Smoothness of contraction algebras in general

Establish whether every contraction algebra is a smooth point of the corresponding algebra-structure scheme, beyond the specific two-generator formal E6 family treated in the paper.

Background

The paper proves smoothness and uniqueness of the semisimple deformation target for the formal family of Jacobi algebras associated with potentials x^3+xy^3+p(y), using symmetry, bimodule four-periodicity, and the equality of the first two Hochschild dimensions. It explicitly distinguishes this family-specific result from the broader question for arbitrary contraction algebras.

The broader smoothness statement is identified as Conjecture 1.4(1) of Jelisiejew and Smoktunowicz. Thus, although the paper resolves the issue for its E6 family, the general contraction-algebra case remains conjectural in the cited formulation.