Traczyk's infinite-generation conjecture for skein modules of simply connected 3-manifolds

Let $M$ be a simply connected $3$-manifold, possibly with holes, and let $S_{2,\infty}(M)$ denote its Kauffman bracket skein module at parameter $2$ and infinity. Traczyk's conjecture. If $M$ is other than $S^3$, then $S_{2,\infty}(M)$ is infinitely generated. This conjecture contrasts with the finite-generation result for small $3$-manifolds established in the surrounding discussion; its status is not determined by the supplied text.