Graham–Lagarias–Mallows–Wilks–Yan local-global conjecture for Apollonian circle packings

Let $\mathcal P$ be a primitive integral Apollonian circle packing, and let $S$ be the set of residue classes modulo $24$ of the curvatures in $\mathcal P$.

Graham–Lagarias–Mallows–Wilks–Yan conjecture. All sufficiently large integers with residues in $S$ occur as curvatures in $\mathcal P$.

This is the local-global principle for curvatures of an integral Apollonian packing: congruence obstructions modulo $24$ should be the only obstruction to representing sufficiently large integers. The source does not provide evidence of a resolution.