alpha_s_coupling_derived
plain-language theorem explainer
The theorem establishes that the predicted strong coupling α_s at the Z scale equals 2/17, obtained from the wallpaper group count in the Recognition Science ledger. A physicist comparing gauge unification predictions to PDG data would cite this equality when testing the crystallographic derivation. The proof reduces the claim by unfolding the geometric definition and normalizing the rational value.
Claim. The predicted strong coupling constant satisfies $α_s = 2/17$, where the prediction is obtained by casting the wallpaper fraction $2/17$ to the reals.
background
The module derives the three Standard Model gauge couplings from RS ledger geometry. The geometric strong coupling is defined as the rational wallpaper fraction 2/17. The predicted value is this fraction cast to reals. This forms part of registry item C-014, which asks what fixes α, α_s and α_w from the underlying structure. The upstream from theorem extracts four structural conditions plus three definitional facts from seven independent axioms.
proof idea
The term-mode proof applies simp to unfold the definitions of the predicted coupling and the geometric wallpaper fraction, then uses norm_num to verify the resulting rational equality.
why it matters
This result completes the strong-coupling entry C-014.2 in the gauge-couplings derivation chain. It supplies the geometric origin α_s = 2/W with W = 17 and supports the unification hint that the three couplings converge near the GUT scale. The derivation sits alongside the electromagnetic and weak-angle results, all obtained from ledger and crystallographic structure rather than free parameters.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.