The cubic hypergraph bootstrap quadratic running-time conjecture

Let $M_4^3(n)$ be the maximum running time of the $K_4^3$-bootstrap process over all initial $3$-uniform hypergraphs on $n$ vertices. The paper gives a quadratic lower bound for this process. Quadratic running-time conjecture.

$$M_4^3(n)=O(n^2).$$

Together with the paper's quadratic lower bound, this would determine the running time up to a constant factor. The supplied text does not state a resolution.