Polarized Donovan–Wemyss conjecture for contraction algebras

Let $k$ be a field and let $l=ke_1+\cdots+ke_t$. A polarized $l$-algebra is an $l$-algebra $\Lambda$ equipped with a class

$$[\Phi]\in HH_0(\Lambda,\Lambda)=\Lambda/[\Lambda,\Lambda],$$

called a polarization. A polarized morphism preserves the distinguished class. Suppose that $Y\to X=\operatorname{Spec}R$ and $Y'\to X'=\operatorname{Spec}R'$ are 3-dimensional flopping contractions for complete local $\mathbb C$-algebras $R$ and $R'$, with associated contraction algebras $\Lambda(Y,\Phi)$ and $\Lambda(Y',\Psi)$.

Polarized Donovan–Wemyss conjecture. The spaces $X$ and $X'$ are formally isomorphic at their singular points if and only if $\Lambda(Y,\Phi)$ and $\Lambda(Y',\Psi)$ are isomorphic as polarized algebras. This is proposed as an enhancement of the Donovan–Wemyss conjecture; the source gives no resolution.