So how simple would it be for today's Ashkenazi Jews to take such a <"23andMe"> test en masse to determine their percentage of Semitic heritage, and thus verify their claim on Israel?

Well, that's been done already, and it's not surprising we haven't heard much about these studies.

Dr. Areilla Oppenheim of the Hebrew University in Jerusalem, conducted the first comprehensive DNA study of Israelis and Palestinians in 2001. She concluded that Ashkenazi Jews were of Mongolian 40% and Turkish 40% genome.

There was no Semitic blood connecting them to the original Middle Eastern Hebrews of 4,000 years ago in Jerusalem or Biblical territory. Jews were found to be more closely related to groups in the north of the Fertile Crescent (Kurds, Turks, and Armenians) than to their Arab neighbors.
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We've seen a lot of this lately, this "up is down" and "black is white" reversal of the truth from the Ashkenazi Jew-owned media and governments: men can have babies, vaccines protect your health, and farming is killing us.

Ever since 9/11, I decided to take the philosophy of just thinking the opposite of what the media tells me. When the media said the Muslims carried out the 9/11 attacks, I just replaced the word Muslims with their mortal enemies, the Ashkenazi Jews. I also started to realize that this tactic of reversing the truth goes back way further than I imagined.

They tell us people of European descent shipped the slaves over to North America from Africa: no, it was primarily Ashkenazi Jews who did that. They tell us the Jesuits were Catholics: no, Ignatius Loyola was a Marrano, or "crypto-Jew". So was Christopher Columbus.
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My prediction: when people finally see through the way that the Ashkenazi Jews claimed Israel on false pretenses, they will shift out of the Middle East back towards their original homeland--the country currently known as Ukraine. The 2022 Russian-Ukrainian war has been planned for quite a while for just that reason.