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Stories involving time-travel often suggest that history can be changed, like in Back to the Future or Star Trek (2009). However, some such stories suggest that all events within a given timeline are set in stone, and that time-travel to the past merely fulfills history, rather than altering it. A good example of this would be the film, Predestination. See also Novikov's self-consistency principle.

Can anyone help me track down the earliest known example of such a story, within movies, TV, published literature or comics?

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    From an information perspective any prophecy especially the ironically self fulfilling kind would be consistent time travel for the information. So while not really the question a minor trivia case could be made for some mythology and religious events. The Greek Cassandra story comes to mind. I suspect Heinlein is early example of time travel so self consistent it's circular. HG Wells' the Time Machine i don't recall being concerned about changing things or paradoxes thus is implicitly self consistent time. I believe that's considered first mechanical time travel vs getting a concussion. Jan 1 at 22:20
  • It's certainly a well-worn trope; it's been around long enough for Douglas Adams to parody in The Restaurant at the End of the Universe
    – Spencer
    Jan 1 at 22:23
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1881: The TVTropes page for Stable Time Loop suggests "The Clock That Went Backward" (1881) by Edward Page Mitchell.

Two students at the University of Leyden learn about a pivotal battle that occurred there 300 years earlier, then find themselves hurtled back to the battle and becoming key players in the outcome.

Of course the page also notes that if informational time travel (as opposed to physical) is counted then any self-fulfilling prophecy (going back at least to the Greeks) might count.

This trope is actually Older Than Feudalism, since, while time travel is a relatively new concept, prophecy (which is basically information time travel) is not, and Self-Fulfilling Prophecy is the earliest form of stable time loop.

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