The good-function conjecture for hypergraph matching

Let $H=(V,E)$) be a hypergraph. A function $g$ on the edges of $H$ is called good for $H$ in the sense of the paper's preceding proposition, which characterizes the weighted matching guarantee used in its algorithmic framework.

Good-function conjecture. If

$$g(e)=\frac{1}{|e|-1+1/|e|}$$

for every edge $e$ of $H$, then $g$ is good for $H$.

This conjecture would, in particular, imply the Füredi–Kahn–Seymour conjecture. The supplied context does not provide the full definition of “good” or evidence that the conjecture has been resolved.