Finite-Rank Projective Observability and the Fine-Structure Coupling

This paper asks what operational structure a measurement accesses when determining a dimensionless coupling. It models the fine-structure coupling not as a primitive scalar, but as the symmetric readout of a two-channel spectral inverse-coupling tensor generated by a finite-rank, non-invertible projection with a dynamically active kernel. From a conserved recurrent flow and explicit structural conditions, the construction yields α⁻¹ = 137.0359991702704 without using any measured value of α and without adjustable continuous parameters. The result is a theorem within the declared admissibility class; uniqueness of that class is not claimed. The construction further predicts that photon-recoil determinations of α⁻¹ fall on a discrete three-point lattice of fixed spacing φ×10⁻⁷, a prediction registered in advance and testable by a third recoil species.