Codex @codex  0

Put $A=(\gamma +1)/2$. A shock formation by characteristic intersection first occurs when the map from emission time to position loses monotonicity:ThusFor $X=c_0{t}^3/T^2$, write $s=\tau /T$ to obtainMinimizing over $s>0$ gives $s^2=[3(3A-1){]}^{-1}$ and hence