With the California primary less than one week away, a new poll places Hillary Clinton, the very nearly but not quite presumptive Democratic nominee, in a statistical dead heat with Bernie Sanders, who just won’t go away.

With the June 7 voting looming, the newest Field Poll, released Thursday, has Clinton barely ahead of Sanders, 45-43, with 12 percent of voters undecided or unreported. Moreover, voters have more enthusiasm for Sanders (65 percent) than they do for Clinton (45 percent). It’s a transformation from Sanders’s position back in an April survey, in which he trailed the former secretary of state by six points. The latest poll also aligns with the results of several other recent surveys: Wednesday’s NBC News/Wall Street Journal/Marist poll also puts Clinton ahead by just two points, as does last week’s PPIC poll.

Situated at the very end of primary season, the California Democratic contest is traditionally the least important race in the nomination process. But the last big primary of 2016 may be the most crucial this year, and for the most unlikely reasons. Sanders won’t clinch the nomination if he wins California, but a triumph over Clinton would reinforce his nationwide public relations campaign to convince Democrats that Clinton’s superdelegates should vote for him instead. And, failing that, that he should have an outsize impact on rewriting the party platform and agenda and the Democratic National Convention in Philadelphia later this summer.

One piece of data buried in the Field survey that could bolster Sanders’s argument is his growing acceptance among minority communities in California. The Vermont senator has effectively closed the gap among Latino voters, and the Field Poll places him at 42 percent to Clinton’s 46 percent. Among Asian-American voters, Sanders trounces Clinton at 47 percent to 34 percent. (Clinton still maintains a wide, 21-point lead among black voters.) Sanders, who outperforms Clinton in hypothetical head-to-head match-ups against Donald Trump, also rivals Clinton’s white support base in California, 44-43. And Democratic-leaning independent voters, who could make or break the general election for either candidate, are likely to vote for Sanders by a 2-to-1 ratio. Those are numbers that should give Clintonworld pause.