In Satan in Goray, Isaac Bashevis Singer mentions several ways in which it's "proven" that Shabbtai Tzvi is the Messiah:
During the time Rabbi Benish still dwelt in Lublin he had heard amazing things. All men were discussing the Jerusalemite rabbinical emissary, Baruch Gad, who, in journeying through a desert, had blundered across the other side of the river Sambation; he had brought back with him a parchment letter from the Ten Lost Tribes supposedly written by the Jewish king, Achitov, the son of Azariah.
The greatest cabalists in Poland and other lands uncovered numerous allusions in the Zohar and in antique cabalistic volumes proving that the days of the Exile were numbered. Chmelnicki's massacres were the birth-pangs of the Messiah.
Satan in Goray, part 1, chapter 3: "Extraordinary Rumors" (translated by Jacob Sloan)
Now, I now that the basic backdrop of Shabbtai Tzvi and his "prophet" Nathan are true events; I remember reading about those in my history book. But how accurate are these mentions of other rumors? (There are other rumors of mystical happenings in the chapter, but I couldn't type out half the chapter into the question.)
Were these rumors of mystical happenings based on actual rumors from the time of Shabbtai Tzvi? Was this letter from the Ten Tribes based on something - a hoax, even - from the time period?
How historically accurate are the "extraordinary rumors" presented in this chapter when compared to actual rumors at the time of Shabbtai Tzvi?