Curvature-dimension failure conjecture for sub-Finsler Carnot groups

Let $G$ be a sub-Finsler Carnot group, endowed with a positive smooth measure $\mathfrak m$. For $K\in\mathbb{R}$ and $N\in(1,\infty)$, consider the curvature-dimension condition $\mathsf{CD}(K,N)$ on the metric measure space $(G,\mathsf d_{SF},\mathfrak m)$.

Sub-Finsler Carnot group curvature-dimension conjecture. The metric measure space $(G,\mathsf d_{SF},\mathfrak m)$ does not satisfy the $\mathsf{CD}(K,N)$ condition for any $K\in\mathbb{R}$ and $N\in(1,\infty)$.

The paper proves this assertion for the sub-Finsler Heisenberg groups, for arbitrary reference norms and positive smooth measures. The conjecture concerns extending that failure to all sub-Finsler Carnot groups and was previously formulated in the cited work.