The general nilpotent nullhomotopy volume upper-bound conjecture

Let $Y$ be a $c$-step nilpotent space, and let $\operatorname{V\delta}^{n}_{Y}(L)$ denote its volume of nullhomotopies in degree $n$ at scale $L$. General nilpotent upper-bound conjecture.

$$\operatorname{V\delta}^{n}_{Y}(L)=O(L^{3nc}).$$

This conjecture proposes a refinement of the general upper bound for volume distortion of nullhomotopies in $c$-step nilpotent spaces. The surrounding results establish coarser upper bounds, while this sharper exponent is presented as expected and remains unresolved in the supplied text.