Variational Derivation Program for the Fine-Structure Constant: Asymmetry, Closure Functional, and Charge Duality in QMU

This work develops a variational derivation program for the fine-structure constant within the Aether Physics Model (APM) using Quantum Measurement Units (QMU). A preceding paper established the Singularity as a pre-geometric bifurcation event in which first stable closure separates into boundary and torsional sectors. The present work extends that framework by asking whether the fine-structure constant \ (\) can be derived as the normalized geometric residue of first stable asymmetry. The paper begins from a quadrupolar perturbation of the first admissible closure geometry, () =R₀ (1+ P₂ () ), \ (\) is a dimensionless asymmetry parameter. Since the fine-structure constant is dimensionless, the derivation program treats \ (\) as a normalized function of this asymmetry. The charge duality relation is written as²{eₑmax²}=8. factor \ (8\) is interpreted as the product of full spherical angular closure, \ (4\), and a dual-sector factor, \ (2\). The remaining factor is identified as the asymmetry residue of the bifurcated loxodromic closure. A concrete loxodromic candidate is proposed: \₋₎ₗ () =4{5²}1+4{5²}. function arises by relating the normalized surface-area excess of a quadrupolar perturbation to the pitch fraction of a loxodromic traversal. In this model, \ = ₋₎ₗ (_), \ (_\) is the stationary asymmetry selected by the closure functional. The closure functional is constructed from boundary, torsional, and volumetric contributions: [=S_+S_+Sₕ. \]To leading order this gives a quartic stability form, [=S₀+k₂²+k₄⁴+, \]with a nontrivial bifurcated solution when \ (k₂<0\). The resulting stationary asymmetry satisfies\_²=T₀ b₂-A₀ a₂2V₀ c₄. \ The paper does not yet claim a final numerical derivation of \ (\). Its contribution is to convert the fine-structure constant problem into a constrained variational problem in closure topology. In this interpretation, \ (\) is not an externally inserted parameter, but the residual geometric phase of the first stable bifurcation that relates localized electrostatic boundary manifestation to distributed magnetic charge capacity.