Small-volume triple-bubble attachment conjecture in the cubic three-torus

Let $T^3$ be the cubic three-torus, and consider the triple-bubble problem in the case where one of the three prescribed volumes is small. The double bubbles of Figure 2 are the relevant two-volume candidates.

Small-volume triple-bubble conjecture. The minimizers will look like the double bubbles of Figure 2 with a small ball attached, and the phase diagram will look just like Figure 3.

This conjecture extrapolates the computed double-bubble phase diagram to the triple-bubble problem. The source offers it as a final expectation rather than a proved result.