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

Version 1.0.1: Minor correction to bibliographic citation links.Article 3 of the PEW series derived the fine-structure constant as α_em = 3/(16π²φ²) × (1 + sin(1/φ)/(32π)) = 1/137.018, leaving a residual of 0.013% relative to CODATA. This Article 19 identifies the origin of this residual as a small metric correction due to the local curvature of the PEW vortex at the gate (ρ=1). We derive the correction ε = (κ−5)²(κ−4)/e, where κ = √(8π) is the fundamental coupling, φ is the golden ratio, and e is the Mother Wave growth rate. The corrected formula becomes α_em = 3/(16π_m²φ²) × (1 + sin(1/φ)/(32π_m)), with π_m = π(1 + ε). This yields 1/α_em = 137.036053, reducing the residual to 5.4×10^{-5} (precision 0.000039%, improvement by a factor of 334). No free parameter is introduced. The two-π distinction (topological π vs metric π) and the D5 symmetry arguments are discussed in detail. This article partially resolves PO-α at level [B].