Preservation of minimality under layered solid torus adjustment

Determine whether, in a triangulated 3-manifold obtained by Dehn filling, performing the standard adjustment of a layered solid torus (i.e., replacing the layered solid torus via the layering/diagonal-flip move on the boundary 1–punctured torus) on a minimal triangulation always yields a new triangulation that is also minimal.

Background

For larger parameters p and q, the authors’ conjecturally minimal triangulations are obtained by adjusting a layered solid torus within a Dehn-filled manifold. The minimality of the resulting triangulations is heuristically supported by a broader conjecture in the triangulations literature.

They explicitly reference this conjecture, which, if true, would imply the minimality of their constructions after performing the layered solid torus adjustment.