2 problems

Sard conjecture. For every $x\in M$ and every integer $r\in[m,n-1]$, the set $\operatorname{Abn}^{r}_{\Delta}(x)$ has zero Lebesgue measure in $M$.

Minimal rank Sard conjecture. For every $x\in M$, the set $\operatorname{Abn}^{m}_{\Delta}(x)$ has zero Lebesgue measure in $M$.