Mharman said this back in May, but he tends to be pretty consistent with his modding when it comes to numbers:
"the rule i operate with is that town should be able to survive as many mislynches as there are scum. Vaarka taught me that, so I refer to it as Vaarka's Golden Rule (he may have been taught by someone else, but idk who). I taught the concept to Whiteflame and Casey btw. 9players, 2 scum. 13 players, 3 scum. 17, 4. So 5,9,13,17,etc is a sequence in those numbers halfway between numbers in a sequence, I put 0.5 scum, a tp.
So since two mislynches equals a town loss, going by mharmans logic, I am guessing there could be one scum and one third party, since this game is an in between number of that sequence.
There is the off chance that mharman didn't stick to that logic, so take this with a grain of salt, but if mharman is consistent with this then there is probably just one scum (with a fake claim) and one third party (not sure if he would have given a third party a fake claim, and he didn't clarify in the OP). So characters claims may be useless here, or at best only might expose a third party.