The conjecture on TF-equivalence classes and cones of g-vectors

Let $\Lambda$ be a finite-dimensional algebra, let $K_0(\operatorname{proj}\Lambda)_{\mathbb{R}}$ be its real Grothendieck group, and let $g$ be a g-vector. Write $[g]_{\operatorname{TF}}^{\circ}$ for the interior of the $\operatorname{TF}$-equivalence class of $g$, and let $\operatorname{ind}(\mathbb{N}g)$ denote the set of indices associated with the nonnegative integer multiples of $g$. For a set of vectors, write $\operatorname{Cone}^{\circ}$ for the relative open cone that they generate. The conjecture. One has

$$[g]_{\operatorname{TF}}^{\circ}=\operatorname{Cone}^{\circ}\{\operatorname{ind}(\mathbb{N}g)\}.$$

This is a modified version of a conjecture of Asai and Iyama concerning $\operatorname{TF}$-equivalence classes and generic decompositions of g-vectors. The equality is known under additional hypotheses such as $E$-tameness or heredity, while the general case remains open.