  We continue our investigations into Toda's algorithm [14,3]; a
Weierstrass-type representation of Gauss curvature $K=-1$ surfaces in
$\mathbb{R}^3$. We show that $C^0$ input potentials correspond in an appealing
way to a special new class of surfaces, with $K=-1$, which we call $C^{1M}$.
These are surfaces which may not be $C^2$, but whose mixed second partials are
continuous and equal. We also extend several results of Hartman-Wintner [5]
concerning special coordinate changes which increase differentiability of
immersions of $K=-1$ surfaces. We prove a $C^{1M}$ version of Hilbert's
Theorem.
