The elementary type conjecture for finitely generated pro-$p$ Galois groups

Let $p>2$ be a prime and let $F$ be a field containing a primitive $p$-th root of unity. Write $F(p)$ for the maximal $p$-extension of $F$, let $G=\operatorname{Gal}(F(p)/F)$, and let $\gamma_F$ denote the cup product pairing associated with $F$. A finite $p$-quaternionic pairing is of elementary type if it can be constructed from pairings of weakly $p$-local type by taking direct products and group extensions by nontrivial elementary abelian $p$-groups. Elementary type conjecture. If $G$ is a finitely generated pro-$p$-group, then the cup product pairing $\gamma_F$ is of elementary type. This conjecture proposes a structural classification of finitely generated maximal pro-$p$ Galois groups, using the direct-product and group-extension constructions described above; its resolution is not established by the supplied text.