Massey vanishing conjecture for Galois cohomology

Let $k$ be a field, let $p$ be a prime, and let $n\geq 3$. For cohomology classes

$$\alpha_0,\dots,\alpha_{n-1}\in H^1(k,{\mathbf F}_p),$$

consider the $n$-fold Massey product $\langle\alpha_0,\dots,\alpha_{n-1}\rangle\subseteq H^2(k,{\mathbf F}_p)$. Massey vanishing conjecture. If this Massey product is non-empty, then it contains $0\in H^2(k,{\mathbf F}_p)$. The conjecture extends the vanishing of triple Massey products from coefficients in ${\mathbf F}_2$ to all primes and all lengths, and connects arithmetic Galois cohomology with the topology of link complements. It remains open in general.