The equivalence conjecture for sealing principles

Assume that there are unboundedly many Woodin cardinals and that the class of measurable cardinals is stationary. The principles $\sf{Sealing}$, $\sf{Sealing}^+$, $\sf{Weak\ Sealing}$, $\sf{Sealing}^-$, and $\sf{Tower\ Sealing}$ are the theories defined in the paper. The equivalence conjecture for sealing principles. Under these assumptions, the following are equivalent:

$$\sf{Sealing},\quad \sf{Sealing}^+,\quad \sf{Weak\ Sealing},\quad \sf{Sealing}^-,\quad \sf{Tower\ Sealing}.$$

The conjecture is proposed as an ultimate analogue of the cited main result of Steel. The supplied passage does not state that it has been proved or refuted.