= Solution
For the <Landau intermittency counterexample>, combine two locally homogeneous turbulent populations, with the same sufficiently wide inertial interval but different <viscous dissipation> rates $\epsilon_1$ and $\epsilon_2$. This can mean an ensemble randomly selected between two intensities, or large turbulent patches whose small-scale increments are sampled away from the patch boundaries. Suppose each population individually obeys the proposed universal coefficient $\beta_p$. If their proportions are $w$ and $1-w$, the combined <longitudinal structure function> is
$$
S_p(r)=\beta_pr^{p/3}\left[w\epsilon_1^{p/3}+(1-w)\epsilon_2^{p/3}\right],\qquad
\epsilon=w\epsilon_1+(1-w)\epsilon_2.
$$
Its effective coefficient referenced to the global mean <viscous dissipation> is therefore
$$
\boxed{\beta_p^{\rm eff}=\beta_p\frac{w\epsilon_1^{p/3}+(1-w)\epsilon_2^{p/3}}
{[w\epsilon_1+(1-w)\epsilon_2]^{p/3}}}.
$$
For a concrete example let $w=1/2$ and $\epsilon_{1,2}=\epsilon(1\pm d)$, with $0<d<1$. Then
$$
\frac{\beta_p^{\rm eff}}{\beta_p}=\frac{(1+d)^{p/3}+(1-d)^{p/3}}2.
$$
For $p=6$ this is $1+d^2$, explicitly dependent on the strength of the large-scale modulation. For $p=2$ it is less than one by concavity. Thus \b[coefficients based solely on mean <viscous dissipation> cannot be universal under arbitrary <integral-scale intermittency>]. The common inertial interval can be maintained by taking both local <Reynolds numbers> sufficiently large.
At $p=3$ the ratio is exactly one. This exception is consistent with the signed third-order energy-flux law and must not be used to rescue universality of all other orders. For noninteger orders one uses absolute increments; the even-order examples already establish the counterexample without a sign convention ambiguity. The issue is the difference between a <moment> of the local <viscous dissipation> and the same power of its mean, not a failure of averaging itself.
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