Quandle-ring cocycle enhancement for prime knots up to 12 crossings

Let $X$ be a quandle and let $\phi:X\times X\to A$ be a $2$-cocycle. Let

$$Y=\mathcal{I}(\mathbb{Z}_2[X])$$

be the set of idempotents in the quandle ring $\mathbb{Z}_2[X]$, assume that $Y$ is a quandle, and let $\psi:Y\times Y\to A$ be a $2$-cocycle. Quandle-ring enhancement conjecture. The cocycle invariant $\Psi_{(Y,\psi)}(K)$ is an enhancement of the cocycle invariant $\Phi_{(X,\phi)}(K)$ for all prime oriented knots up to 12 crossings. The conjecture is based on computations distinguishing the listed knots and proposes that passing to idempotents in a quandle ring yields strictly more informative cocycle invariants in this range.