Where does the final -ς in genitive feminine singularis -ᾱς/-ης/τῆς come from?

Question

The declination pattern for the case endings, as well as the article ὁ, ἡ, τό, seems to fairly closely match that of the grammatical endings you find in Latin:

Case	Latin	Greek	Latin	Greek	Latin	Greek
NOM	-us	-ος	-a	-α/-η	-um	-ον
VOC	-e	-ε	-a	-α/-η	-um	-ον
ACC	-um	-ον	-am	-αν/-ην	-um	-ον
GEN	-ī	-ου	-ae	-ᾱς/-ης	-ī	-ου
DAT	-ō	-ῳ	-ae	-ᾱͅ/-ῃ	-ō	-ῳ
ABL	-ō	—	-ā	—	-ō	—

The -us/-ος similarity is plain to see (and makes perfect sense considering how Old Latin /-os/ was raised to /-us/); the same pattern happened with Old Latin /-om/ > /-um/, and the interchangability of /m/ and /n/ we see in several other languages, such as German -n for accusative, but English or Norwegian -m for the same (him/ham for instance) is a common pattern in Germanic and Latin languages, as far as I know. Thus we have a place for the accusative -um/-ον|-am/-αν/-ην relationship. The relationship between -ō and -ου/-ῳ are again plain enough to see, as well as -ae/-ᾱͅ/-ῃ (considering the overlapping of the dative and ablative in Latin with the genitive and dative in Greek). The odd one out, it seems, is the -ᾱς/-ης in genitive feminine singularis.

Viewing the etymology of the Greek article on Wiktionary, we are informed that it stems from PIE *só, *séh₂, *tód, almost exactly matching ὁ, ἡ, τό; I would assume the initial s- was muted fairly early on, and the same for the final -d.

I have by way of Latin and German come to expect /-m|-n/ and /-s/ to be signs of an accusative (and verily the /-s/ is exactly what you find in the plural both in Latin and in Greek (though not in German). How did that pesky /s/ end up sneaking its way into the Greek genitive feminine singularis, and not in masculine/neuter?

Answer 1

It's the other way around, actually: Latin lost this -s, and Greek retained it! In older Latin, and fossilized phrases like pater familiās "father of the household", you see the genitive singular in -ās.

The standard explanation I've seen for this change is influence from the second declension (-us -ī). The second declension in Latin originally had a nominative plural looking something like -oi (as in Greek), and ended up with a similar genitive singular, so by analogy the first declension nom pl -ai spread to the gen sg. Later, final -oi became -oe became -ī, as seen in Classical times.

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P.S. So where did this second-declension genitive singular marker come from?

The predecessor of the genitive singular for the second declension is reconstructed as *-os-yo, as seen in Sanskrit -asya, Homeric Greek -oio, and Old Latin -osio. In Attic, -oio got contracted to -ou, as expected. But in Latin, -osio got completely displaced by a different form…of unclear origin. So the best we can say is that it happened somewhere in the Old Latin period and we're not sure why.

Answer 2

You have it backwards. The sigma is original. From Sihler 263.7:

Gen.sg. PIE *-es, *-os, *-s are all attested forms of the gen.sg. marker and all three would yield much the same results in the historically attested IE languages when added to the stem *-eH₂-. Most authorities assume a full grade form, and G ending-accented forms in *-ᾱς, Att.-Ion. *-ης, are easier to explain if one starts from *-éH₂os (48) or *-éH₂es.

The ending is attested unchanged, apart from regular phonetic developments, in InIr., Gmc., Celt., G, and Ital. It is retained in Sab., but in L it occurs only in a few forms in inscriptions and early authors, as MOLTAS 'multae' and Enn. viās. But if survived in fossilized phrases, of which pater familiās 'head of the household' is doubtless the best known, and also in several adverbs like aliās 'at another time/place'.

The usual L ending in -ae is a purely L creation. Its makeup is revealed in its OL manifestations like Plaut. fīliāī gen.sg. 'daughter': -ī imported from the o-stems (**259.8B) was added to the stem in -ā-.