An open question for $d$-tilting bundles on Geigle-Lenzing projective spaces

We construct a family of $2$-tilting bundles on a Geigle-Lenzing projective space of type $(2,2,p,q)$ via the action of iterated $2$-APR mutations. As an application, we give some non-examples for an open question raised by Herschend, Iyama, Minamoto and Oppermann in the paper “Representation theory of Geigle-Lenzing complete intersections”.