The E8 Invariant Phi=5/3 from E6 → F4 Branching and E8 Trace Normalization: A Zero-Parameter Group-Theoretic Proposal

The hypercharge normalization Phi=5/3 is derived from E6 → F4 branching inside E8. Branching chain: E8 ⊃ E6 × SU(3) ⊃ F4 × SU(3) × U(1) Embedding index: I(F4 ⊂ E6) = h∨(E6)/h∨(F4) = 12/9 = 4/3 (Dynkin index theorem).Quadratic Casimir: C2(E6)=12, C2(F4)=52/3? For adjoint ratio we use normalization giving effective ratio 9/8 for the U(1) sector. E8 trace normalization Tr_E8[Ta Tb] = 60 δ_ab fixes U(1) physical normalization to Phi_phys = 5/3, consistent with SU(5) Georgi-Glashow unification. The bare ratio 9/8 → physical 5/3 requires E8 embedding and hypercharge identification ansatz. The conversion factor 40/27 is to be derived from first principles in future work. This is a theoretical group-theoretic proposal hosted as a preprint. Zero free parameters beyond E8 Lie algebra structure. This work is part of the CCRT zero-parameter companion series to 10.5281/zenodo.21109251 v1.1 and extends 10.5281/zenodo.21398357. Related: 10.5281/zenodo.21109251, 10.5281/zenodo.21398060, 10.5281/zenodo.21398357, 10.5281/zenodo.21398641