Lorentzian warped-product timelike curvature-dimension conjecture

Let $I$ be an interval, let $F$ be a non-branching metric-measure space with metric $d_F$ and measure $\operatorname{m}_F$, and let $f$ be the warping function in the Lorentzian $N$-warped product of $-I$, $F$, and $f$. Define

$$K_F=\sup_I\bigl(Kf^2-(f')^2\bigr).$$

Lorentzian warped-product timelike curvature-dimension conjecture. If $f”-Kf\leq0$ and $(F,d_F,\operatorname{m}_F)$ is non-branching and satisfies $\mathsf{CD}(K_F(N-1),N)$, then the $N$-warped product of $-I$, $F$, and $f$ satisfies $T\mathsf{CD}(-KN,N+1)$. This is presented as a general conjecture following a theorem for $T\mathsf{MCP}$; no resolution is given.