Geometric encoding of pseudo-Anosov flows

Prove that every transitive pseudo-Anosov flow can be encoded by a geometric veering triangulation.

Background

Many veering triangulations are non-geometric, although the authors found geometric veering parents for every non-geometric census example considered through 16 tetrahedra. The conjecture asks whether drilling can always produce a geometric encoding of the same transitive pseudo-Anosov flow.

References

Every transitive pseudo-Anosov flow can be encoded by a geometric veering triangulation.

— Drilling veering triangulations with applications to pseudo-Anosov flows  (2610.12302 - Parlak et al., 8 Oct 2026) in Section 5.2, Conjecture 5.8 (label conj:geometric)