Sikora's conjecture relating the recurrence ideal and the A-ideal

Let $K$ be a knot, let $\mathcal A_K$ be its recurrence ideal in the quantum torus, and let $\mathcal A_K^\sigma$ be its invariant part under $\sigma(M^kL^l)=M^{-k}L^{-l}$. Let $\varepsilon$ denote specialization at $t=-1$, let $\mathfrak p$ be the $A$-ideal of $K$, and let $\sqrt{\,\cdot\,}$ denote the radical of an ideal.

Sikora's conjecture.

$$\sqrt{\varepsilon(\mathcal A_K^\sigma)}=\mathfrak p.$$

The conjecture compares the classical algebraic information from the $A$-ideal with the specialization of the quantum recurrence ideal. It was proposed by Sikora, and its resolution is not indicated in the supplied text.