The zeta-map correspondence for unit interval orders

Let $P$ be a unit interval order corresponding to an incomparability graph $G(d)$ and to a lex-maximal part listing encoded by ${\bf a}=(a_1,\ldots,a_n)$. Let $d'$ be the Dyck path with area sequence ${\bf a}$, and let $\zeta$ denote Haglund's zeta map on Dyck paths. Zeta-map conjecture. One has

$$d=\zeta(d').$$

The source states that this conjecture was proved independently by Gélinas–Segovia–Thomas and by Fang, so it is solved.