  From an open set of initial data, we construct a family of classical
solutions to the 1D nonisentropic compressible Euler equations which form
$C^{0,\nu}$ cusps as a first singularity, for any $\nu \in [1/2,1)$. For this
range of $\nu$, this is the first result demonstrating the stable formation of
such $C^{0,\nu}$ cusp-type singularities, also known as pre-shocks. The proof
uses a new formulation of the differentiated Euler equations along the fast
acoustic characteristic, and relies on a novel set of $L^p$ energy estimates
for all $1 < p < \infty$, which may be of independent interest.
