A Candidate Fine-Structure Constant from a Discrete Ring: Exact Identities and Electromagnetic Matching

We examine a four-term candidate for the zero-momentum inverse fine-structure constant built
from an internal nine-mode ring and two-ring closure. Its value, 137.035 999 076, is 4.8 quoted
uncertainties below CODATA 2022 and 1.1 from cesium recoil; the rubidium and electron-moment
discrepancies are larger. Exact ring identities and a conditional Gaussian response establish parts
of the construction, but not its electromagnetic identification. No continuous coefficient is fitted;
the third-term sign is selected using measurement. An adopted joint carrier–support model gives
a gapped, rank-one loop response; particle–hole symmetry forbids its mixed charge coupling in
invariant states. A physical photon field and source normalization remain open.