Balogh–Kostochka–Treglown degree-sequence conjecture for perfect clique packings

Let $n,r\in\mathbb{N}$ with $r$ dividing $n$, and let $G$ be a graph on $n$ vertices whose degree sequence is $d_1\leq\cdots\leq d_n$. Balogh–Kostochka–Treglown conjecture. If

$$d_i\geq (r-2)n/r+i$$

for every $i<n/r$, and

$$d_{n/r+1}\geq (r-1)n/r,$$

then $G$ contains a perfect $K_r$-packing. This degree-sequence condition is a sufficient-condition conjecture for perfect clique packings; the source does not specify whether it has been resolved.