Write a PREreview

The conformal embedding E8(1) ⊃G2(1) ×F4(1), with the Planck mass as sole dimensional inputand zero free dimensionless parameters, determines the electroweak scale, nine charged-fermionmasses, four CKM parameters, the strong coupling constant, the Higgs boundary condition, and thePMNS mixing angles including δCP.All three charged-lepton masses are reproduced to 0.002% [2]. The electroweak scale vEW =MPl exp(−(9π2/2 −6 + 15/512)) = 246.2 GeV (−0.005%) emerges from the F4 Casimir shift anda 30-mode QED instanton vertex. Six quark masses follow from triality, WZW emergence, andKoide closure, all within 0.3% of PDG 2025 [3]: mt = (1165/12) mτ = 172.5 GeV (−0.03%),mc = (217/18) mμ = 1273.8 MeV (+0.06%), light quarks from √me:√mu:√md = 1:2:3, and heavyquarks from the unified relation Q = 2/3 + hrep/K3. The mass difference md −mu = 5 me lies insidethe Hogan window for nuclear stability.The D(6) modular invariant of SU(3)3 provides four Wolfenstein parameters: λ = tan(2/9),A = √2/3, ̄η = π/9, ̄ρ = √2/9. Over fifteen CKM observables: χ2/n = 0.69, maximum pull 1.40σ.The electromagnetic coupling α = π/512 follows from the Singh ratio αs/αem = 16 [13]; thephysical fine-structure constant is the algebraic identity 1/α(0) = 256(2π −1)/π2 = 137.036 (to0.0003%). The embedding index j(SU(3)⊂G2) = 1 fixes αs(MZ) = 0.1177 (−0.3%). The F4(1)fusion rule forces λ(MPl) = 0; two-loop RG evolution gives mH ≈ 131 GeV, consistent with theNNLO window 126 ±2 GeV.The conjugation modular invariant of SU(3)3 gives tribimaximal PMNS mixing at leading order.The charged-lepton rotation shifts all three angles to within 0.1σ of NuFit 6.0 [34] (χ2/n = 0.57)and predicts δCP = 77◦(testable by DUNE/Hyper-K)