A Special $Π^0_1$ Class with the Join Property but without Pseudojump Inversion

Jananthan and Simpson showed that special $Π^0_1$ classes exist in three of the four possible cases determined by whether the Join Property and the Pseudojump Inversion Property hold, leaving open the existence of a special $Π^0_1$ class with the Join Property but not the Pseudojump Inversion Proper