Johansson's uniqueness conjecture for the parabolically shifted Airy process

Let $\mathcal{A}:\mathbb{R}\to\mathbb{R}$ be the Airy process, and consider the parabolically shifted process $x\mapsto\mathcal{A}(x)-x^2$.

Johansson's conjecture. Almost surely, $x\mapsto\mathcal{A}(x)-x^2$ attains its maximum at a unique point $Y\in\mathbb{R}$.

This conjecture concerns the uniqueness of the maximizer governing the scaling limit of a point-to-line geodesic in geometric last passage percolation. It was proved by Corwin and Hammond, with alternate proofs by Pimentel and by Flores and collaborators.