A single coupling in the atomic spectrum

We apply the spectrum arithmetic of Reacher Endogenous Theory (RET) to the atomic spectrum, and we use one face of it. That face is the coupling, read from a register function: a fixed closed form that maps one number, the universe's position on a one-dimensional axis, to another number, the inverse finestructure constant. RET calls that position the health axis, and we keep the name. The architecture carries no atomic-scale value, and we state that as the central result rather than as a deficiency; that statement is a boundary statement, graded [d]. The fine-structure constant enters as a measured value read through the closed form, which locates where the universe now sits on the axis. Every atomic level energy remains external quantum-electrodynamic content. The first tier holds ten measured rows. Seven of them carry no framework value at all; one carries a framework-side dimensionless forecast whose grade is below the sealed record and which lies about two per cent below its measured counterpart; and two carry the coupling coordinate itself. The emptiness follows from four independent blockers, and we report it as a negative result, graded [d]. What the architecture does supply is narrow. It supplies a time dependence of the coupling whose direction is fixed; a terminal value, graded [b] because it is a conditional output of an effective-potential assembly, that the coupling approaches asymptotically; and the ratio 2.005800366 between the drift of a line at leading power four and the drift of a line at leading power two. That ratio is not itself a threshold: the framework predicts neither the absolute rate nor the mapping from the coordinate to redshift, so no measured ratio is ever excluded by it. What is falsifiable, and equally calibration-free, is the relation between the two 1 offsets, which one campaign can test. The theory itself is not re-derived here.