The quarter-order bound for power domination in connected hypergraphs

Let $\mathcal{H}=(V(\mathcal{H}),E(\mathcal{H}))$ be a connected hypergraph on at least four vertices, with every edge $e\in E(\mathcal{H})$ satisfying $|e|\geq 3$. Write $\gamma_{P}(\mathcal{H})$ for its power domination number and $\gamma_{P_{I}}(\mathcal{H})$ for its infectious power domination number.

Quarter-order bound.

$$\gamma_{P_{I}}(\mathcal{H})\leq\gamma_{P}(\mathcal{H})\leq\frac{|V(\mathcal{H})|}{4}.$$

The conjecture proposes that the observation or infection step improves the general domination bound from $|V(\mathcal{H})|/3$ to $|V(\mathcal{H})|/4$ for connected hypergraphs whose edges all have size at least three. Its status is not resolved in the supplied source context.