The Lorentzian conjecture for normalized Schur P-functions

Let $\lambda$ be a partition whose nonzero parts are distinct, and let $P_\lambda$ be its Schur $P$-function. Schur-$P$ conjecture. The normalized function

$$\mathrm{N}(P_\lambda)$$

is Lorentzian for every such partition $\lambda$. The source reports computational evidence for bounded largest part and number of parts; the assertion remains open.