Derived Morita reconstruction conjecture for infinity-contraction algebras

Let $X\to Y$ and $X'\to Y'$ be three-dimensional flopping contractions in smooth quasi-projective threefolds, contracting to points $p$ and $p'$ respectively. Associate infinity-contraction algebras $A^\infty_{con}$ and $B^\infty_{con}$ to them. Write $\widehat{\mathcal O}_{Y,p}$ and $\widehat{\mathcal O}_{Y',p'}$ for the completions of the stalks.

Infinity-contraction algebra reconstruction conjecture. The completions of the stalks at $p$ and $q$ are isomorphic if and only if $A^\infty_{con}$ and $B^\infty_{con}$ are derived Morita equivalent.

This is proposed as a refinement of the Donovan–Wemyss conjecture, replacing algebra isomorphism by derived Morita equivalence of the infinity-contraction algebras. The paper proves one special case, while the general assertion remains open in the source.