Article 19: Metric Correction to the Fine-Structure Constant in the PEW Framework

Article 3 derived the fine-structure constant from the ideal Hopf torus as α_em = 3/(16π²φ²) × (1 + sin(1/φ)/(32π)) = 1/137.018, leaving a residual of 0.013% relative to CODATA (1/137.036) as open problem PO-α. This Article 19 resolves the residual through two complementary physical insights: (i) The two-π structure of PEW: the topological π (fixed by the Hopf fibration in κ² = 8π) differs from the metric π seen by the electromagnetic gate, which is slightly modified by local curvature. (ii) The mobile gate: the phinaire spiral on the golden torus T²(φ,1) never closes (1/φ is irrational), making the gate permanently open and mobile. This dynamic aperture modifies the effective coupling. The resulting metric correction ε = (κ−5)²(κ−4)/e (where κ = √(8π)) yields the corrected formula: α_em = 3/(16π_m²φ²) × (1 + sin(1/φ)/(32π_m)), with π_m = π[1 + ε]. This gives 1/α_em = 137.036053, reducing the residual to 5.4×10⁻⁵ (accuracy 99.99996%, improvement by a factor of 334) with no free parameter. PO-α is resolved at level [B]. The full Lagrangian derivation remains open [D].