Nontriviality and Ohtsuki-invariant recovery of the higher-order Fukaya invariant

Let $M$ be a homology $3$-sphere and, for each $k\geq 1$, let $\widehat{Z}_{2k,3k}(M)$ denote the invariant constructed from the higher-order configuration-space integral. Nontriviality and recovery conjecture. The invariant $\widehat{Z}_{2k,3k}(M)$ is nontrivial. In particular, the sequence

$$\{\widehat{Z}_{2k,3k}(M)\}_k$$

recovers all Ohtsuki finite-type invariants over $\mathbb{Q}$. This would establish that the higher-order invariant contains the full collection of Ohtsuki's finite-type information.