Milnor's conjecture on dilogarithm values at roots of unity

For an integer $N\geq 3$, let $D_2$ denote the Bloch–Wigner dilogarithm, and consider the real numbers $D_2(e^{2\pi\sqrt{-1}j/N})$ indexed by integers $j$ relatively prime to $N$ with $0<j<N/2$. Milnor's conjecture. For each integer $N\geq 3$, these real numbers are linearly independent over $\mathbb{Q}$. The conjecture is motivated by the interpretation of $D_2$ as the volume of an ideal tetrahedron and connects dilogarithm values with hyperbolic geometry and $K$-theory; its resolution status is not specified in the source.