> 1.  In the sentence "It is defined analogously to the Saffman integral
> in hydrodynamics and is given by...", it is unclear whether "it" refers
> to the Hosking integral or the more general correlation integral. The
> former is the one that is defined analogously to the Saffman integral,
> but it is the latter that appears in (2.1).

We have now rephrased it and write

  We recall that the Hosking integral, $\cIH$, is defined analogously to
  the Saffman integral in hydrodynamics, and emerges as the asymptotic
  limit of the integral of the two-point correlation function of the local
  magnetic helicity density $h(\bmx,t)=\bmA\cdot\bmB$. The latter, which
  we call $\intIH$, is given by \citep{HoskingSchekochihin2021prx}

> 2.  As far as I can tell, (2.4) is the authors' definition of
> the Hosking integral. However, the latter is the large-R limit of
> \mathcal{I}_H even before any assumption is made about equivalence of
> volume and ensemble averages. I therefore think it would be clearest to
> define \mathcal{I}_H and then to state that I_H is the constant value
> taken by \mathcal{I}_H in the range xi_M^3 << V_R << L^3. One can then
> go on to assume the equivalence of volume and ensemble averages and so
> arrive at (2.4), which gives a useful alternative expression for I_H.

we have now replaced 

  equation~\eqref{eqn:Iv_def1} can be written in an equivalent form by
  assuming that the volume average approximates the ensemble average

by

  {$\intIH$ reaches a constant asymptotic value, $\cIH$, independent
  of $R$. Assuming that the volume average approximates the ensemble
  average \citep{HoskingSchekochihin2021prx}, we have

> 3.  I also note that equations (2.1)-(2.4) do not have anything to do
> with the "box-counting method" per se; I would therefore suggest that
> §2.1 might be renamed "definition of the Hosking integral" or similar,
> with a section entitled "the box-counting method" beginning after (2.4).

We have done this now.