It seems agreed upon that one or more representatives from Lvov traveled to either investigate, visit or out Shabtai Tzvi in 1666 when he was still claiming to be the mashi'ach. Immediately following this meeting he [at least nominally] converted to Islam. It also seems accepted that the visitors had some relationship to the Ta"z, who was the av bes din at the time.
Encyclopedia Judaica has at least three conflicting stories of the nature and events of this meeting written by three different authors - one of whom (Abraham David) cites the work of another (Gershon Scholem) as a source. And I've heard yet other versions elsewhere.
What really happened? Who was sent from Lvov? What was their mission? What happened at the meeting in Gallipoli?