N_c
plain-language theorem explainer
N_c is defined as the integer 3 for the number of colors in the SU(3) gauge group of QCD. QCD running-coupling calculations and Recognition Science models cite this constant when evaluating the beta-function coefficients beta0 and beta1. The implementation is a direct constant assignment with no computation or lemmas applied.
Claim. The number of colors is defined by $N_c = 3$.
background
The Two-Loop QCD Running module extends one-loop alpha_s running to the two-loop beta function in the MS-bar scheme. With N_c fixed at 3 the coefficients read beta0 = (11 N_c - 2 N_f)/(12 pi) and beta1 = (102 - 38 N_f/3)/(8 pi^2). Upstream structures establish the SU(3) content: SpectralEmergence shows that Q3 simultaneously forces SU(3) x SU(2) x U(1) gauge groups together with exactly three particle generations, while PhiForcingDerived supplies the underlying J-cost minimization that selects discrete tiers.
proof idea
The declaration is a one-line definition that directly assigns the natural number 3; no tactics or lemmas are invoked.
why it matters
N_c supplies the color factor to beta0, beta1, and the mass anomalous dimension c0 in AlphaRunning and MassAnomalousDimension. It realizes the D = 3 result from the forcing chain (T8) as shown by the downstream theorem three_colors_from_D3, which proves that face-pair counting in Q3 yields exactly three colors. This supplies the geometric origin of the SU(3) gauge group inside the Recognition framework.
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