0-coconnectivity conjecture for the loop scheme of a smooth affine scheme

Let $Z$ be an affine smooth scheme of finite type over the ground field, viewed as a $0$-coconnective DG scheme, and let $Z\qqart$ denote its loop DG scheme. 0-coconnectivity conjecture. The DG scheme $Z\qqart$ is $0$-coconnective. This is a special case of the question of which classical schemes have $0$-coconnective loop schemes; the paper notes that the property can fail for non-smooth schemes but gives no resolution of this smooth affine case.