You don't seem to be very bright, but please try re-reading the paper. Nowhere in it is there any evidence given of a major turnover of mtDNA 6000 years ago, mostly because that didn't happen.
I never claimed there was a major turnover of mtDNA 6,000 years ago. You did and the evidence is in the posts above.
Regardless of what the authors of the paper said in terms of generalities, when they do get around to discussing specifics, they admit that H was present in small part fairly early on but the first major uptick of mtDNA H seems to have happened with Bell Beaker and another wave of increased H happened during the Bronze Age, as I previously discussed.
No, the authors very obviously state that the major portion of European mtDNA H diversity and distribution was established by the middle Neolithic, around 6,000 years ago. This is stated several times in the posts above, including your own.
And no, there was no "other wave" of mtDNA H into Central Europe during the Bronze Age. The phylogeography of the full mtDNA sequences studied in the paper show that Neolithic farmers and Bell Beakers from the Atlantic facade can explain almost all of the mtDNA H in Europe (the rest can be explained by Corded Ware and other expansions from the east which carried Eastern European-specific mtDNA H subclades).
So what most likely happened was that the Neolithic and Bell Beaker-derived populations, sitting in Western and Central Europe, where population densities were relatively high and could get much higher than in Eastern Europe, experienced large population growth during the metal ages, thereby pushing up the frequencies of mtDNA H and the Atlantic-derived subclades of mtDNA H even further.
Do you see any evidence there that mtDNA H became dominant 6000 years ago?
Yes, it's stated in the paper including in the abstract. Here's that quote again.
Our results reveal that the current diversity and distribution of haplogroup H were largely established by the Mid Neolithic (~4000 BC), but with substantial genetic contributions from subsequent pan-European cultures such as the Bell Beakers expanding out of Iberia in the Late Neolithic (~2800 BC).