Solving Alpha — Version 5.2 presents a derivation of the fine structure constant from self-reference axioms and geometric structures. The Pentagon formula reproduces the Morel 2020 atomic recoil determination to within 0.05σ with no free parameters.
Solving Alpha — Version 5.2 presents a derivation of the fine structure constant from self-reference axioms and geometric structures. The Pentagon formula α⁻¹ = 360/φ² − 2/φ³ + additional terms reproduces the Morel 2020 atomic recoil determination to within 0.05σ with no free parameters. Version 5.2 establishes internal uniqueness — showing the Pentagon formula is the sole structurally admissible match within a pre-specified coefficient pool — and external overdetermination, demonstrating that the same α⁻¹ value emerges independently from cosmological, gravitational, and expansion rate measurements. An asymptotic series with coefficients Cₖ = 2^(k²) is presented, with optimal truncation near k = 6 settling within 1.65σ of precise measurements. The framework commits to Morel 2020 as the correct α⁻¹ value and falsifies itself if alternative determinations prove correct at high significance.