Experts suggest that Michigan, Pennsylvania and Wisconsin should manually review paper ballots, but Hillary Clinton’s campaign has shown no support for a recount.

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Hillary Clinton’s lead in the popular vote is growing. She is roughly 30,000 votes behind Donald Trump in the key swing states of Michigan and Wisconsin, a combined gap that is narrowing. Some of her impassioned supporters are urging her to challenge the results in those two states and Pennsylvania, grasping at the last straws to reverse Trump’s decisive majority in the Electoral College.

In recent days, the supporters have seized on a report by a respected computer scientist and other experts suggesting that Michigan, Pennsylvania and Wisconsin, the keys to Trump’s Electoral College victory, need to manually review paper ballots to ensure the election was not hacked.

“Were this year’s deviations from pre-election polls the results of a cyberattack?” J. Alex Halderman, a computer-science professor at the University of Michigan who has studied the vulnerabilities of election systems at length, wrote on the online-publishing platform Medium on Wednesday as the calls based on his conclusions mounted. “Probably not.”

More likely, he wrote, pre-election polls were “systematically wrong.” But the only way to resolve the lingering questions would be to examine “paper ballots and voting equipment in critical states,” he wrote.

Tellingly, the pleas for recounts have gained no support from the Clinton campaign, which has concluded, along with outside experts, that it is highly unlikely the outcome would change even after an expensive and time-consuming review of ballots.

But that has not quieted some Clinton supporters, who see the inequity of her growing lead in the national popular vote, which is now more than 2 million votes, or 1.5 percent of all ballots cast, according to the nonpartisan Cook Political Report, which regularly updates its count as states continue to tally and to certify votes.

Since there is no effort to review the paper ballots — which exist in Michigan and Wisconsin, but only in parts of Pennsylvania — conspiracy theories about the 2016 election may live on for years. After U.S. intelligence agencies accused Russia of trying to influence the election by stealing and publishing emails from the Democratic National Committee and a range of other institutions and prominent individuals, the United States went on high alert to determine if there was any attempt to sabotage the vote count. So far, no one in the Obama administration has indicated there is any such evidence.

In the three battleground states, Clinton is behind by 1.2 percent or less, and the final results have not yet been certified.

Uniting around the social media hashtag #AuditTheVote, the campaign-after-the-campaign has picked up momentum among grass-roots activists still mourning Trump’s victory and who echo, paradoxically, his pre-election complaint that the vote was “rigged.”

“Based on the information of the intelligence community that Russia was actively trying to screw around with our election, I thought why not take the time and question this,” said Michelle Zuckerman-Parker, an engineer in Pittsburgh, who planned to petition her county election board for a recount of the Nov. 8 vote.

That view spread quickly on social media late Tuesday when New York magazine published an article about Halderman and others who had contacted the remnants of the Clinton campaign.

It also generated pushback by experts who said that even though it was theoretically possible to hack voting machines, it would be enormously difficult — because it would have to be highly targeted in key precincts and conducted on a scale required to ensure Trump’s victory.

“Left-wing conspiracy theories of vote rigging” are “pathetic,” Dave Wasserman of the Cook Political Report said on Twitter.

Pennsylvania allows individual voters to petition for a recount, but the deadline was Sunday, said Wanda Murren, a spokeswoman for the Pennsylvania Department of State. A candidate can also contest an election in court, and the deadline is Monday.

Michigan and Wisconsin have not reached their deadlines for seeking a recount, but they will in days. Clinton has not requested any action, said Reid Magney, a spokesman for the Wisconsin Elections Commission.

Until the publication of Halderman’s work, Clinton supporters had few reasons to hope. He did not offer them much: He noted that while the voting machines used in those states are not connected to the internet during the election, they are programmed before the election. The data is usually transferred on an USB stick or other data card.

“If attackers can modify that software by infecting the machines with malware, they can cause the machines to give any answer whatsoever,” Halderman wrote.

The problem, as security expert Bruce Schneier noted in an interview, is that the usual triggers for a recount — a very close margin between two candidates — make little sense in a world of state-sponsored computer hackings. A truly sophisticated hacking would result in a wider margin of victory that would not set off an automatic recount.

Clinton would have to triumph in all three states to win the Electoral College. The electors will meet in December to formally choose the president. Trump is ahead by 290 votes to Clinton’s 232, with Michigan still officially uncalled.

As of Wednesday, Trump’s lead in Michigan had shrunk to 10,704 votes, or 0.2 percent, according to the National Popular Vote Tracker maintained by the Cook Political Report.

Trump’s lead in Wisconsin has narrowed to 22,525 votes, or 0.8 percent. In Pennsylvania, his lead slightly grew Wednesday, to 70,010, or 1.2 percent.

The Clinton campaign did not respond to requests for comment. Other Democrats said it was time to move on.

“I’m not sure it’s possible to undo the results, and all the people are focusing their energy on opposing the worst ideas of this administration at this point, not the legitimacy of the results,” said Daniel Doubet, an organizer for Keystone Progress, a liberal group in Pennsylvania.

On social media, supporters pleaded with the campaign to act. “Please @HillaryClinton @timkaine call for #AuditTheVote,” wrote Writerchick on Twitter, appealing to Clinton and her running mate, Sen. Tim Kaine of Virginia. “We are all working so hard for you, make the call, the nation is depending on you.”

The Audit the Vote crowd uncovered what appeared to be anomalies in the counting. Helen Manich, of National Harbor, Md., noticed that Sauk County, Wis., reported that 31,838 ballots were cast overall, but the total votes for presidential candidates numbered 34,323.

Such glitches are not uncommon, election experts said. They are usually ironed out in the process of certifying results. Although those certifications might change the results by several hundred or several thousand votes, they are highly unlikely to move tens of thousands.