Two-dimensional scission-branch conjecture for the liquid-drop model

Let $\chi$ be the fissility parameter and let $\chi_3\approx0.428$ be the two-dimensional analogue of the Businaro–Gallone point. A scission point is a transition state on the separate branch described in the paper; for $\chi>\chi_3$ it resembles a lemniscate. Scission-branch conjecture. Each scission point is a transition state for $\chi>\chi_3$. For $\chi<\chi_3$, the scission point becomes unstable against mass-asymmetric perturbations, but the branch continues to arbitrarily small $\chi$, and the scission point on this branch converges to two touching disks as $\chi\to0$. This is a numerical conjecture about the two-dimensional asymptotic branch; the supplied text gives no proof or resolution.