Ketterer’s synthetic curvature conjecture for general $N$-warped products

Let $B$ be a metric-measure base of dimension $d$, let $F$ be an essentially non-branching metric-measure space, and let $f$ be a Lipschitz nonnegative warping function. Let $B^\dagger$ be obtained by gluing two copies of $B$ along the closure of the boundary points where $f$ is nonvanishing, and let $f^\dagger$ be the tautological extension. Write

$$K_F=\sup_B\bigl(Kf^2+|Df|^2\bigr),$$

where $Df$ is the Alexandrov differential. General $N$-warped-product curvature conjecture. The $N$-warped product of $B$, $F$, and $f$ satisfies $\mathsf{CD}(K(N+d-1),N+d)$ if $B$ is $CBB(K)$, $f$ is $fK$-concave, $B^\dagger$ has $CBB(K)$ and $f^\dagger$ is $fK$-concave, and $F$ is an essentially non-branching $\mathsf{CD}(K_F(N-1),N)$ space. This proposes a synthetic curvature-dimension theorem extending the preceding smooth and interval-base results; the source presents it as a conjectural general statement.