Until this week, I also believed that the information written in books about the origin of the Halevi Horowitz family and that they are descendants of Rabbi Zerachyah Ha'Levi, is incorrect information...
This week I found an article written by Naftali Wakstein:
מגילת היוחסין של משפחות רושגולד ומרגליות,פרק נ,עמוד 66
And in page 66, Naftali Wakstein verifies the fact that the Ha Levi Horowitz family is a descendant of R' Zerachyah Ha'Levi
And it also has a lot of information about the branches of the Halevi Horowitz family
I put up a post on the subject in the rabbinic genealogy group, where Randy Schoenberg is also a member
And a man who is from the Ha Levi Horowitz family (son after son) replied to me that it is known in the family that they are descendants son after son to R' Zerachyah Ha'Levi.
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I wonder, does anyone have proven information about the Halevi Horowitz family