Quillen's conjectures on André–Quillen homology

Let $\varphi\colon R\to S$ be a ring homomorphism, and let $\operatorname{D}_n(S\!\mid\!R,-)$ denote André–Quillen homology with arbitrary coefficients. Quillen's conjectures. Assume that $\varphi$ is essentially of finite type.

(a) If $\varphi$ is locally of finite flat dimension and $\operatorname{D}_n(S\!\mid\!R,-)=0$ for all $n\gg 0$, then $\varphi$ is locally complete intersection.

(b) If $\operatorname{D}_n(S\!\mid\!R,-)=0$ for all $n\gg 0$, then $\operatorname{D}_n(S\!\mid\!R,-)=0$ for all $n\geqslant 3$.

These are two conjectures discussed together in the source; the first is attributed there as solved by Avramov, while the supplied status information does not separately resolve the second.