Arithmetic Structure of PMNS Mixing Angles and a Prediction for the Solar Angle

I observe that the three PMNS neutrino mixing angles are each consistent with exact rational values whose denominators involve only the primes 2, 3, and 13, where 13 = 2² + 3². Specifically, the reactor and atmospheric angles take 3-smooth values sin²θ₁₃ = 16/729 = 2⁴/3⁶ and sin²θ₂₃ = 9/16 = 3²/2⁴, while the solar angle takes the value sin²θ₁₂ = 4/13 = 2²/(2² + 3²), carrying the single additional prime 13 in its denominator. Each prediction is compared independently to the most recent experimental data. All three agree with the NuFIT 6.0 global fit within 0.12σ, and sin²θ₁₂ = 4/13 agrees with the first JUNO reactor measurement at 0.17σ. The solar angle prediction sin²θ₁₂ = 4/13 ≈ 0.3077 is the falsifiable test of this ansatz. JUNO will measure sin²θ₁₂ to sub-percent precision within the next few years. No theoretical derivation from a specific flavor symmetry or Lagrangian is offered here.