Structural 9CG Fermion Coefficients and an Internal PMNS Parametrization in the TTOE Framework

This manuscript gives a bounded public formulation of the fermion/PMNS block of the TTOE framework. The 9CG table is presented as a Coxeter/branching-motivated selection of rational coefficients along the chain E8 → E6 → D5 → A4 → G_SM. These coefficients are compared with a historical Clebsch/GUT target table CG_req, which is treated as an external input. A finite-table audit supports a local rarity statement. The PMNS part records an internal parametrization and a type-I seesaw mass scale under the explicit input Y_nu=1. The reactor angle sin²(θ₁₃)=19/900 is presented as a structural selection. v02: The CKM sector is no longer excluded — a reproducible pipeline with mean error 1.5% and CP phase at 0.2σ is developed in the companion paper PAP_TEO_10 using the w₀-breaking spurion framework. Additionally, the theorem w₀ = −id (PAP_TEO_10) provides a structural explanation for why the Coxeter reflection pairs appear complete in the 9CG table (p = 0.0001).