Delaunay-chain first-transition conjecture for equal small volumes

Let $T^3$ be the flat cubic three-torus, and consider two small volumes that are equal or close to equal as they increase. The standard double bubble and a chain of two bubbles bounded by Delaunay surfaces are candidate minimizers.

Delaunay-chain transition conjecture. The first phase transition as small equal, or close to equal, volumes grow is from the standard double bubble to a chain of two bubbles bounded by Delaunay surfaces.

The claim is motivated by numerical computations and the geometry of Delaunay surfaces, but remains conjectural in the source.