The Semispatha and the Saex

[Thomas V.]

Trouble is, Vegetius (II.15) is probably thinking of the old gladius and pugio arrangement as described in his source texts [..].

You might very likely be right: "Secundus liber ueteris militiae continet morem, ad quem pedestris institui possit exercitus."

So maybe there never was a Roman semispatha? Maybe Vegetius indeed just used the terminology of his time to describe the gladius and pugio arrangement of "the good old days" (in Epitoma Rei Militaris V. glorifies the past, after all) when writing about the spatha and semispatha arrangement?