Proposition: A junction, not a patch collapse

At $s=0$, all four planes meet at the origin and the central lengths vanish, but every face contains a two-dimensional open region. The incidence change is

Proof. Here $F_0=\max \{p|x|,q|y|\}$. For example, $E$ is strict on $x>0,px>q|y|$. The other regions follow by symmetry; the four-way intersection is only the origin.