Mináč–Tăn's vanishing conjecture for higher Massey products

Let $F$ be a field, let $p$ be a prime, let $n\geq 3$, and let $\chi_1,\dots,\chi_n\in H^1(F,\mathbb Z/p\mathbb Z)$. The Massey product $\left\langle\chi_1,\dots,\chi_n\right\rangle\subset H^2(F,\mathbb Z/p\mathbb Z)$ is defined when it is non-empty, and it vanishes when it contains $0$.

Mináč–Tăn's conjecture. For every field $F$, every prime $p$, every $n\geq 3$, and all $\chi_1,\dots,\chi_n\in H^1(F,\mathbb Z/p\mathbb Z)$, if the Massey product

$$\left\langle\chi_1,\dots,\chi_n\right\rangle\subset H^2(F,\mathbb Z/p\mathbb Z)$$

is defined, then it vanishes.

This conjecture proposes that every defined higher mod-$p$ Massey product in the cohomology of an absolute Galois group contains zero. The triple-product case is known for arbitrary fields, while the general case remains open in the stated formulation.