Huh–Matherne–Mészáros–St. Dizier's Lorentzian conjecture for normalized Schubert polynomials

Let $w\in S_n$, let $\mathfrak{S}_w(x)$ be the Schubert polynomial indexed by $w$, and let $N$ be the normalization operator on monomials, defined by

$$N(x^\alpha)=\frac{x_1^{\alpha_1}}{\alpha_1!}\cdots\frac{x_m^{\alpha_m}}{\alpha_m!}.$$

A homogeneous polynomial is Lorentzian when its support is M-convex and every quadratic form obtained by differentiating it $d-2$ times has at most one positive eigenvalue. Huh–Matherne–Mészáros–St. Dizier's conjecture. For any $w\in S_n$, the polynomial $N(\mathfrak{S}_w(x))$ is Lorentzian. This conjecture extends the known result for permutations avoiding the patterns $1432$ and $1423$; the paper proves it when the corresponding Grothendieck polynomial is zero-one, giving partial confirmation, while the general case remains open.