We propose that the fine-structure constant α is the electromagnetic vernier scale of the gravitational Efimov coupling. The Randers–Finsler substrate framework produces a collective 1/r2 potential with coupling g0 = 24π² from six metric degrees of freedom. Electromagnetic windings, carrying global holonomy 2πα per cycle, deplete this coupling by C = αµ² 0 per winding, where µ² 0 = g0 − 1/4 is the above-threshold available coupling. The threshold 1/4 is unavailable to electromagnetic depletion because: (i) the Coulomb potential falls as 1/r, not 1/r², and cannot independently enter the Efimov conformal window (α/gc ≈ 0. 029 ≪ 1) ; and (ii) the 1/4 is committed to the quantumscale anomaly that stabilizes the 1/r2 potential against fall-to-center. The stability edge condition geff (n∗) = 1/4 then gives n∗ = µ² 0 = 1/α, so ⌊n∗⌋ = 137. The fine-structure constant is the ratio at which electromagnetic cycling tunes the gravitationalEfimov coupling to its critical threshold: gravity is the main scale, electromagnetism is the vernier.
David J.C. Smith (Tue,) studied this question.