A First-Principles Information-Projection Derivation of the Low-Energy Fine-Structure Constant

The fine-structure constant is the zero-momentum charge normalization relating a canonically normalized massless photon to a conserved unit-current class. Quantum electrodynamics takes this normalization as an input and then determines radiative corrections and the running coupling. We derive the normalization on the electromagnetic branch of the eleven-to-four-dimensional information-projection theory. The parent framework supplies the generative geometry, the seven-term action, and the admissible projection and readout structures; their electromagnetic specialization is carried out here as a conventional effective-action problem. The source-normalized photon operator is obtained from one reduced parent functional. A relative Gram operator on paired Hermitian source and readout spaces fixes the finite base normalization. The rank-seven vertical support, three representation channels, the mixed source--support derivative, and a positive impedance operator determine the static response through a single constrained stationary reduction. A current-preserving map from the ternary information coordinate to the compact $U(1)$ Maxwell coordinate completes the static normalization. The first registered event contributes a separate bounded term through a completely positive quantum instrument, and the two contributions are combined in the same photon two-point function. For the canonical electromagnetic branch we obtain\[ Z_\alpha=137.035999176528643537\ldots .\]With the same conserved current, on-shell zero-transfer subtraction, and soft-photon normalization, the completed coefficient satisfies $\alpha_{\OS}^{-1}(0)=Z_\alpha$. The calculation also determines the one-plus-six impedance spectrum and an independent scale-separation quantity. No measured electromagnetic constant enters the construction. The result is exact for the declared finite effective branch; matching its constitutive response to a particular microscopic parent and establishing a full continuum completion remain separate physical problems.