The identification of the unframed invariant with the LMO invariant

Let $M$ be an integer homology $3$-sphere, let $\widetilde{I}_n(M)$ be the decoration-independent unframed invariant obtained by subtracting the framing correction from $I_n(M)$, and set

$$\omega(M)=\sum_n m^n\widetilde{I}_n(M),$$

where $m=|H_1(M;\mathbb{Z})|$. LMO identification conjecture. The invariant $\omega(M)$ equals the surgery-defined invariant of Le, Murakami, and Ohtsuki. This is equivalent to asserting that $\widetilde{I}_n$ satisfies the Le–Murakami–Ohtsuki surgery formula. The paper states that the equality is known to highest order because both invariants are universal, but the full identification remains unproved.