alpha_s_within_pdg_bounds
plain-language theorem explainer
The Recognition Science prediction for the strong coupling at the Z scale equals 2/17 and lies inside the PDG interval centered at 0.1179. Collider physicists and unification model builders would cite the bound when testing ledger-derived couplings against precision data. The proof is a direct term application of the matching identity that equates the wallpaper count derivation to the experimental tolerance.
Claim. $ |2/17 - 0.1179| < 0.0009 $ where the left-hand side is the Recognition Science value obtained from the wallpaper group count at the Z-boson mass scale.
background
In Recognition Science the three gauge couplings are fixed by ledger geometry and crystallographic invariants rather than free parameters. The strong coupling is set by the wallpaper group count W = 17, giving α_s = 2/W ≈ 0.1176 at the Z scale. This value is compared directly to the PDG 2022 central value 0.1179 with tolerance 0.0009. The module derives electromagnetic, strong and weak couplings from the same three-dimensional ledger: α^{-1} incorporates a voxel-seam gap correction, sin²θ_w follows from SU(2) × U(1) symmetry, and α_s follows from the discrete count of wallpaper groups. Upstream results on the phi-ladder and forcing chain supply the discrete spectrum in which these integers appear.
proof idea
The proof is a one-line term that applies the strong-coupling match identity. That identity equates the wallpaper-derived fraction 2/17 to the numerical target 0.1179 and verifies the absolute difference falls inside the stated tolerance.
why it matters
The declaration supplies the low-energy experimental closure for the strong sector inside the C-014 gauge unification program. It confirms that the crystallographic origin for α_s reproduces the measured central value to the quoted precision. In the Recognition Science chain this step supports the claim that all three couplings descend from the same ledger geometry that forces D = 3 and the eight-tick octave. The module notes that full renormalization-group evolution to the GUT scale remains open for later work.
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