Fermion Mixing Angles from Three Algebraic Parameters

I present closed-form formulas for all eight independent CKM and PMNS mixing parameters from three discrete algebraic quantities: dc= 7 (the maximum parallelizable sphere dimension, from Adams'theorem), Ngen = 3 (the number of fermion generations, derived from five independent mathematical arguments including Spin (8) triality and anomaly cancellation), and Q = 2/3 (the Koide mass-ratio parameter, derived from Kocik's generalized Descartes circle theorem via geometric self-consistency). Six mathematical constraints from three distinct lines of argument uniquely select (dc, Ngen) = (7, 3), eliminating any post-hoc fitting concern. Compared against PDG 2024 and NuFIT 6. 0 data, seven independent predictions and one texture-derived relation yield a combined chi-squared of 2. 63 (p = 0. 96) with zero continuous free parameters. A Monte Carlo test over 10⁶ random integer theories places this result in the top 0. 035% (p = 3. 5 x 10^-4).