The KP–ABT partition-function equality

Let $Z_{\rm KP}$ and $Z_{\rm ABT}$ denote the partition functions associated with the Kontsevich–Penner and Alexandrov–Buryak–Tessler constructions. KP–ABT equality conjecture. One has

$$Z_{\rm KP}=Z_{\rm ABT}.$$

The equality would identify two matrix-model descriptions of the same open-intersection-theory generating function; the source gives no resolution.