Root-system realization conjecture for extended restricted roots

Suppose that $\tilde{\Phi}$ is not of type $\mathsf{B}\mathsf{C}$. Let $\tilde{\mathbf A}$ be the Cartan matrix whose realization is given by the vector space ${}^e\!{\mathfrak s}$, the extended restricted roots ${}^e\!{\tilde{\Phi}}$, and their coroots ${}^e\!{\tilde{\Phi}}\spcheck$. Let $\Psi$ be the root system of the associated Kac–Moody algebra. Root-system realization conjecture. Then

$$\Psi={}^e\!{\tilde{\Phi}}.$$

This conjecture asks whether the extended restricted roots form exactly the root system associated with the displayed Cartan matrix, clarifying the relation between the extended restricted root system and its Cartan matrix. The source gives no resolution or partial result here.