To be considered to be a “Native Hawaiian” you need 50% Hawaiian blood.
I wonder what the Cherokees demand for proof.
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Cherokee tribe does not count blood or even lineage unless you can PROVE direct relation to someone on the Dawes Roll, also known as the final Roll. If you could somehow prove you were a Cherokee if you cannot prove/document that you are directly related to someone on that Roll and become enrolled in the tribe you are not considered a Cherokee, not legally in any way. Other tribes have their own determination but it is cut and dried with the Cherokee.
https://www.cherokee.org/Portals/0/Documents/2012/8/31660Application_Instructions.pdf
For the Eastern Band of Cherokee it is the Baker Roll that is relied on. I seem to recall she claims the Oklahoma Cherokee as her heritage but this is for the Eastern Band.