The extension-frequency conjecture for unramified [2,2]-extensions

Let $K$ be a cyclic cubic field. An unramified $[2,2]$-extension means an unramified extension of $K$ with Galois group $[2,2]$, and an unramified $\langle8,4\rangle$-extension means one with that Galois group.

Extension-frequency conjecture. Precisely one half of unramified $[2,2]$-extensions of cyclic cubic fields extend to unramified $\langle8,4\rangle$-extensions.

The conjecture is motivated by the observed split between the tower groups $[2,2]$ and $\langle8,4\rangle$ and is intended to reconcile extension frequencies with the Rubinstein–Salzedo data. It remains open in the source.