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It's not proven at all. He takes speculative jumps to close gaps:

> My conclusion is that his younger sister, Queen Nana (AD 295–337), married King Mirian III of Caucasian Iberia (AD 290–362).

In a footnote he admits that the ancestry of the wife of Mirian III is unknown.

Yes, I noticed that, but that is a different kind of problem.

There's no such thing as a proven genealogy extending back so far. Such a proof cannot exist.

But as far as reasonably-well-documented claims go, going back to Saxon times is not even impressive on a worldwide basis.