= Solution
For $0<g<g_*$, the positive <beta function> makes the <running coupling> increase toward the <ultraviolet fixed point> $g_*$. Assume a continuous locally Lipschitz <beta function>, a continuous <anomalous dimension> at the fixed point, and a finite nonzero reference value $C(r,g_*)$. Then $g(t)\to g_*$ and
$$
\log f(t)=2\gamma(g_*)t+o(t),\qquad C(e^{2t}r,g)=e^{2\gamma(g_*)t+o(t)}C(r,g_*).
$$
Thus the high-momentum factor has exponent $\gamma(g_*)$ in $p^2$, and the propagator scales as $(p^2)^{-1+\gamma(g_*)}$ up to slower corrections. If the fixed point is simple and attractive, $\beta'(g_*)<0$, the approach is exponential; suitable smoothness then gives $f(t)\sim A e^{2\gamma(g_*)t}$ with finite $A$. The stated beta-function information alone supplies no numerical value for the <anomalous dimension> and does not exclude slower corrections at a nonsimple fixed point. This is <two-point scaling at an ultraviolet fixed point>.
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