Charged-Lepton Mass Ratios from a Tetrahedral-Quotient Spectral Readout in Recursive Interval Geometry
Abstract
We give a static three-sector construction for charged-lepton mass ratios in Recursive Interval Geometry (RIG), using the same inherited static carrier as the companion fine-structure-constant paper. The fixed static data are \( D_1=3, D_2=7, D_3=127 \), \( N_{\mathrm{sk}}=137 \), and \( \Omega=2667 \); no new substrate or carrier is introduced. On the octet-truss face layer, the unsigned face-edge incidence matrix gives \( K=MM^{\mathrm T}=3I_8+A_{Q_3} \). Antipodal identification reduces the cube layer to a tetrahedral quotient, splits the operator into the two blocks \( 3I\pm A_{K_4} \), and leaves three nontrivial spectral levels with eigenvalues \( 4 \), \( 2 \), and \( 0 \) after removal of the isotropic mode. The charged-lepton-specific part is stated explicitly as a readout prescription, while the readout machinery is constrained by minimality, three-sector covariance, mean-one normalization, and the equal-budget condition between the isotropic line and the traceless plane. The only scalar interface is the one-cell rule \( c_{\mathcal O}=\pi/4+4/(3\Omega) \), lifted by the lowest normalized threefold invariant relation \( \cos(3\theta)=c_{\mathcal O} \). On the positive-amplitude branch, the Koide value \( Q_\ell=2/3 \) is equivalent to the balanced condition \( \|P_Uq\|=\|P_Wq\| \) rather than imposed as a separate empirical equation. For \( \Omega=2667 \), the outputs are \( R_{\mu/e}^{\scriptscriptstyle\mathrm{RIG}}\approx 206.702495554 \) and \(…
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