*ǵʰésr̥'s inflection
Tom, not to go into great detail, but it is a matter of some scholarly debate at the moment of whether proterokinetic inflections exist at all. While the Erlangen and Leiden models reconstruct them, compositional models like those favored by Kiparsky, Halle, and Probert neither predict nor accept the existence of proterokinetic inflection. There has actually been a recent concerted effort by some to explain all proposed evidence for that paradigm (or indeed for paradigmatic inflection itself). We give the proterokinetic inflections here for *-tis, *-tus, *-us, and *-mn̥ because it is the traditional model, but there is in truth little unproblematic evidence to support the proposed paradigm. I might take a look at this Kiparsky paper to see this alternative view.