strongCoupling_approx
plain-language theorem explainer
Recognition Science predicts the strong coupling α_s(M_Z) exactly as 2/17. The theorem confirms 0.117 < 2/17 < 0.119, bracketing the PDG value 0.118 within 0.001. QCD phenomenologists and precision model builders would cite this bound when aligning RS parameters with collider data. The proof is a one-line term reduction that unfolds the RS definition and normalizes the numerical comparison.
Claim. The Recognition Science strong coupling constant at the Z-pole satisfies $0.117 < α_s^{RS} < 0.119$, where $α_s^{RS} = 2/17$.
background
The module derives the strong nuclear force parameters from Recognition Science via a wallpaper-fraction argument. α_s(M_Z) emerges as exactly 2/17, with five QCD parameters matched to the configuration dimension D. Upstream, PhiForcingDerived.of supplies the J-cost calibration while SpectralEmergence.of forces the SU(3) gauge sector from the Q3 structure, yielding 3 colors and 8 gluons.
proof idea
The proof is a one-line wrapper. It unfolds the definition of the RS strong coupling and applies norm_num to verify the strict bounds around 2/17.
why it matters
This supplies the coupling_band field in the StrongForceCert definition, which also records the equality, PDG proximity, and five-parameter count. It anchors the A1 SM Depth step in the Recognition Science framework, where the 2/17 value follows from the phi-ladder and Recognition Composition Law. The result closes numerical certification for the strong coupling without touching open questions.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.