Blackadar–Handelman Choquet simplex conjecture for dimension functions

Let $A$ be a $C^*$-algebra, and let $DF(A)$ denote its affine space of dimension functions.

Blackadar–Handelman Choquet simplex conjecture. The affine space $DF(A)$ is a Choquet simplex for any $C^*$-algebra $A$.

This is the second Blackadar–Handelman conjecture discussed in the paper. The paper obtains classes of algebras for which it holds by combining the first conjecture with finiteness of the extreme boundary of the quasitrace simplex, but the assertion for arbitrary $C^*$-algebras remains open.