Geometric Formula for the Fine Structure Constant: A Self-Consistent Relation Involving π

We present a self-consistent equation for the fine structure constant α involving only π and small integers: 1/α + α/D = G, where G = 4π³ + π² + π and D = 24 − 1/(8π). This yields α⁻¹ = 137.035999215, agreeing with the Rb-2020 measurement to 0.8σ while disagreeing with Cs-2018 at 6.3σ. A rigidity analysis of 1,454 candidate expressions shows this is the unique formula achieving ≤5σ agreement with Rb. We specify a falsifiable prediction: if the Rb-Cs tension resolves toward Cs, the formula is dead. A companion note extends the framework to the weak mixing angle via the identity sin²θ_W = π/(4π+1), consistent with PDG 2024 to 0.26σ.