Quark and Lepton Mixing from the G2 Algebra: CKM and PMNS Parameters and a Reactor-Angle Prediction

We examine the quark and lepton mixing matrices within the G2 algebraic framework of Papers I–V. Several CKM parameters follow from operator ratios with good accuracy: the Wolfenstein A parameter A = S/TSM = 90/109 = 0.8257 (0.04%), confirmed independently by ALMS/KHYAS = 0.8256; the Cabibbo angle via the Gatto-Sartori-Tonin relation sin _C = √(m_d/m_s) = 0.2224 (1.1%); and the CP-violating θ phase from two independent constructions, arccos(TS/KHYAS) = 69.28° and 9×w_constraint×360° = 69.34°, agreeing to 0.06° and consistent with the measured phase within one standard deviation. For the PMNS matrix, the atmospheric angle is given by arcsin(TS/S) = 50.1° (1.8%), and the reactor angle by sin² = = 1/42 = 0.0238 (7.2%), which we put forward as a falsifiable precision prediction testable by θ₁₃ ε JUNO, DUNE, and Hyper-Kamiokande. We are explicit about the framework's current limitations in this sector: the solar angle is not cleanly derived, the Wolfenstein parameter is not yet obtained from the η algebra, and the neutrino mass ratios are order-of-magnitude only. Mixing is the least complete sector of the framework, and we present it as such — strong where the operator ratios are clean, openly incomplete where they are not. Structural integers are sourced in the Appendix. Keywords: CKM matrix, PMNS matrix, quark mixing, neutrino mixing, Cabibbo angle, reactor angle, CP violation, G2 algebra, Wolfenstein parameters