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 αₑm = 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: αₑm = 3/ (16πₘ²φ²) × (1 + sin (1/φ) / (32πₘ) ), with πₘ = π1 + ε. This gives 1/αₑm = 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.