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I remember in The Chamber of Secrets during the flashback scene that while Dumbledore distrusted Riddle, there didn't seem to be any indication that he knew that Tom was the one unleashing the basilisk. That said, we also know Dumbledore is a great chess master and may not have had a reason to show he knew at that time. At the same time, we can't know if Dumbledore could at the time verify Hagrid's innocence (or even knew of it himself). It wasn't until Armando Dippet retired that Dumbledore was able to hire Hagrid, and at that point there may or may not have been several intervening years for Dumbledore to discover the true culprit.
Is there conclusive canon evidence to show if or if not Dumbledore knew the true culprit during the first time the chamber was opened?