Fermion Mass Geometry: Koide, Cabibbo, and Quark Distortions from $S^7/\mathbb{Z}_3^3$ Orbifold Structure

Derives the Koide formula $K=2/3$ for charged leptons in the $S^7/\mathbb{Z}_3^3$ orbifold lane. The $\sqrt{3}$ ratio $\beta/\alpha$ emerges from Cartan normalization in an $SU(3)\to SU(2)\times U(1)$ restriction. Electron smallness is treated via a constrained enhancement-point perturbation in Koide-locked geometry. A Cabibbo-angle normalization template $\theta_C = 45^\circ/\sqrt{12}=12.99^\circ$ is presented at the model/program level, with operator-level extraction explicitly flagged as an open derivation target. Quark deviations are modeled via a distortion operator with a $Z_2$ involution mechanism yielding an $s=\cos\phi$ template.For a series overview, reading order, and claim‑hygiene guide, see…