Short-time existence conjecture for three-dimensional complete Ricci flows with non-negative Ricci curvature

Let $(M^3,g_0)$ be a $3$-dimensional complete Riemannian manifold with non-negative Ricci curvature, meaning $\operatorname{Ric}(g_0)\geq 0$. A Ricci flow is a smooth family of metrics satisfying

$$\frac{\partial}{\partial t}g(t)=-2\operatorname{Ric}(g(t)).$$

Short-time existence conjecture. There exists $T>0$ and a smooth family of complete metrics $g(t)$ on $M\times[0,T)$ such that $g(0)=g_0$ and $g(t)$ solves the Ricci flow equation on $M\times(0,T)$.

This is the three-dimensional short-time existence problem for complete initial metrics under a non-negative Ricci-curvature assumption. The source presents it as a well-known conjecture arising naturally from Shi's work; the supplied text gives no resolution, so its status is open.