Erez's class-group conjecture for the square root of the inverse different

Let $L/K$ be a weakly ramified Galois extension of number fields for which the square root of the inverse different $\mathcal{A}_{L/K}$ exists, and set $G=\operatorname{Gal}(L/K)$. Let $\Omega(L/K,2)$ be Chinburg's canonical $\Omega(2)$-invariant, and let $\mathcal{J}_{2,S,L/K}$ be the class-group element defined from the signs of the second Adams-operator-twisted modified Galois–Jacobi sums. Erez's conjecture. In $\operatorname{Cl}(\mathbb{Z}[G])$, one has

$$\Omega(L/K,2)=[\mathcal{A}_{L/K}]+\mathcal{J}_{2,S,L/K}.$$

The conjecture refines the comparison between the class of the square root of the inverse different, Chinburg's invariant, and root-number classes; the source explains that the correction term has order at most $2$ and that this conjecture contains Vinatier's odd-degree conjecture as a special case. Its status is not resolved in the supplied source.