All 26 Standard Model Parameters from the Fibonacci Cayley Network C(Z25, {1,3,8,13}): A Complete Derivation Including the Fine Structure Constant

We derive all 26 free parameters of the Standard Model from the Fibonacci Cayley network C(Z_25, {1,3,8,13}) without free parameters. The main result is a complete derivation of the fine structure constant alpha using only the algebraic structure of Z_25: the maximum eigenvalue lambda_max is produced by mode k=11, which has order |<11>|=5=sqrt(N) in Z_25 and permutes the generators. The ratio Nc*|<11>|/k = 3*5/8 = 15/8, derived purely from the group structure, yields alpha^-1 = 137.03601 (experimental: 137.036, error: 0.000006%). A falsifiability test confirms that no other generator set summing to N=25 achieves error below 1%. Additional results: delta_CP = arctan(phi^2) = 69.09 deg (error 0.13%); Yang-Mills mass gap Delta = 5.039 > 0 independent of N; Ollivier-Ricci curvature kappa = Nc/(4k) = 3/32 (exact); spectral moments zeta_L(-2) = 1800 and zeta_L(-1) = 200 (exact integers). All results are reproducible from the attached Python script.