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So I'm trying to render the Irish name Ó Catháin in Primitive Irish, but my knowledge of Irish in general is pretty weak. According to Wiktionary, the ó is from PI avi 'grandson', the cath is from PI cattu 'battle', and the -áin is from the PI -agni, genitive of the diminutive -agnas.

Firstly, where does the double tt in cattu come from? Apparently it is from Proto-Celtic *katus, and I would have thought a geminate would be resistant to lenition - am I wrong or is it only orthographic or is Wiktionary just wrong? Secondly, as cattu is a u-stem, I'm not sure how the diminutive suffix should attach to it. Cattagnas, cattuagnas, cattovagnas or something else?

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Here's a thread on Oscan.

Matasovic gives PC *katu-, and cites an Ogam inscription RO-CATOS.

If there is something odd happening, it might reflect the origin. Matasovic gives two theories: an early loanword from Germanic (etc); or an epenthetic *a added to break up a *ktw- cluster.

However, I suspect it's something about the inscriptions. Just looking at Wikipedia, there are examples of form of words with and without doubling (it gives both MAQI and MAQQI for 'mac' and both AVI and AVVI for 'ó'. And there also seem to be cases of orthographic geminates being lenited: wikipedia gives MAQQI > maicc (ok), but also LUGUDECCAS > Luigdech and ANAVLAMATTIAS > Anfolmithe.

So I'd conclude: either the spelling was just random, or something complicated was going on.

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Thanks for this! Hunting a bit further I found this resource, which shows a few names that start with catu with variation between a single and double t. So it seems probable that the geminate is simply orthographic.

It doesn't really help with my second question though. The only form where the second part of the word starts with a vowel is Catuoconi, which is part of a Latin inscription and supposedly Brythonic so it isn't much help. On the Goidelic side, Catabar is listed as an Ogham inscription with the translation 'head (chief) in battle'. The second a seems to be part of catu-, possibly reflecting vowel reduction as this inscription is on the slightly later side.

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If you cannot change your mind, are you sure you have one?

Here's a thread on Oscan.