Avramov–Conca–Iyengar subadditivity conjecture for syzygies of Koszul algebras

Let $R=Q/I$ be a Koszul algebra, and let $t_i(R)$ denote the maximal degree of a minimal generator in homological degree $i$ of the minimal graded free resolution of $R$ over $Q$. Write $\operatorname{pd}_Q R$ for its projective dimension over $Q$. Avramov–Conca–Iyengar's subadditivity conjecture. The inequality

$$t_{a+b}(R)\leq t_a(R)+t_b(R)$$

should hold whenever $a+b\leq\operatorname{pd}_Q R$. This conjecture concerns subadditivity of syzygies, equivalently of Koszul homologies. To the authors' knowledge, it remains open, with results of Eisenbud, Huneke, and Ulrich and of Herzog and Srinivasan providing supporting evidence for its validity.