Which α

A fair question from a metrologist. Which α is being raised to the twenty-first power?

Claim. The corpus’s α is the fine-structure constant at zero momentum transfer, α(0). That is the value the constant is defined at. CODATA tabulates it. It is identified with the leakage constant at the electromagnetic boundary (AP06 §10.7). Twenty-one gates compound one number. D-EM.1 is untouched.

Intuition. The grain is the constant. Its coupling capacity is read at the neck. One grain at a time. At rest. Nothing has yet been assembled for it to run against. That is the model’s reason for choosing α(0). The specification stands without the reason.

Givens. AP06 §10.7. The author’s ruling (“the grain of sand is the constant — and the flow rate is constant”). CODATA 2022.

The audit, closed. Twenty-one powers of a per-mille ambiguity compound to (1 + α/π)²¹ = 1.04993 at CODATA-2022 α = 7.2973525643 × 10⁻³. Recomputed at source. The corpus does not deny that the effective coupling runs. Running is a statement about scattering at momentum transfer. The corpus’s α is not read in a scattering process. B8 on the wall is the specification.

What stays open. D-EM.1: what the corpus’s α-dependence is relative to the electromagnetic coupling. Tens of keV at the proton, against a self-energy of order a MeV. This section says which α. It does not say what the dependence means. In the author’s words: “this I can’t do now yet — this is the name of the exercise — to find the loose strings.”

Grade. Ruled. The audit closed at source.

One grain. One number — with no unit, because it is the now. Twenty-one times.