The prime-level double-shuffle conjecture for multiple polylogarithms

Let $N>1$, and consider multiple polylogarithms evaluated at $N$-th roots of unity. The double-shuffle and distribution relations are families of relations among these values. Prime-level double-shuffle conjecture. If $N$ is prime and one restricts to the case in which weight equals depth, then the double-shuffle and distribution relations give all relations among multiple polylogarithms at $N$-th roots of unity. For composite $N$, the source explicitly states that these relations do not provide all relations; the prime, weight-equals-depth case is left as a conjectural exception.