Complete classification conjecture for double bubbles in the three standard tori

Let the three tori be the standard cubic torus and the special FCC and BCC tori considered in the paper. Let the catalog in Figure 1 list the ten candidate double bubbles, and let the Hexagonal Honeycomb in Figure 4 be the additional candidate for the special rhombic-prism torus.

Complete-classification conjecture. The double bubbles of Figure 1 together with the Hexagonal Honeycomb of Figure 4 comprise the complete set of area-minimizing double bubbles for all three tori.

This is a global classification claim based on the computed phase diagrams and the displayed candidates. The source does not provide a proof.