qcd_beta_nf6
plain-language theorem explainer
The one-loop QCD beta coefficient for three colors and six flavors evaluates to seven. Particle physicists checking the sign of the running coupling in asymptotic freedom calculations would cite this evaluation. The proof reduces to direct numerical evaluation of the closed-form expression via native_decide.
Claim. The one-loop beta-function coefficient for QCD with $N_c=3$ colors and $N_f=6$ flavors equals 7, where the coefficient is given by $(11N_c - 2N_f)/3$.
background
In the module on anomalies arising from 8-tick phase mismatches, the QCD beta coefficient is introduced via the definition qcdBetaCoeff Nc Nf := (11 * Nc - 2 * Nf) / 3. This expression encodes the one-loop running of the strong coupling and appears in the discussion of conformal anomalies, where scale invariance is broken by quantum effects tied to discrete phase structure. The local setting frames anomalies as mismatches between continuous classical symmetries and the eight-tick discreteness of Recognition Science.
proof idea
The proof is a one-line wrapper that applies native_decide to evaluate the arithmetic expression for the beta coefficient at the specific values Nc=3 and Nf=6.
why it matters
This evaluation feeds the downstream theorem qcd_asymptotic_freedom_nf6, which rewrites the result to conclude the coefficient is positive and hence the theory is asymptotically free. It fills the concrete numerical step in the paper proposition on quantum anomalies from discrete time structure, linking the positive beta to the conformal anomaly generated by 8-tick phase quantization. The result sits inside the Recognition Science treatment of the conformal anomaly within the eight-tick octave.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.