No, the logical fallacy is yours because the ground of our belief is not something that is merely in the realm of logic or thought. There is no circular assumption of authority because our belief is grounded, not just by claims of authority, but by things that happened in space/time history. Events of the past are not just a logical or mental construct of some kind. Your assumption that our beliefs are grounded merely in circular claims of authority is false.
Cordially,
Quite the contrary. Chrstianity acknowledges the Revelation at Sinai, which also occurred historically. Chrstianity then claims to be the "fulfillment" of that Revelation, despite the fact that that Revelation requires no further "fulfillment" whatsoever. All chrstians can do is point to messianic prophecies and claim J*sus fulfilled them based on his own, chrstianity's, and the "new testament's" claims that he did so.
The fact that the claims of chrstianity are based on historical events itself means nothing. Many religions are based on historical events. Mormonism claims that "gxd" appeared to Joseph Smith. Catholics claim that a great multitude (including atheists) witnessed the "miracle of the sun" on October 13, 1917. Does that make mormonism or Catholicism true? Of course not.
The Revelation at Sinai, unlike every other claim of revelation in history, was a national revelation in which some three million people experienced the Revelation of G-d Himself. Chrstianity acknowledges this. On what basis, then, does it claim to "fulfill" this Revelation? On the basis of its own claims, which are assumed to be "self-evidently true" and "self-evidently authoritative." They are neither.
Better sit down. You're going to get dizzy.