alpha_s_geom_eq
plain-language theorem explainer
The theorem states that the geometric strong coupling constant equals exactly 2/17 when interpreted in the reals. Physicists deriving particle couplings from symmetry counts in Recognition Science would cite this to fix the T15 prediction. The proof is a one-line wrapper that unfolds the rational definition and normalizes the arithmetic.
Claim. The geometric strong coupling constant satisfies $alpha_s^{geom} = 2/17$.
background
The module formalizes T15 for the strong force, positing that the coupling arises from planar symmetries of the ledger and equals the reciprocal of half the symmetry group count W=17. This yields the explicit prediction $alpha_s = 2/W = 2/17 approx 0.11765$, which lies within 0.2 sigma of the PDG 2022 measurement 0.1179 plus or minus 0.0009. The upstream definition alpha_s_geom supplies the rational value 2/17, labeled the wallpaper fraction and the predicted strong coupling.
proof idea
The proof is a one-line wrapper that applies simplification to unfold the definition of alpha_s_geom followed by numerical normalization of the resulting rational expression.
why it matters
This declaration supplies the exact real-number statement of the T15 strong-coupling prediction inside the Recognition Science framework. It anchors the geometric interpretation that the strong force couples to pairs of symmetries and closes the formal verification step referenced by the sibling T15Cert and t15_verified declarations. The result directly supports the module claim that the prediction matches observation to within 0.0003.
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