Hacon–Lamarche–Schwede subadditivity conjecture for $+$-test ideals

Let ${\mathscr X}$ be a regular scheme projective over the mixed-characteristic base scheme considered in the paper. For an effective ${\mathbb Q}$-divisor $B$ on ${\mathscr X}$, let $\tau_+({\mathcal O}_{\mathscr X},B)$ denote the associated $+$-test ideal.

Hacon–Lamarche–Schwede subadditivity conjecture. Given effective ${\mathbb Q}$-divisors $D$ and $E$ on ${\mathscr X}$, one has

$$\tau_+({\mathcal O}_{\mathscr X},D+E)\subset \tau_+({\mathcal O}_{\mathscr X},D)\cdot \tau_+({\mathcal O}_{\mathscr X},E).$$

This is the subadditivity property for $+$-test ideals. The conjecture remains open; the paper notes that Bhatt, Ma, Patakfalvi, Schwede, Tucker, Waldron and Witaszek prove subadditivity for different perturbation-friendly test ideals.