The latest reviews had nothing to say about the scientific content of our
paper, only about its relevance to Physical Review Letters. For resubmission to
Physical Review Research, we have therefore changed nothing except to expand on
our reasoning regarding the relevance of this work to the broader physics
community, and indeed across disciplines. The end of the fourth paragraph now
reads:

> [...] In order to do this correctly, features of the action's landscape in
> complex space---such as the relative position of saddles and the existence of
> Stokes lines joining them---must be understood.  This is typically done for
> simple actions with few saddles, or for a target phenomenology with
> symmetries that restrict the set of saddles to few candidates. Given the
> recent proliferation of `glassiness' in condensed matter and high energy
> physics, it is inevitable that someone will want to apply these methods to a
> system with a complex landscape, and will find they cannot use approaches
> that rely on such assumptions. Their landscape may not be random: here we
> follow the standard strategy of computer science by understanding the generic
> features of random instances of a simple case, expecting that this sheds
> light on practical, nonrandom problems. While in this paper we do not yet
> address analytic continuation of integrals, understanding the distribution
> and spectra of critical points is an essential first step.