We show that the geometric structure of quantum state space — CP^n with the Fubini-Study metric (K=4) — contains substantially more physics than previously recognized. From this single structure, we obtain: the Born rule as a geometric identity including at dim H = 2 where Gleason's theorem does not apply; the Standard Model gauge group SU(3) × SU(2) × U(1) from CP^n isometries and stabilizers; and the Weinberg angle sin²θ_W = 3/8 from SU(5) = Isom(CP^4). The framework is checked against 61 numerical tests, all consistent. We validate experimentally on IBM Quantum hardware: the Bures (Riemannian) mean outperforms Euclidean averaging in quantum tomography, scaling from +0.003% (1-qubit) to +1.332% (3-qubit), providing direct evidence that state space curvature has measurable physical consequences.