The Antieau-Williams sharp topological period-index conjecture

Let $X$ be a finite $2d$-dimensional CW-complex, and let $\alpha\in\operatorname{Br}(X)$ have period

$$m=p_1^{r_1}\cdots p_k^{r_k}.$$

Here $v_{p_i}$ denotes the $p_i$-adic valuation.

Antieau-Williams' conjecture.

$$\operatorname{ind}(\alpha)=m^{d-1}\prod_{i=1}^{k}p_i^{v_{p_i}((d-1)!)}.$$

This formula is presented as a conjectural strengthening that would include the stated six-dimensional examples. The source does not provide evidence that this sharper conjecture has been resolved.