Flatness of Toda’s geometric deformation families

Establish whether the geometric deformation families constructed by Toda for all contraction algebras are flat.

Background

Toda constructed geometric deformations for all contraction algebras, but the paper records that flatness of these families has not been established in general. Flatness is essential for interpreting the generic fibre as a deformation of the original contraction algebra and for comparing geometric constructions with the algebraic deformations studied in the paper.

References

Toda constructed geometric deformations for all contraction algebras, but it is not clear whether these families are flat.

— On computing deformations of contraction algebras of type E  (2610.10157 - Smoktunowicz et al., 7 Oct 2026) in Section 1, Introduction