The strongly stratified and locally conical reflection arrangement conjecture

Let $W$ be a well-generated reflection group acting on a complex vector space $V$. A frame $\Lambda$ is the auxiliary structure used to define the properties strongly stratified and locally conical for the system $(W,R,\Lambda)$. The strongly stratified and locally conical reflection arrangement conjecture. For each well-generated reflection group $W$, there exists a generating set $R$ and a frame $\Lambda$ such that

$$|R|=\dim V,$$

$(W,R,\Lambda)$ is strongly stratified, and $(W,R,\Lambda)$ is locally conical. This is proposed as a partial extension of the paper's preceding results on stratification and conicality; the existence of such a generating set and frame is not established in the supplied text.