Proposition: All lengths and no peripheral collapse

The complete bounded patch lengths are in tab:certificate. Every noncentral actual edge has length greater than $1/2$ throughout the window. All eight faces remain two-dimensional. The central exchange is the only incidence event.

Proof. The north-east incoming arm displacement is $X_s(p,1,p/q)$, of spacelike norm $X_s\sqrt{1921}/25$. The outgoing displacement is $Y_s(q,q/p,1)$, of norm $Y_s\sqrt{1921}/39$. Reflection gives the other arms.

Resting lengths are $X_s,Y_s,(4-s)/3,(4-s)/5,R_x,R_y$. Their minimum is $3/5$; arm lengths are at least $3\sqrt{1921}/25>1/2$. Each core face has a strict-maximum neighbourhood immediately inside its inner side midpoint. Every collar polygon has nonempty interior by the strict margins. Central endpoints remain strictly inside ${\mathcal{R}}_s$, and all peripheral incidence is fixed.