Ai–Gutin–Lei–Yeo–Zhou's converse-invariant tree conjecture

Let $T$ be an orientation of a tree with maximum degree at least $3$. An oriented graph $D$ is converse invariant if $f_T(D)=f_T(\overline{D})$ for every tournament $T$, where $\overline{D}$ is obtained by reversing every arc of $D$. An oriented graph is self-converse if it is isomorphic to its converse. For a digraph $D$ and $u\in V(D)$, its bridge-mirroring at $u$ is obtained by taking two copies of $D$ and adding an arc between the two vertices corresponding to $u$. Ai–Gutin–Lei–Yeo–Zhou's conjecture. $T$ is converse invariant if and only if it is self-converse or $T$ can be obtained by the bridge-mirroring operation recursively from an orientation of a path. Converse invariance is known for every oriented path and cycle, and bridge-mirroring preserves converse invariance; the conjecture proposes that these constructions account for all converse-invariant trees of maximum degree at least $3$.