Existence of a 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. The fundamental-condition conjecture. Any smooth forms theory admits a fundamental algebraic condition. The proposed framework aims to extend geometric obstruction results beyond the theories treated in the paper; the source gives no resolution of this speculation.