Nilpotency conjecture for the composition structure of the D-particle field category

Let ${\mathfrak{l}}$ denote the composition structure on the category ${\rm \ker}\,\mathbf{Q}$, where the propagators of open string fields are defined from the Poisson-type sigma model as in the construction above. Nilpotency conjecture. The composition structure ${\mathfrak{l}}$ satisfies nilpotency, so the category ${\rm \ker}\,\mathbf{Q}$ is an $L_\infty$ category. This conjecture is the condition needed for the proposed D-particle field category and its subsequent Hochschild-cohomological construction; the source provides no resolution.