Symmetric-lens conjecture for the two-dimensional strip-to-disk transition state

Let $\omega=(4\pi-3\sqrt{3})/18\approx0.4095$ be the fixed volume fraction, and let $c$ and $K$ be the phase-field parameters. A transition state is the saddle point along the minimum energy path from a strip to a disk. A symmetric lens is the region formed by two intersecting circles of equal radius $R$. Symmetric-lens conjecture. As $c\to0$ and $K\to\infty$, the transition state from a strip to a disk converges in $L^2$ to the indicator function of a symmetric lens. This is the proposed sharp-interface description of the numerically observed transition state; the supplied text gives no proof or resolution.