The normal-complex diameter conjecture

Let $C$ be a pure normal simplicial complex of dimension $d-1$ with $n$ vertices. Normal-complex diameter conjecture. The diameter of $C$ is at most

$$(n-1)d.$$

This conjecture strengthens the polynomial Hirsch conjecture by imposing normality rather than considering arbitrary complexes. The source presents it as a conjecture motivated by known bounds for normal complexes; its resolution is not stated.