Fact
Descent from the Vilna Gaon
Freedman considers it proven that the Komisaruks descend from the Vilna Gaon. Whether the Zhmoods belong to that branch depends on Khana Reizel being a Komisaruk, and no document confirms it. The 1858 census calls her a daughter of Zalka, which rules out her being Berel's daughter, as had been proposed.
Unverified
The Argentine family said for generations that the Smuds/Zhmuds descended from a rabbi or a rabbinic family. It is oral tradition: it does not name the Gaon and proves nothing, but it partly matches the framework found in Freedman’s work.
A single link is missing: a document naming the parents of the Khana Reizel who married David. Freedman’s proposal changed over time, and the version long taken as correct, which makes her a daughter of Berel and Ester, is contradicted by the 1858 census. The whole question, with what supports it, what is missing and what could settle it, is in the open questions. Later on, a genetic comparison between descendants of the Zhmood branch and the branches Freedman used as controls might also settle it. The details are in the entry for the 2020 report.
What each source says
The 1858 census · documented
In household 47/92, David's wife is recorded as “Хана Залкова”, Khana daughter of Zalka, aged 38. It is the only fact about her family of origin: it gives the father's given name and nothing more.
The Komisaruk family, according to Freedman (February 2020) · documented
Genetic testing proved that the Komisaruk family descends from the Gaon. Khana-Reizel, David Zmud's wife, would be the daughter of Dov-Ber Komisaruk and Ester, a granddaughter of the Gaon: a proposal based on the oral tradition of the Komisaruk, Zmood and Grinblat families, who said they came from a common ancestor.
Chaim Freedman's work · documented
Eliyahu's Branches (1997) reconstructs the Gaon's descendants, including the line going up from Khana Reizel, through her mother, to him: the one the 1858 census contradicts.
Relationships among the Komisaruk, Zmood and Yovel families, according to Freedman (2020) · documented
With the full 1858 census, it rules out Khana being Shlomo-Zalmen Komisaruk's sister, since she would then have been recorded as “Berelova” and not “Zalkova”. It proposes, as a theory, that she was his daughter. On genetics, it says only one Zmood has taken a test.