Need advice for testing of hypotheses related to the self-citation method

[Mauro]

To apply Bayes one does not need a prior probability at all. Indeed, discriminating between prior and evidence is ihmo unnecessary and misleading. Start from a condition of absolutely zero knowledge, that is to say P(H) = 0.5 and P(notH) = 0.5 This is the only 'prior' one needs, and it's trivial.

But that is not "no prior", it is "prior prob of hoax = 0.5".

We would have absolutely zero knowledge if hypothesis H was "the Hraxx is a foobar" and we have no idea of what those terms mean.  But even then, if the other party tells us that "note that, if it is not a foobar, it must be either a quxqux or a blooop", then should we set Prob(H) = 1/3?

Exactly as you said. But for simplicity it's preferabler to work with only one hypothesis. In the VMS case I'd propose H = meaningful versus notH = meaningless.

But we do have a lot of knowledge about the issue.  Everything we know about the VMS and its history, manuscripts from that time, the world as it was then, what people knew or could have known, how forgers and their marks would probably think and act... 

Yes of course, but nothing of the knowledge one has, needs to go into a 'prior'. Knowledge = evidence, and it can be uniformly treated as such without separating some of that evidence into a 'prior' and calling 'evidence' only what remains. That's why saying that 'the prior is the weak spot in the Bayes formula' is not correct. Assigning probabilities (or odds, which are easier to work with) is a big problem, yes, but this is true whichever epistemological method one uses, Bayesian or not Bayesian: all inductive reasoning is probabilistic, by its very nature. So the difficulty in determining the odds (of each piece of evidence) cannot be used as a criticism of Bayesian logic: it's a problem inherent in the data at hand, not a specific feature of Bayesian reasoning.

Can Bayesian logic (which, as you may have understood, I'm quite fond of) help with the VMS? Unfortunatley I'm not sure it can, even for the most basic case, meaningless vs. meaningful. We do have a lot of knowledge, but all those pieces of evidence point sometimes toward 'meaningful', sometimes toward 'meaningless', while most of them are equally probable under the meaningful or the meaningless hypothesis, and thus are of no help. I can't see how even Bayesian logic could shed light on this problem in this situation, but at least a Bayesian analyisis would require as a pre-requisite a one-stop list of all the available evidence, which would already be a precious resource (*).

(*) not an easy task, but one could start with a list in an online page where other people can add entries, wiki-style.