Stieltjes-property conjecture for the diagonal two-point function

Let $G_{aa}$ be the diagonal matrix two-point function of the $\lambda\phi^4_4$ model on noncommutative Moyal space, and let $\lambda_c$ denote the critical coupling. In the limit of infinite noncommutativity, consider $G_{aa}$ as a function of $a$.

Stieltjes-property conjecture. The function $a\mapsto G_{aa}$ is a Stieltjes function for

$$\lambda_c<\lambda\leq 0.$$

The Stieltjes property is presented as necessary for reflection positivity, and the numerical results provide strong support without a proof. The text also reports that the property is excluded outside the window $[\lambda_c,0]$ according to the numerical analysis.