An old question just popped up in my mind, and it first came cross to me when I was being taught the various forms of εἰμί; it’s the apparent and inexplicable irregularity of the present active participle of εἰμί. I was using the Hansen and Quinn, but the book contained no explanation as to the origin of this alien formation, other than that it “is irregular”. The book mentions that all forms of εἰμί are built on the full grade stem ἐσ- and zero grade stem σ-.
My first thought was that the initial sigma must have dropped out from an imaginary *σών, σόντος, as they regularly do in Greek. Then my mind drifted to the lack of the spiritus asper, and then that athematic verbs have participle suffix without the theme vowel, so it couldn’t be *σών, which would imply prehistoric *σόντς.
If εἰμί were a regular athematic verb, I’d expect the participle to take the weak stem (as they do in τίθημι, as τιθέ-ντ-; ἵστημι, as ἱστά-ντ-) in σ- with the participle endings attached directly, giving rise to monstrosities *σντς, *σντός (!). If the participle marker drops out (as it does in the nominative, cf. τιθεῖς), the former becomes a more bewildering *σς.
I tried to look into Smythe for verbs like εἰμί, but apparently it is the only verb (in the active voice at least) that has a consonant stem and doesn’t take a thematic vowel.
Of course, I’m simply letting my imagination run wild on this post, because I’m no historical linguist, but I’d be interested to hear your take on the origin of the participle. I don’t believe that the Greeks simply invented a form out of thin air for εἰμί, but I can’t otherwise find any satisfactory explanation as to its etymology.