qcd_critical_flavors
plain-language theorem explainer
The theorem establishes that the one-loop QCD beta coefficient for three colors is positive at sixteen flavors and negative at seventeen. Researchers mapping the conformal window in strong-coupling gauge theories would cite this integer bound. The proof splits the conjunction and resolves the two inequalities by direct evaluation and a supporting lemma.
Claim. In SU(3) Yang-Mills theory with $N_f$ Dirac fermions the one-loop beta-function coefficient satisfies $b(3,16)>0$ and $b(3,17)<0$, locating the loss of asymptotic freedom between these integers.
background
The module derives conformal anomalies (running couplings) from eight-tick phase mismatches between discrete time and continuous symmetries. The beta coefficient is evaluated in RS-native units where $c=1$ and the gauge scale is set by the tick and voxel. Upstream results supply the coefficient definition together with structural and unit conventions that fix the numerical evaluation.
proof idea
Term-mode proof begins with constructor to split the conjunction. The first inequality is discharged by native_decide. The second is obtained exactly by applying the lemma that establishes loss of asymptotic freedom at seventeen flavors.
why it matters
The result supplies a concrete numerical anchor for the conformal-anomaly section of the QFT-014 paper proposition on anomalies from eight-tick phase mismatch. It sits inside the broader forcing-chain landmarks (T5-T8) that fix three spatial dimensions and the eight-tick octave, yet leaves open a first-principles RS derivation of the beta function itself.
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