How did PIE *h₂énti-h₃kʷós get lengthened to Proto-Italic *antīkʷos?

Question

The word antīquus has a long vowel in the middle, but the proposition ante is short; indeed, if I am not mistaken (it has been a while since I read and wrote about Saturnian), both of its morae are short. If looking at only the word ante, we notice that its origin is the same as the first half of antīquus (*h₂énti), and the Greek is indeed with a short i (ἀντί: /an.tí/), as is also the Sanskrit (अन्ति (ánti)).

The vowel length of Classical Latin antīquus, according to what is stated at Wiktionary, goes back to Proto Italic. Now, I don’t know which Greek cognates (if any) there are, but Wiktionary lists अन्तिक (antika) for Sanskrit, again with the short vowel. My question thus, restated: How did the i in antīquus get lengthened, all the way back in its Proto Italic form *antīkʷos, when this does not seem to appear in its cognates, nor in Latins own ante¹?

¹ Though that could be iambic shortening and lowering, I presume.

Answer 1

A laryngeal following a vowel disappears (after colouring that vowel if it's *e), lengthening that vowel. This process is most prominent within roots, since ablaut means *e ends up next a laryngeal especially frequently, but it happens across morpheme boundaries within a word as well. In this case, the *h₃ at the start of *-h₃kʷós lenghtened the *i at the end of *h₂énti-, even though they're separate members of the compound word.

The Sanskrit antika, though strikingly similar, is not actually cognate: the first part does also reflect *h₂enti- (the locative singular of *h₂ent- 'front'), but the second part is the adjective-forming suffix *‑kos, which does not start with a laryngeal, rather than the zero-grade root *‑h₃kʷ- 'to see' and the thematic termination *‑os seen in the Latin.
In a satem language like Sanskrit, the labiovelar *kʷ ended up falling together with the plain velar *k, so the only clue that these two words aren't cognate is the length of that vowel, as you spotted—etymology is a subtle science.