Smoothness of the non-monotone Floer A∞-algebra at isolated critical points

Establish that, in the non-monotone setting over a Novikov field, for a Lagrangian torus L equipped with a rank-1 local system corresponding to an isolated critical point of the weak bounding-cochain potential function 𝔓𝔒 on H^1(L; Λ_{>0}), the A∞-algebra CF^*(L^, L^) is homologically smooth.

Background

The main results of the paper rely crucially on homological smoothness of the endomorphism A∞-algebra CF^*(L^, L^) for monotone Lagrangian tori at isolated critical points, deduced via a comparison with matrix factorizations (Dyckerhoff's smoothness).

To extend the theory beyond monotone tori, one must work over a Novikov field and use the potential function 𝔓𝔒 arising from weak bounding cochains. The conjecture asserts that the analogous smoothness should hold in this broader, non-monotone context at isolated critical points. Proving this would enable the extension of the automatic split-generation and quantum cohomology factorization results to the non-monotone setting.