Cieliebak–Mohnke's monotone-extremal conjecture for projective space

Let $\omega_{\mathrm{FS}}$ denote the Fubini–Study form on $\mathbb{CP}^n$. For a closed Lagrangian torus $L\subset(X,\omega)$, call $L$ extremal when $A_{\min}(L)=C^{\mathrm{CM}}(X,\omega)$. Cieliebak–Mohnke's monotone-extremal conjecture. A Lagrangian torus in $(\mathbb{CP}^n,\omega_{\mathrm{FS}})$ is monotone if and only if it is extremal. The source explains that this would make extremal Lagrangian tori a replacement for monotone tori, which only exist in monotone symplectic manifolds, and states that the paper does not prove it.