If I understood well what Wobbit said, and certainly an alternative that crossed my mind, is that an equally unprovable theory was that Geoffrey had a copy of the History of the Lombard in his bedroom and used it as a source when he was looking for a bunch of names for his fiction. This of course does not make Authari any more Arthur than any of the previous stuff on this thread, but at least it's not nearly as contrived.
This is exactly it. If you can make a reasonable case that Geoffrey had access to the Historia Langobardorum and a reasonable case that there were signifcant similarities between the stories then you can make the case that Geoffrey appropriated parts of the Historia Langobardorum for elements of his story about Arthur. This would be an interesting and academically worthwhile argument. However, sweeping statements like "Arthur was Authari" or even "Geoffrey stole the story of Arthur from Paul the Deacon's account of Authari" are much less valid. Geoffrey may have used elements of Paul's work for parts of his account but he demonstrably used a lot of other stories to flesh out his description of Arthur and this period of British history. The difference between this argument and the broader "Arthur was Authari" is the difference between academic research and Dan Brown.
As others have indicated, thinking about Arthur as a real person isn't very useful. Arthur is an amalgam of a lot of different stories. Some of them were based on the lives of various Celtic Kings. It looks like some of them came from Anglo-Saxon Kings. Others came from classical and biblical litterature and others, as would be the case with the Authari / Arthur, came from stories about medieval kings. Others would have been passed down through oral traditions with all the local variation that implies. Others were made up. If there was a Celtic (or Anglo-Saxon or Lombard or whatever) king called Arthur, then he bears very little resemblance to any of the various stories about him.
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