= Characteristic diamond for speed one minus y squared
{title2=$|x|+|\operatorname{artanh}y|<S$}
For <Cauchy data> prescribed on $x=0$ over $|y|<a<1$, put $S=\operatorname{artanh}a$. The maximal region determined solely by those data is
$$
\left\{(x,y):|x|+|\operatorname{artanh}y|<S\right\}.
$$
In the <travel-time coordinate for a one-dimensional variable-speed wave equation> $(x,s)$ this is the ordinary characteristic diamond $|x|+|s|<S$, as follows from <finite propagation speed>.
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