Where does the -τ- come from in the oblique stem of some Greek neuter nouns with nom/acc sing forms in -ς?

Question

I just learned that some Greek neuter nouns of the third declension with a nominative/accusative singular form ending in -ς have oblique stems in -τ-, which surprised me.

I expected τ-stem neuter nouns to have a nominative/accusative singular that simply drops the -τ-, and s-stem nouns to simply have loss of intervocalic s in the oblique forms (as in γέρας, γέραος/γέρως).

A Wiktionary appendix makes a vague but somewhat informative comment about the appearance of -τ- in -μα, -ματ- words and -r/-n- heteroclites (which seem to be fairly well represented in Greek; e.g. ἧπαρ, ἥπατος):

Interestingly, the τ in the stem is a common feature of Ancient Greek words derived from PIE neuter n stems, which is not well explained.

However, I haven't heard before of s/n heteroclites, so I'm not sure if this is related to the appearance of -t- in the oblique stems of neuter nouns ending in -s.

The original example I ran into was κέρας/κέρᾰτ-, from this discussion. It apparently was variable in declension.

A bunch of other examples I took from Wiktionary: οὖς, σταῖς (Wiktionary suggests "influence from" στέαρ), φῶς, ἅλας, δέρας, πέρας, τέρᾰς, ὄπεᾰς (Wiktionary suggests it replaced older *ὄπεαρ), κρέας (variable), (also πᾰ́γκρεᾰς), σέλᾰς (variable), ἐρῠσῐ́πελᾰς

Answer 1

This appears to be a mostly or wholly Greek-internal analogical development. It's actually not confined to neuters. Some animates with nom. in -ς show variation between stems without and without -τ-, e.g. γέλως, Homeric acc. γέλω vs. Attic γέλωτα, and similarly for ἔρως, ἱδρώς, χρώς. These are original s-stems (cf. the Latin type honōs) that acquired a stem in -t- by analogy with animate t-stems. Presumably the analogy was then extended to neuters. It's often hard to figure out why a specific analogy happened, but in this case it might have to due with simplicity of declension (not having to deal with vowel contractions).

This added -t- occurs outside of this class, too, most notably in the -μα neuters you mention. There's also the type χάρις, gen. χάριτος but acc. χάριν, where the -t- only appears in part of the declension. There are other scattered examples, e.g. δαίς-δαῖτα (cf. δαίομαι), and even ἄναξ, which has inscriptional t-less forms like ϝανακων.