Restricted-type orthonormal Strichartz conjecture at endpoint A

Let $n\geq1$, and let $A=(1/p,1/q)=((n-1)/(n+1),n/(n+1))$. For an orthonormal family $\{f_j\}_{j\in J}\subset L^2(\mathbb{R}^n)$ and a sequence $\{\lambda_j\}_{j\in J}\in\ell^{q,1}$, consider the mixed norm of the Schrödinger evolutions. Restricted-type endpoint conjecture. The estimate

$$\bigg\|\sum_{j\in J} \lambda_j|e^{it\Delta}f_j|^2\bigg\|_{L^q(\mathbb{R}, L^p(\mathbb{R}^n))}\lesssim \|\{\lambda_j\}_{j\in J}\|_{\ell^{q,1}}$$

holds at the endpoint $A$ for all such orthonormal families and coefficient sequences. This conjecture was raised by Frank–Lewin–Lieb–Seiringer and Frank–Sabin, and the supplied status evidence says it was proved by Bez–Hong–Lee–Nakamura–Sawano using a semiclassical limit and a geometric argument involving Nikodym sets.