Small-volume standard double-bubble conjecture in the three-torus

Let $T^3$ be the flat cubic three-torus, and consider the double-bubble problem for two prescribed volumes, both sufficiently small.

Small-volume standard double-bubble conjecture. For two small volumes the standard double bubble is optimal.

This is one of the intuitive double-bubble conjectures identified from the phase diagram. The paper proves a related result for comparable small volumes but presents this broader formulation as conjectural.