On Saturday, in Springfield, Massachusetts, Elizabeth Warren officially became the Democratic nominee in the race for the Senate seat currently held by Scott Brown. She won votes from nearly ninety-six per cent of the delegates, preventing a primary challenge, and she struck a defiant note. In the verdict of one Boston Globe columnist, “Warren needed an A-game speech and she delivered one.” She seemed passionate, and a not a little bit irritated:

So how does a Wall Street, big oil, Mitt Romney Republican plan to win? His answer is to talk about anything except how he votes on jobs, education, the environment, oil subsidies, or special deals for Wall Street. His answer is to talk about my family, and to tell me how I grew up.

And now, apparently, Warren’s answer is to talk about Brown talking about her family. This topic has roiled the campaign since late April, when the Boston Herald reported that Warren’s employer, Harvard Law School, cited her as Native American. In response, Warren has waged two defensive campaigns at once, seeking to explain, on the one hand, that she never sought or received special benefits because of her Native American heritage, while insisting, on the other hand, that this heritage is an authentic and important part of who she is. These two explanations are not incompatible, but they do require her, awkwardly, to simultaneously minimize and maximize the importance of the heritage she claims.

Faced with demands for genealogical proof, the Warren campaign has mainly responded that Warren has long understood herself to be Native American. She contributed to a 1984 cookbook called, “Pow Wow Chow: A Collection of Recipes From Families of the Five Civilized Tribes: Cherokee, Chickasaw, Choctaw, Creek, and Seminole.” (In it, Warren is identified as Cherokee.) The cookbook is out of print, but its Amazon page is now full of spurious reviews, like this one: “Seems that all the recipes by Lizzie Warren call for a bunch of baloney! Q: Why was Warren refused a room at the Marriott? A: She couldn’t prove she had a reservation.”

Plenty of Americans believe that some of their ancestors were Native Americans. Last week, in an e-mail to supporters, Warren asked, “What kid asks their grandparents for legal documentation to go along with their family stories?” But in a recent interview with the Associated Press, she went further, explaining her ancestry as a kind of family trauma. “My father wanted to marry my mother, his parents objected, because she was part-Cherokee and part-Delaware,” she said. “My parents eloped, in order to marry. It’s something my brothers and I grew up with. We always understood the difference, between our father’s family and our mother’s family.”

This is a familiar enough story of a forbidden interracial marriage, with a twist: in the more common version, the non-white spouse is black. In Warren’s telling, her mother’s Native American identity functioned the way black identity often has, throughout American history: as a genealogical stain, generating social stigma. Black Americans had rarely been asked to prove their blackness, partly because the thought of fraud seemed so absurd—who would invent something like that? On the contrary, in certain places and times, a rumor of African ancestry was considered to be as good—that is, as bad—as the real thing.

By contrast, a trace of Native American heritage has sometimes been viewed not as a liability but as an asset, and one with not inconsiderable value. Long before the era of casino royalties and pro-diversity law schools, there were people who talked up their Native American heritage, even if there was only a little, or less than a little. And many white Americans discovered that a hint of Native American heritage could coëxist with white identity, and might even enhance it.

And so, as Warren is discovering, questions of authenticity have long been asked—and answered. In recent weeks, one of Warren’s most persistent critics has been Twila Barnes, the proprietor of Polly’s Granddaughter, a blog devoted to Cherokee genealogy and pseudo-genealogy. Last week, during an interview with the talk-radio host Laura Ingraham, Barnes tried to explain Cherokee identity as a form of citizenship. “Being Cherokee is not a race of people—it’s a nation of people,” she said. “And we descend from a group of people who always stayed with their nation, rebuilt their nations after destructive things like the Trail of Tears or the Civil War. Those people always stayed together as a nation.” Her definition hints at the violations that have served, perversely, to sanctify this identity, and also at the responsibilities that usually accompany the privileges of citizenship.

Barnes and Ingraham spent a few pleasant minutes dissecting Warren’s unproven claims, and then Ingraham asked Barnes about her own background.

Ingraham: “So, Twila, are you full-blooded Cherokee, yourself?” Barnes: “No.” Ingraham: “What’s your lineage?” Barnes: “My blood quantum is—” Ingraham, laughing: “‘Quantum’! I like this. What is it?” Barnes: “It’s blood quantum, and mine is seven thirty-secondths.” Ingraham: “What the heck does that mean? I don’t even know what that means!” Barnes: “That means I am—my grandfather was just below being a full-blood Cherokee.” Ingraham: “O.K.” Barnes: “And then my grandmother was white, so my mother got half of his blood. And my father’s white, so I got half of my mother’s.”

Seven over thirty-two: we only bother with this kind of precision if the seven is considered extremely valuable. (If the seven isn’t quite so precious, or if it’s considered toxic, then descendants are free—that is, forced—to round up, to eight over thirty-two, or one over four.) In “Dreams From My Father,” Obama writes about his own ancestry, which can be expressed as a simpler fraction—one over two. Nevertheless, he writes, “I ceased to advertise my mother’s race at the age of twelve or thirteen, when I began to suspect that by doing so I was ingratiating myself to whites.” On matters of race and identity, every calculation is a political calculation. Perhaps Warren now wishes she had made some different ones, regardless of her family history.