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She would be part of the Eastern Cherokee tribes BUT the Eastern Cherokee Nation does NOT recognize blood quantum as a means of ancestry. They go by the mother of a clan. If your mother is Cherokee, you belong to her clan. If the clan is not known, then that clan has been lost.
Some nations, such as the Navajo Nation, do use blood quantum for tribal enrollment. All members of the Navajo Nation must be at least one-quarter Navajo in order to be enrolled members of the tribe. Similarly, the St. Regis Mohawk Tribe in New York and the White Earth Nation in Minnesota also require members to have one-quarter blood quantum from their nation. The Cherokee Nation did use blood quantum before and to be recognized as a descendant of the Cherokee Nation, you needed a DIRECT LINEAL ANCESTOR that appeared on the Baker Roll and you needed to posses at least 1/16 of Eastern Cherokee blood, NOT 1/32 like Warren is claiming.
The Cherokee Nation requires documented lineage connecting the applicant to a direct ancestor who was listed on the Dawes Rolls. Others, such as the Cheyene Rive Sioux Tribe, require that one of the parents of the applicant be an enrolled member.
Another problem Warren has is that she never realized that some members of the Cherokee Nation are fighting to disenroll descendants of black Cherokee Freedmen. The Cherokee Freedmen were formerly enslaved by the Cherokee, after which they received Cherokee citizenship following the American Civil War. The Cherokee were one of the so-called Civilized Tribes and kept black slaves.
So, I hope you now understand a bit about claiming Native American status. Oh, and another thing...the Cherokee do not rely on "stories handed down by the generations" as proof that you are a part of the Cherokee Nation tribe. In 2012, The Boston Globe wrote an article on Warren's claims and she was unable to document the claims. Other newspapers have tried to document her claims but couldn't find proof either. Just because someone has high cheekbones doesn't mean you're Native American.