https://en.wikipedia.org/wiki/Northeast_Caucasian_languages NOT PIE (mountain, little Dagestan coast) ≠
https://en.wikipedia.org/wiki/Northwest_Caucasian_languages SOME PIE (mountain and Abkhazia)≠
https://en.wikipedia.org/wiki/South_Caucasian_languages VERY PIE Georgian Kartvelian
https://en.wikipedia.org/wiki/Kartvelian_languages
https://github.com/pannous/hieros/blob/master/dicts/swadesh/caucasian.tsv

The centrality of CHG in the spread of PIE is evident in that often all roots are represented in the 3 Caucasian families (plus Armenian)

ma.skin ⇔ ka.skin kašiⁿ կաշ 𒋢 KUŚ
mas.kɑni კანი skinᵐᵉˢ 𓄟𓂓𓄛
masken մաշկ mɑʃka 𓄟𓂓𓄛

Vocabulary of Göbekli Tepe:
𒊺𒇷𒁍 še'le-bu تعلب taʿlab de'lape@Prussian/Lithuanian vulpe “fox” !! ⇔ lupus!

Anatolians

Anatolians received a 50% CHG admixture at the beginning of the Chalcolithic 5000BC diverting from EEF.
Caucasian is evident both in the genome and in the linguistic of Anatolian and their hieroglyphs (lacking Steppe!)
𔑣 tá/ta/da tur тур@NE-Caucasian π form 𒉺𒋫𒀀𒀸 patās
See Linear-A Linear-B and anatolian.abc

Toponyms:
Circassia

Ethnonyms:
Kaskian (also language)
Ḫatti (Cats ⇔ Luwians)
Hittite

PIE: armenian

Pontic Northwest_Caucasian_languages
Verb suffix -та do 𓂡 -дан -dən tun
Verb suffix -а -ːə -ə ⋍ -er -en -ω -o

Caspic Caspian Northeast_Caucasian_languages
“Not descendants of Neolithic farmers” Bulayeva 2003b (slightly revised?)
Verb/Noun prefix ɑpʰ- abstract bu-! ubiquitous
Verb suffix -ɑrɑ -rɑ ⇔ -ier -er 𓂻

Kartvelian South_Caucasian_languages:
Verb prefix და- dɑ- de- (dis¬ des¬ off-) -дан -dan tun done -dələ -dele do
Verb prefix გა- ga- ge-
Verb prefix ʃɛ- se- 𓇉 - mutual causative ?
Verb prefix სანა- sana- შენ ʃɛn- syn- ?
Verb prefix mɔ- m- im- µ- ma- miɑ- miɛ-
Verb suffix -ება -ɛbɑ аҧ- ɑpʰ- up- ab- аҧы- epi- -ba -ɛbs opus -𓈐 pass -ubis bist > -be -va -vis > -ავს -vs -is (-dis?)
Noun suffix -li მატყლი Tüchle ⇔ -erle -al ⇔ ler
Adjective suffix -li -ly -tʰɛli -del (of,like) qˀvitʰɛli quittelig (yellow) ʃɑvitʰɛli schwatt

itˀqˀvis out.qvis 𐌵𐌹𐍃𐍃 𐌵𐌹𐌸𐌰𐌽 say!
გადაიხდის ɡɑdɑixdis ge.tax(t).is : pay (for)
გამოაკეთებს ɡɑ mɔɑkˀɛtʰɛbs ge.make.tops : make-better < makha
ბანაობს bɑnɑ.ɔbs baden banyar bain baño ва́на vána < balneum βαλανεῖον balaneîon აბაზანა abazana ab-waschen @ Wanne
შეკრებს ʃɛkˀrɛbs se.grabs syn?gather
სანახავად მიდის sɑnɑxɑvɑd midis syn.axa.meat : visit
აღზრდის ɑɣzrdis a'chird.is raise a chird
შეახებს ʃɛ.ɑx ɛbs 𓇉𓄿𓎼𓂻 touch

ხმაურობს xmɑur ɔbs 𓐍𓂋𓊤𓃭𓅱𓀁 Gemurre Klamauk

"uma Tüchle, máo.textile 毛 "

Darginian, Avar and Chechen are closets related to Yamnaya

From the first Eneolithic farmers who appeared at Unakozovskaya in the northwest Caucasus about 4600 BC to the Maikop culture, all of them had significant CHG ancestry, on a cline of 28-60%. But the other 72-40% of their ancestry can be modeled as an admixture of Anatolian Farmer (the great majority), Levantine Neolithic, and Ganj-Dareh-type Iranian Farmer ancestries

the Y-chromosome haplogroups of the Eneolithic Meshoko and Maikop men were typical Anatolian- Iranian Neolithic haplogroups (L, J2, and G2) unlike the paternal haplogroups of the steppes. Yamnaya men were almost exclusively R1b, and pre-Yamnaya Eneolithic Volga-Caspian- Caucasus steppe men were principally R1b, with a significant Q1a minority. Maikop men did not father a significant number of Yamnaya males.

The variety of CHG that constituted more than half of Yamnaya ancestry could have been the Mesolithic/Early Neolithic variety, like Hotu Cave or Kotias Cave, not yet admixed with Anatolian Farmer ancestry. If the CHG element in Yamnaya came from a non-admixed CHG population of this kind, they could have walked into the steppes from northwestern Iran/Azerbaijan at any time before about 5000 BC—before admixture with Anatolian Farmers began.

Without any doubt, a CHG population that was not admixed with Anatolian Farmers mated with EHG populations in the Volga steppes and in the North Caucasus steppes before 4500 BC.

After 5000 BC domesticated animals appeared in these same sites in the lower Volga, and in new ones, and in grave sacrifices at Khvalynsk

among 48 individuals with whole-genome aDNA from 16 Neolithic and Copper Age cemeteries in Bulgaria and Romania dated 5800-4300 BC, only three showed any ancestry from a steppe mating network (Mathieson et al. 2018). Around 95% of the southeastern European farmer population tested had no steppe relatives over a period of 1500 years. They must have actively avoided marriage with steppe people, a rule broken only among the elite towards the end of the Eneolithic.
All three of the steppe-admixed exceptions were from the Varna region (Mathieson et al. 2018). One of them was the famous “golden man’ at Varna (Krause et al. 2016).

After this 4300-4200 BC event, Anatolian Farmer ancestry began to pop up in the steppes. The currently- oldest sample with Anatolian Farmer ancestry in the steppes in an individual at Aleksandriya, a Sredni Stog cemetery on the Donets in eastern Ukraine.

Reuniting old Anatolian Iranian CHG herders with old Anatolian European WHG farmers in EHG land.

In short: the closer one looks the more complicated and detailed the myriad paths of history become.

Pliny the Elder's Natural History (AD 77–79) derives the name of the Caucasus from the Scythian kroy-khasis = ice-shining, white with snow (cf. Greek cryos = ice-cold).