That's a theory from the 1800s that has been disproven by DNA testing.
Ashkenaz patrilineal DNA shows a 95-98% correlation with Sephardic DNA.
Ashkenaz matrilineal DNA shows an 80-95% correlation with Sephardic DNA.
It is scientifically impossible for those results to represent a different ethnicity for Ashkenaz vs. Sephardim.
Was there some possible mixing? Sure. But the data shows a remarkably minute amount of it.
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