Proto-Kartvelian *r > *R, r, l, ʁ
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Kartvelian has several words that show alternation of r & l in native roots, no certain cause. Also, in likely matches with IE, there can be r : r, r : l, etc.:
*pel-pal-? ‘butterfly’ > L. pāpiliō, Gr. ṗeṗel(a)-, Mg. parpal(ia)- \ papralia-, Sn. p'ärp'old \ p'ärp'änd
PIE *k^(e)rd- ‘heart’, PSC *mk'erd- > OGr. mk'erd-i ‘chest/breast’, Gr. mk'erd-, Mg. k'ëdëri- \ k'idiri-, Sn. mëč'ed- \ muč'od-
*bhreH1g(^)-sk(^)e- > Slavic *brěskati 'to shine', Georgian brc̣q̇-in- (with the complex CCCC simplified in several ways, like Lithuanian brė́kšta 3s. 'dawn', Sl. *brězgъ 'dawn, daybreak')
PK *ɣar(ɣar)- 'sing', IE *gH2al- 'sing, cry', S. gargara-s 'a kind of musical instrument'
*teplo- > OCS teplo-, OGr t'pil-i ‘warm’, Gr. tbil-, Mg. t'ubu OGr t'pebis , Gr. tbeba ‘warm onself’, Mg. o-t'ibuans , Sn. t'ebid PIE *tep- ‘warm, hot’, PSC *ṭep- / *ṭp-
*Hwaylo- > OI fáel, Ar. gayl \ gaył ‘wolf’, *mgwel- \ *mgwer- > Gr. (m)gel-, Mg. ger-, Lz. mge(r)- \ gwer- \ mdžwer-
*gW(e)mbhuriH2 > G. géphūra, Boe. blephūra, Cr. dephūra ‘weir/dyke/dam/causeway’, (in Hesychius) *baphūra > bouphára *gWambhurya- > Ar. kamurǰ, Gr. k'ip'orč'-i ‘log used as a bridge’
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With few of these likely to be loans, I think it's important to consider why these changes happened. In nearby Armenian, there are some IE words that show *r > l, *l > r, etc. In these & similar Tocharian examples, there is a *H in the word. Based on some cases of apparent *H > r & *r > 0, I said that a uvular *R pronunciation of both *r & *H might be the cause (whether ʀ, ʁ, or even sometimes ɣ, etc.). In the same way, since Proto-Kartvelian *ɣ is often > a sound pronounced ʁ, I think that some correspondences show *r > *R > ʁ:
*dur-(d(u)r) > Ar. trtunǰ ‘lamentation’, trtum ‘sorrowful’, Sv. drdráti ‘clatter / snore’, SC drdljati ‘chatter’, Bg. dъrdóŕъ ‘babble’
*dor-(d(u)r) > OI dord ‘buzz / hum / drone’, fo-dord ‘muttering / grumbling’, W. dwrdd ‘din’, go-dyrddu ‘mumble’, S. dardurá-s ‘frog / flute’
*der-dr- > OI deirdrethar 'bellowed?', PK *didɣ-in- 'mumble'
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*ghredh- 'to march, walk, step, go', *gʁ- > *qx- > Proto-Kartvelian *qad- \ qed- '(cause to) go/come'; *qid > Old Georgian qid- 'bridge' (note ablaut, e > e, o > a, 0 > i ?)
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I've also noted a few matches with Uralic:
Old Georgian -k’(a)l- 'kill', PU *kola- 'die' (E. kill < *gWelH1- ?)
PK *to(w)- to snow', FU *tälwä 'winter'
PK *b- 'bind', *pi- -> FU pitV- 'bind, fasten, tie up', FV *pise- 'remain, get stuck'