Herzog's generalized eventual cotangent homology conjecture

Let $\varphi\colon R\to S$ be a map of commutative noetherian rings that is locally of finite flat dimension. The cotangent homology modules are denoted by $\operatorname{T}_n(S/R,S)$.

Herzog's generalized conjecture. If

$$\operatorname{T}_n(S/R,S)=0$$

for $n\gg0$, then $\varphi$ is locally complete intersection.

This statement is presented as equivalent to Herzog's conjecture for quotients of regular local rings, and would strengthen known results on detecting locally complete intersection maps through cotangent homology. The supplied resolved status should be verified against the paper's simultaneous statement that the conjecture remains open in general.