者,不判断对错,不提供修补。三档标记只显影读数路径的合拢状态。以下位置显影为**边界采样点**:10 步 = \\(2 \\times 5\\) 步、相位区间划分、5 步来源、\\(\\tan\\) 与 \\(\\cot\\) 的选择。边界采样点显影为闭链边界在当前认知截面上尚未完全强制合拢的位置,它们标明了读数路径的当前边界,延拓路径由引用文献分别给出。