In the clearest sign yet that Sen. Elizabeth Warren, D-Mass., intends to run for president in 2020, on Monday she released a video featuring her family and the results of a DNA test to defend her claim of native American heritage. The claim has been the source of mockery for years, most notably from President Trump calling her "Pocahontas" at rallies. But the DNA test, which shows only distant traces of Native American ancestry overwhelmed by European ancestry, is unlikely to tamp down the attack.

In the DNA test, published in full by the Boston Globe, Stanford genetics professor Carlos Bustamante concludes, "While the vast majority of the individual's ancestry is European, the results strongly support the existence of an unadmixed Native American ancestor in the individual's pedigree, likely in the range of 6-10 generations ago."

[More: Kellyanne Conway dismisses Elizabeth Warren's DNA test]

So, at most, according to the test, one of Warren's great-great-great-great-grandparents was Native American, but it's possible that the earliest ancestor was one of her great-great-great-great-great-great-great-great-grandparents. The Boston Globe story says it's possible she was just 1/32nd native American, but as Phil Kerpen pointed out and as this chart attests, being 6-10 generations removed means that she was at best 1/64th native American, but potentially 1/1,024th. Even this is only the "likely" range and far from exact.

This is the sort of distant link one might expect, if anything, to come up in a casual conversation with friends. As in, some friends she's having dinner with mention they just came back from a visit to the wonderful National Museum of the American Indian, and she responds, "It is a great museum, and by the way, did I ever tell you I have some distant Native American ancestors?"

But Warren, as the Globe notes, did far more than that. "During her academic career as a law professor, she had her ethnicity changed from white to Native American at the University of Pennsylvania Law School, where she taught from 1987 to 1995, and at Harvard University Law School, where she was a tenured faculty member starting in 1995." When she taught there, Harvard Law promoted the idea that she was Native American to help demonstrate the diversity of the school's faculty.

It's true that Warren, in running for the Democratic nomination, will likely have bigger obstacles to overcome — including questions as to whether she can expand her appeal beyond liberal elites and win working class voters and minorities, especially in a field where she'll be competing against candidates with much more direct claims of minority status.

But as far is this issue is concerned, the big reveal of a DNA test showing she's at most 1/64th Native American isn't exactly going to do away with the jokes.