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beyond a threshold and are locally protected from Stokes points, whereas
those of ``many step replica-symmetry broken'' lie at the threshold and
Stokes points immediately proliferate.
-
-% Contrary to the real case, the index of saddles is not itself
-% relevant, as it is always half the total dimension. The relevant topological
-% objects here are Stokes trajectories, gradient lines joining two saddles, where
-% Lefschetz thimbles merge. The well-studied `threshold level', separating
-% regions with minima from regions with saddles in the real case, here separates
-% regions where Stokes lines are rare, from region where they proliferate.
-% Likewise, when a real landscape is prolonged to complex variables, the
-% distinction between "one step replica-symmetry breaking" and "many step replica
-% symmetry breaking" is that in the former case the saddles are at first free of
-% Stokes lines, while in the latter these immediately proliferate.
\end{abstract}
\maketitle