Did voter fraud swing New Hampshire away from Donald Trump in the 2016 election? Absolutely not, according to an exhaustive investigation conducted by the state’s attorney general and secretary of state, which, counter to Trump’s persistent allegations, turned up no evidence of “serious voter fraud.” Instead, the inquiry provided further evidence that the tools Republicans use to detect voter fraud are fatally flawed, churning out a huge number of false positives. And while the New Hampshire investigation ultimately debunked Trump’s paranoia, it came perilously close to disenfranchising thousands of lawful voters.

Republicans have seized upon New Hampshire as the putative epicenter of American voter fraud for two reasons. First, elections there are often quite close—in 2016, for instance, Hillary Clinton carried the state by fewer than 3,000 votes—meaning a relatively small amount of fraud could have a huge effect. Second, the state allows same-day voter registration under a deal with the federal government that exempts it from the stringent requirements of the National Voter Registration Act. Unlike most states, New Hampshire is not obligated to let voters register at the Department of Motor Vehicles; instead, they can register when they show up at the polls on Election Day.

Some Republicans have asserted that same-day registration is especially susceptible to fraud, and though there’s no actual evidence that it is, this fear has taken hold among many conservatives. A number of GOP officials—including state legislators, Gov. Chris Sununu, and Trump—claim Democrats bus in out-of-state voters to cast illegal ballots. “The Democrats [are] very sly,” Sununu said shortly before winning the 2016 gubernatorial election. “We have same-day voter registration, and to be honest, when Massachusetts elections are not very close, they’re busing them in all over the place.”

Not true, New Hampshire Secretary of State Bill Gardner and Associate Attorney General Anne Edwards declared on Tuesday. Edwards explained that while political parties sometimes rent buses from neighboring states to transport voters to the polls, the people riding the buses were legitimate New Hampshire voters. “Each time we have sent an investigator out to the polling place,” Edwards said, “they have been able to determine that the bus company is from Maine or Vermont or Massachusetts, but not the voters on the bus.” She also noted that DOJ officials sent investigators to Salem following reports that the polls were “full of” cars with Massachusetts tags. It turned out Massachusetts residents simply “came up to hold signs in New Hampshire.”

Gardner has quashed one of Trump’s favorite talking points—and undermined the case for draconian voter-suppression measures that he still supports.

The myth of rampant voter impersonation proved more complicated to dispel. Gardner’s office began by using Crosscheck, a tool favored by Kris Kobach that has a 99.5 percent false positive rate. Crosscheck is supposed to locate individuals who are registered to vote in multiple states; although multistate registration isn’t illegal, it could indicate that the voter is no longer active in one of those states. Kobach has insisted that the program helps states clean up their voter rolls by removing inactive voters. In reality, it has led election officials to try to purge thousands of lawful voters from the rolls.

Gardner—who is nominally a Democrat, but served on Trump’s voter-fraud commission and now supports disenfranchisement measures—decided to use the tool despite all of those documented problems. In New Hampshire, Crosscheck initially flagged a whopping 94,610 individuals as possible double voters by matching first names, last names, and birthdays. Gardner’s office eliminated most of those matches by weeding out people who voted in one state and not the other, or who didn’t vote at all. That left 4,579 possible double voters, of whom 3,624 were ruled out because they had different middle names or initials. Gardner’s team whittled down the remaining 955 names to 142 possible matches by examining Social Security numbers, death records, post-office data, and other publicly available information. His office referred 51 of those cases to the attorney general and will continue to narrow down the final 91—partly by comparing their signatures, a notoriously unreliable method.

In all, the state had found five cases of actual wrongful voting, though not all were the voters’ fault. One college student voted in the wrong location on the faulty instruction of an election official. An elderly woman appears to have filled out her recently deceased husband’s absentee ballot. Two people cast a ballot in Dixville Notch’s famous midnight primary without establishing domicile there. Just one person actually voted twice; he was fined $2,500 and threatened with criminal prosecution if he ever did it again.

Bradford Cook, chairman of the state’s Ballot Law Commission, described these cases as “a bunch of idiosyncratic issues” rather than “massive voter fraud,” a characterization Edwards, the associate attorney general, agreed with. Yet Gardner isn’t yet willing to concede that voter fraud is a nonissue.

“For the first time, we really have an idea about this,” the New Hampshire secretary of state declared, “And so it raises the question of, what does someone mean by widespread voter fraud? Does this come anywhere near that? And that’s a judgment call that people individually have to make.” He also used the meeting to promote a controversial “poll tax” bill that would compel out-of-state college students to register their cars in New Hampshire if they choose to cast ballots there, costing them hundreds of dollars in fees. The GOP-controlled state legislature has already passed the bill; Sununu is awaiting an advisory opinion from the state Supreme Court before deciding whether to sign it.

Civil rights groups breathed a sigh of relief upon the release of Tuesday’s report, as it was not at all clear that the secretary of state’s office would conduct this investigation responsibly. When Gardner introduced Crosscheck, his office presented the program as a tool to expedite an immediate purge of voters. In September, election officials were instructed to strike from the rolls each voter flagged by the program—before eliminating false positives. And they were explicitly told they did not have to notify each voter before purging them.

Emails obtained under the state’s Right to Know law by Colin Van Ostern, who wants to replace Gardner as secretary of state, demonstrate that officials balked at the command. After Crosscheck flagged 859 names in Manchester alone, assistant city clerk JoAnn Ferruolo chose a random sample of 34 matches to study more closely. She quickly found that 15 of those 34 were obvious false positives. “I do not feel comfortable,” she wrote a superior, “removing 859 voter records where 44% of the sample was found to be an active voter in Manchester.”

When the American Civil Liberties Union of New Hampshire challenged the state’s legal authority to purge these voters, the secretary of state’s office backed down. (State law expressly requires the government to notify voters before canceling their registration.) Gardner’s office claimed the purge instructions were a “miscommunication, pure and simple,” though it did not persuasively explain exactly how its “miscommunication” came about.

This early skirmish raised the possibility that, like Kobach before him, Gardner would use Crosscheck to disenfranchise thousands of perfectly eligible voters. For now, at least, that has not come to pass. To the contrary, the secretary of state has quashed one of Trump’s favorite talking points—and undermined the case for draconian voter-suppression measures that he still supports. Even as New Hampshire concludes that voter fraud is vanishingly rare, its governor is seriously considering signing a bill to address that nonexistent problem. That’s no surprise. Despite mounting evidence to the contrary, nearly half of Republicans have convinced themselves that up to 5 million people voted illegally in 2016. For many in the GOP, the existence of voter fraud is more than what Gardner termed “a judgment call.” It’s an unshakeable article of faith.