On the Geometric Reduction of the Fine-Structure Constant

We present a rigorous assessment of a geometric framework in which electromagnetism emerges from a fundamental one-form field bµ. Previous claims of a parameter-free derivation of the fine-structure constant α are withdrawn. However, the surviving structure reduces the determination of α to a single dimensionless geometric parameter associated with the normalization of a unified connection. We explicitly compute the dressing of the lowest atomic Bohr-loop mode and show that the fine-structure constant is controlled by a single undetermined parameter. The framework is therefore not complete, but achieves a one-parameter reduction of α.