Mirror identification of the corrected differential via polyvector fields

Establish that, under mirror symmetry, the corrected differential δ + {μ^0,·} on the family Floer complex corresponds to deforming the Čech complex of polyvector fields C^*(Y^0; Λ^*TY^0) to the polyvector fields (or an appropriate noncommutative analogue) on the corrected mirror space.

Background

Building on the Maurer–Cartan conjecture for μ^0, the authors propose that the resulting differential matches, under mirror symmetry, a deformation of the polyvector fields on the uncorrected SYZ mirror Y^0 to those on the corrected mirror. This would align the Floer-theoretic correction mechanism with the algebraic geometry of mirror deformations and relate the Floer BV/Schouten–Nijenhuis structures across the mirror.