Elementary Type Conjecture in Lego form

A cyclotomic pro-$p$ pair is a pro-$p$ group equipped with its cyclotomic character; a pair is of Galois type when it arises from a maximal pro-$p$ Galois group, and finite rank means that its first cohomology has finite $\a0\mathbb{F}_p$-dimension. Let $\operatorname{ET}_p$ be the minimal class of cyclotomic pro-$p$ pairs, up to isomorphism, containing the trivial pair $(1,1)$, the pairs $\mathcal{Z}^{\alpha}$ for $\alpha\in\mathbb{Z}_p^{\times,1}$, $\mathcal{E}$ when $p=2$, and the cyclotomic pro-$p$ pairs of $p$-adic type, and closed under extensions $\bar{\mathcal{G}}\mapsto\mathbb{Z}_p\rtimes\bar{\mathcal{G}}$ and free products.

Elementary Type Conjecture in Lego form. Every cyclotomic pro-$p$ pair of Galois type and of finite rank is in $\operatorname{ET}_p$.

This formulation says that finite-rank maximal pro-$p$ Galois groups can be assembled from the listed elementary building blocks using extensions and free products. The supplied text does not specify whether the conjecture has been resolved.