Valiant's conjecture for iterated matrix multiplication

Let $R$ be a field and let $A=\mathscr S$. For the iterated matrix multiplication polynomial $\textup{\textsf{h}}{\Xi}_{n,d}$, let ${w}(f)$ denote its width and let $\textup{\textsf{poly}}(n,d)$ denote polynomially bounded functions in $n$ and $d$.

Valiant's conjecture. Valiant's conjecture for $R$ is

$${w}(\textup{\textsf{h}}{\Xi}_{n,d})\notin\textup{\textsf{poly}}(n,d).$$

This is presented as an equivalent formulation of Valiant's original conjecture $\mathrm{VBP}\neq\mathrm{VNP}$, or, over characteristic different from $2$, the determinant-versus-permanent conjecture. Its resolution is not supplied here.