Axelrod–Singer–Kontsevich identification conjecture for the higher-order Fukaya invariant

Let $M$ be a homology $3$-sphere and let $\widehat{Z}_{2k,3k}(M)$ be the invariant defined from the higher-order configuration-space construction. The configuration-space integral invariant of Axelrod–Singer and Kontsevich is the corresponding invariant of $M$. Axelrod–Singer–Kontsevich identification conjecture. The invariant $\widehat{Z}_{2k,3k}(M)$ agrees with the configuration-space integral invariant of Axelrod–Singer and Kontsevich. Establishing this would identify the higher-order Fukaya construction with the established configuration-space integral invariant.