The 45° Budget: A Conservation Law for Mixing Angles

We conjecture that quark and lepton mixing angles in the 2-3 sector satisfy a conservation law: θ₂₃^CKM + θ₂₃^PMNS = 45°. With θ₂₃^CKM = 2.38° from |V_cb|, this predicts θ₂₃^PMNS = 42.62°, yielding sin²θ₂₃ = 0.458 (lower octant). This value lies within 1σ of current global fits (NuFIT 6.0: 0.470 ± 0.017) and agrees with atmospheric neutrino data (Super-Kamiokande: 0.450 ± 0.02). The prediction is falsifiable: confirmation of the upper octant (sin²θ₂₃ > 0.5) at 5σ refutes the conjecture. Hyper-Kamiokande and DUNE will provide definitive tests by 2031.