6/7/2025 update: Added a little more clarification to number 5 on how global ice age patterns contributed to the decline, since it may not have been clear.

Please note, the highlighted texts are linking to the sources:

My understanding regarding the Aryan Migration theory:

1. No Evidence Yamnaya groups ever migrated to India in the timeframe for any supposed conquest or migration to unite the languages.
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2. No Iranian farmer or Steppe Pastoral genome to support the conquest or migration theory that the idea of an Indo-European language tree hinged on.
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3. To get a clearer picture of how badly this hoax has been debunked, there’s now evidence showing that the upper-half of India was in fact speaking an off-shoot of the proto-Dravidian language. The basis is that there’s good evidence to support that the ancient Indus Valley were multilingual speakers and speaking multiple languages was more commonplace in very ancient times.
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4. Indian Archaeology has thoroughly debunked it too: One and Two.
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5. Finally, Rochester Institute of Technology, Assistant Professor of the School of Mathematical Sciences, Nishant Malik, put the final nail in the coffin with the mathematical model showing a Global Ice Age contributing to an eventual massive drought of the monsoon season of the Indus Valley Civilization was the real reason for the fall of the Harrapan civilization when studying historic weather patterns of the ancient world.

To put it bluntly, as far as I can see from the available evidence, the Indo-European Language tree is more an invented hoax than anything based on evidentiary history.