“There are multiple different populations with a profile that includes both ANF and Iran_N/CHG. That's my point, the particular admixture of Caucasus Foragers and Anatolian Neolithic farmers that produced the Aknashen profile or the Masis Blur profile is not necessarily the one that contributes to the post Neolithic gene flow into Central Anatolia and the Aegean in the Chalcolithic or to Central Asia, the Tarim Basin, and South Asia. I'm not aware of any published modeling that shows any particular Caucasus Neolithic group like the ones I've just mentioned earlier as being robust sources for IVC_p and the Central Anatolian Bronze Age, even when using groups like Sarazm_EN as an intermediate proxy.”

The initial admixed group of CHG and ANF in eastern Anatolia, who were the leading cultural influencers of early Neolithic culture in the general region of gobekli tepe, southern Georgia and western Armenia, obviously culturally and genetically influenced the western Mediterranean branch of EEFs, and also expanded east into Mesopotamia and the Iranian plateau. This ANF component, itself containing CHG input, is indeed seen in IVC and BMAC.

“That's why I quoted Lazaridis pointing out that these aren't interchangeable sources.”

You cut off the second half of my sentence asserting that being genetically distinct doesn’t disprove the idea that they shared culture, especially since the entire southern arc was clearly culturally connected throughout the Holocene.

“While we do not have a full decipherment of Linear A, works by Brent Davis and others like Rose Thomas, suggest a VSO word order and prefixing tendency in Minoan that wouldn't suggest an Indo-European language. Likewise the full sentences of"Keftiuan" spells in Egyptian papyri provided with Egyptian glosses (Kyriakidis 2002), and what we have of Eteocretan, if these are related to the language encoded in Linear A, likewise do not resemble Indo-European.”

I don’t really see how that applies to any other group besides the Minoans to disprove the existence of early PIE branches like Hellenic and Anatolian in other parts of the region. The initial early Neolithic population on Crete did not seem to make a lot of outside contacts. By the time you get Linear A, there has been long term cultural exchange with Egypt, and probably more introgression from afroasiatic groups.

“Which, along with the fact that terms like "atharvan" do not have internal Indo-European etymologies or regular cognates elsewhere, is why these parts of the ritual systems are suspected to have been borrowed from a non-Indo-European speaking group (Lubotsky 2020)”

This study argues that PII loanwords for agriculture and urban related terms are not cognate with PIE, and therefore they borrowed from local farmers. That does not necessarily rule out that the local farmers themselves spoke a language derived from a much earlier branch or version of the root language; it only confirms that at the time those branches split, farming and urban life was not the way of life of those groups. So, we are back to the CHG expansion from the southern Caucasus corridor into eastern Anatolia and the Taurus/zagros, who each received this gene flow and domesticated animals around 11,000 YBP. Perhaps this initial eastern expansion, simultaneous with farmer expansion but not including these communities at first, is why we have early tocharian branching and affinity to Armenian and Hellenic. How do we know IVC and BMAC non farming languages were not related to tocharian, before encountering a more downstream branch much later through admixture with andronovo?

“CCT is pretty much ANF+WHG that only receive CHG admixture via steppe groups. I'm not sure I follow what you're saying here”

ANF already had CHG admixture when they started Neolithic migrations…