Real sheaves/Gromov–Witten correspondence for $K_{\mathbb P^2}$

Let $K_{\mathbb P^2}$ carry its natural real structure, with real locus $K_{\mathbb P^2}^{\mathbb R}$ restricting to $\mathbb R\mathbb P^2$. For each positive integer $d$, let $n_{0,d}^{K_{\mathbb P^2},\mathbb R}$ be the genus-zero degree-$d$ real Gopakumar–Vafa invariant, and let $M_{d,1}(\mathbb R)$ be the real locus of the moduli space $M_{d,1}$, with Euler characteristic $e(M_{d,1}(\mathbb R))$. Real sheaves/Gromov–Witten conjecture. For every positive integer $d$, one has

$$n_{0,d}^{K_{\mathbb P^2},\mathbb R}=(-1)^{\frac{d-1}{2}}e(M_{d,1}(\mathbb R)).$$

This conjecture proposes a direct correspondence between real Gromov–Witten/Gopakumar–Vafa invariants of the local projective plane and Euler characteristics of real sheaf moduli spaces. The source gives no resolution in the provided text.