The sporadic-set conjecture for Apollonian circle packings

Let ${\mathcal{A}}$ be a primitive Apollonian circle packing. Let $S_{\mathcal{A}}$ be the set of missing curvatures that do not lie in any of the quadratic or quartic obstruction classes described in the paper. The sporadic-set conjecture. The set $S_{\mathcal{A}}$ is finite. This conjecture is proposed as a replacement for the false local-global conjecture: after accounting for the quadratic and quartic obstructions, only finitely many additional missing curvatures should remain. The supplied text does not give a resolution of this replacement conjecture.