26 Standard Model Constants from p = 3: A Complete Derivation from GF(9) Arithmetic

We derive 26 Standard Model constants from the algebraic structure of the finite field GF(9) = F₃[a]/(a²+1) and the ring Z/9Z. The single input is the prime p = 3. From the cardinalities |GF(9)| = 8 and φ(9) = 6, we obtain: the fine structure constant 1/α = 2(p²−1)² + p² + p/(p⁴+2) = 137.03614 (0.00076% match); the weak mixing angle sin²θ_W = p/(p²−1) = 3/8 at the GUT scale; spacetime dimension d = 4; the number of generations N_gen = p = 3; the number of gluons |GF(9)| = 8; the CKM matrix angles (α+β+γ = π exactly); the Koide parameter Q = (p−1)/p = 2/3; the Higgs mass m_H ≈ 125.4 GeV with v = 3⁵+3 = 246 GeV; and the hierarchy ratio M_Pl/v ≈ 3³⁵. We test p = 5, 7, 11, 13 and show that ONLY p = 3 produces values within experimental bounds. Five testable predictions are given, including θ_QCD = 0 (no axion) and a neutrino mass ratio of 32 (testable by JUNO, 2026–2028).