= Fold tangency obstruction for characteristic data
If initial data are parameterized by $s$ and their characteristic invariant is $D(s)$, a solution constant on <characteristics> requires $f(s)=F(D(s))$. At a fold $D'(s_0)=0$, equal invariant values must have equal data, and $f'(s)/D'(s)$ must extend continuously if $F$ is <continuously differentiable>. The condition $f'(s_0)=0$ alone is insufficient: for $D(s)=1/4-(s-1/2)^2$, the data $|s-1/2|^{3/2}$ would require a derivative of $F$ blowing up at $1/4$.
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