Existence of an optimal fundamental algebraic condition for smooth forms theories

A smooth forms theory is a classical theory $(\operatorname{Conf},S)$ whose configuration space $\operatorname{Conf}$ is a class of algebra-valued smooth forms. An algebraic condition is optimal when it is the weakest fundamental condition under which the theory becomes trivial. The optimal-condition conjecture. Any smooth forms theory admits an optimal fundamental algebraic condition. This refines the preceding speculation because a single theory may admit multiple fundamental algebraic conditions, such as a stronger nilpotent condition and a weaker solvability condition; the source gives no resolution.