Even if its that old, nobody can prove it was in Anatolia by 4.000 BC, but only that it might have existed by that time, in any other place, most likely the Western steppe.
Corded decorated pottery groups is not the same as "Corded Ware" in the sense of a specific cultural formation. These are Western steppe groups, predecessors not just of Corded Ware, but also of other steppe groups, primarily Cernavoda and other dead ends as well as later branches like Cotofeni and Usatovo among others.
In any case, its Cernavoda and related groups in the Balkans you have to look at, not Central-Eastern European Corded Ware in the narrower sense.
Corded decorated pottery and zoomorphic scepters being an earlier and more Balkan moving Western steppe element from the sphere of Sredny Stog. Central-Eastern European Corded Ware being a different branch from the same tree.
Proto-Anatolians is just one branch, easy to explain from the Balkan Cernavoda related groups, But all the other IE have a direct descendency from Sredny Stog by and large, and those don't have younger Anatolian influences of significance after hte Lower-Middle Don cultures which directly precede Sredny Stog (and Khvalynsk).
They just need to follow the Cernavoda trail.
The problem with this is that the great majority of IE/all LPIE being from the steppe and they have no such influence of significance.
It first appeared when it was written down, we have actual Anatolian speakers in the record. Before that, there is no evidence for an IE presence in Anatolia and in all regions they lived we rather have evidence of preceding and nearby non-IE speakers, which can't be said for the steppe, by the way. Look at the gap between your proposed branching event (4.000 BC) and the first recorded Anatolian language evidence. A lot can happen in more than thousand years.
We are talking about 2.000 years of migrations, fusions, mixtures between the steppe and Anatolia. We just need to have steppe people nearby, which won't be a problem. But even the Cernavoda samples might be highly mixed and only have little steppe, but their migration and sheer existence being clearly steppe induced.
could be reconciled to your views/theory, if DNA can document some EHG into the South Caucuses just before/concurrently with the development of the Anatolian IE branch. From there, a dispersal of the early IE that lead to the Anatolian Branch would not in my review require any Steppe admixture into Bronze Age Anatolia (circa 4200 BC) because as we have seen and as I noted before, the language could have been adopted in Anatolia via trade contacts with IE speaking peoples in the Southern Caucus region. Evidence already suggest that the Hittite language used writing methods they got from Mesopotamia so there clearly was interaction between Anatolia and the Northern Iran, Armenia ancient Iraq (Mesopotamia) not only in the Neolithic period but well into the Bronze age.[/QUOTE]
