Ashkenazi Genetic Origins European?

This thesis obviously leads one to presume that a small exile jwish community after Rome expelled them tried officially to maintain blood purity but as in many cases simply accepted children born who were obviously different from one parent, ignoring that the mother was sleeping around. Slowly this percentage of inofficially mixed children grew from generation to generation until many jews have lost semitic origins completely. I have read that everywhere on earth such children do make up a significant portion of births so that this is entirely normal. The jewish culture however would have remained intact and eventually after the enlightenment mixed marriages and conversions in both directions were allowed. Shepardic jews became arabic in the same way. Ashkenazi settlement of Israel is then a European colonization of the Middle East. Perhaps if they stay there long enough this genetic process will reabsorb them and they will lose again their genetic connection to Europeans and become again true semitics like the arabs they are surrounded by in daily life.