Noetherianity conjecture for fixed subgroups of untwisted automorphisms

Let $A_\Gamma$ be a right-angled Artin group, let $\mathcal{U}\mathsf{Aut}(A_\Gamma)$ denote its untwisted automorphism group, and for an automorphism $\varphi$ define

$$\operatorname{Fix}(\varphi)=\{g\in A_\Gamma\mid \varphi(g)=g\}.$$

Order these fixed subgroups by inclusion.

Noetherianity conjecture. The set

$$\{\operatorname{Fix}(\varphi)\mid \varphi\in\mathcal{U}\mathsf{Aut}(A_\Gamma)\}$$

contains no infinite chain under inclusion.

This is a descending-chain or ascending-chain finiteness assertion for fixed subgroups arising from untwisted automorphisms. The supplied text gives no resolution status or further evidence, so the conjecture remains open in the database.