Classical consistency conjecture for the exceptional diagram category

Let $R$ be a ring and let $\mathsf{Exc}_{R,\lambda}$ be the classical exceptional diagram category, with $\mathsf{Exc}_{R,\lambda}(0)$ its closed-diagram space and the empty diagram its distinguished generator. Classical consistency conjecture. If a certain finite set of nonzero polynomials in $\lambda$ is invertible in $R$, then the map sending $r\in R$ to $r$ times the empty diagram embeds $R$ into $\mathsf{Exc}_{R,\lambda}(0)$. Equivalently, any two reductions of the same closed diagram to an element of $R$ agree. This rules out collapse of the closed-diagram space and supplies consistency of the diagrammatic relations; the source presents it as complementary to classical sufficiency.