Instagram barred Robert F. Kennedy Jr.’s account. Anti-vaccine accounts remain.

A search for the word “vaccine” on Instagram on Thursday showed that four of the top 10 accounts took strong anti-vaccine positions. A search for the hashtag #vaccine got three results, one of which was #vaccinetruthadvocate, a term that anti-vaccine activists often use to spread their message. The hashtag was appended to more than 12,000 posts.

“This is going to take some time, however, but we are working to address what you raise,” a Facebook spokeswoman said in a statement.

Researchers who study misinformation said Facebook continued to struggle to contain Covid-19 falsehoods.

“Months after they promised to crack down on Covid misinformation, we reported hundreds of posts containing dangerous misinformation to Facebook, but just one in 10 of those posts were removed,” said Imran Ahmed, chief executive of the nonprofit Center for Countering Digital Hate. “Millions of people are being fed dangerous lies which lead them to doubt government guidance on Covid and on vaccines, prolonging the pandemic. These lies cost lives.”

Here’s a look at some of the prominent accounts still spreading anti-vaccine misinformation on Instagram.

Children’s Health Defense

The nonprofit regularly promotes seminars and webinars with vaccine skeptics through its Instagram account, and posts misleading accounts of death and injury associated with the Covid vaccine. Many of its posts receive tens of thousands of likes. The organization did not return a request for comment.

Erin Elizabeth

An author and public speaker who has campaigned for years against vaccines, Ms. Elizabeth has over 122,000 Instagram followers on her Health Nut News page and 23,700 on another page she runs. She regularly shares content that argues against “mandatory vaccination.” She did not return a request for comment.

Shiva Ayyadurai

Mr. Ayyudurai, an Indian-American politician, has over 299,000 followers on Instagram. He has spread the false claim that Covid-19 can be treated with vitamin C. He has also accused the “deep state,” or the conspiracy theory that a secret cabal runs the government, of spreading Covid-19. He did not return a request for comment.

Here are the three most popular misinformation narratives about the impeachment proceedings.

Nancy Pelosi is responsible for the Capitol attack: 30,300 mentions

The falsehood that Congresswoman Nancy Pelosi somehow knew that a mob would storm the Capitol and is using the impeachment trial as a “diversion” effort was amplified by Senator Ron Johnson on Fox News on Feb. 7.

“We now know that 45 Republican senators believe it’s unconstitutional,” Mr. Johnson said on Fox News, referring to the impeachment proceedings. “Is this another diversion operation? Is this meant to deflect away from what the speaker knew and when she knew it? I don’t know, but I’m suspicious.”

A video clip of the interview was viewed at least 2.1 million times on Twitter.

The attack on the Capitol was preplanned, undercutting the basis of the impeachment trial: 8,135 mentions

The falsehood that the Capitol attack was preplanned and “undercuts Trump impeachment premise” gained traction on Feb. 8 when a conservative outlet called Just the News published an article detailing the claim. The article was shared 7,400 times on Twitter and at least 3,000 times on Facebook.

The founder of Just the News, John Solomon — a Washington-based media personality who was instrumental in pushing falsehoods about the Bidens and Ukraine — shared the falsehood from his own Twitter account, collecting thousands of likes and retweets. Other Twitter users then picked up the rumor, further amplifying the false narrative.

Focusing on what was planned in advance should have no bearing on the impeachment trial itself, according to 144 constitutional law scholars who submitted a written analysis of the case against Mr. Trump. They said many of them believe that “President Trump can be convicted and disqualified because he is accused of violating his oath through an ‘extraordinary, unprecedented repudiation of the president’s duties to protect the government’ through his ‘further acts and omissions after he incited the crowd to attack the Capitol.’”

Renewed calls to impeach Obama over ‘spying on Trump’: 5,017 mentions

The narrative that it is not too late to impeach former President Barack Obama started to gain traction on Jan. 26 on Twitter. Thousands of Twitter users shared an old suggestion from Representative Matt Gaetz, a Florida Republican, that if a former president can be impeached, Mr. Obama should be tried for spying on Trump.

The false narrative was a revival of “Spygate” — a labyrinthine conspiracy theory involving unproven allegations about a clandestine Democratic plot to spy on Mr. Trump’s 2016 campaign. But the theory fizzled as the past four years saw none of Mr. Trump’s political enemies charged with crimes. And in 2019, a highly anticipated Justice Department inspector general’s report found no evidence of a politicized plot to spy on the Trump campaign.

In the past, Facebook had said it would only “downrank,” or push lower down in people’s news feeds, misleading or false claims about vaccines, making it more difficult to find such groups or posts. Now posts, pages and groups containing such falsehoods will be removed from the platform entirely.

“Building trust and confidence in these vaccines is critical, so we’re launching the largest worldwide campaign to help public health organizations share accurate information about Covid-19 vaccines and encourage people to get vaccinated as vaccines become available to them,” Kang-Xing Jin, head of health at Facebook, said in a company blog post.

The company said the changes were in response to a recent ruling from the Facebook Oversight Board, an independent body that reviews decisions made by the company’s policy team and rules on whether they were just. In one ruling, the board said that Facebook needed to create a new standard for health-related misinformation because its current rules were “inappropriately vague.”

Facebook also said it would give $120 million in advertising credits to health ministries, nongovernmental organizations and United Nations agencies to aid in spreading reliable Covid-19 vaccine and preventive health information. As vaccination centers roll out more widely, Facebook said it would help point people to locations where they can receive the vaccine.

Mark Zuckerberg, Facebook’s founder and chief executive, has been proactive against false information related to the coronavirus. He has frequently hosted Dr. Anthony Fauci, the nation’s top infectious disease expert, on Facebook to give live video updates on the American response to the coronavirus. In his private philanthropy, Mr. Zuckerberg has also vowed to “eradicate all disease,” pledging billions to fighting viruses and other diseases.

Yet Mr. Zuckerberg has also been a staunch proponent of free speech across Facebook and was previously reluctant to rein in most falsehoods, even if they were potentially dangerous. The exception has been Facebook’s policy to not tolerate statements that could lead to “immediate, direct physical harm” to people on or off the platform.

Facebook has been criticized for that stance, including for allowing President Donald J. Trump to remain on the platform until after the Jan. 6 riot at the U.S. Capitol.

For years, public health advocates and outside critics took issue with Facebook’s refusal to remove false or misleading claims about vaccines. That led to a surge in false vaccine information, often from people or groups who spread other harmful misinformation across the site. Even when Facebook tried updating its policies, it often left loopholes that were exploited by misinformation spreaders.

Facebook on Monday said it would also change its search tools to promote relevant, authoritative results on the coronavirus and vaccine-related information, while making it more difficult to find accounts that discourage people from getting vaccinated.

In her livestream, Ms. Ocasio-Cortez recalled hiding in a bathroom and thinking she was going to die as unknown people entered her office and shouted, “Where is she?” They turned out to be Capitol Police officers who had not clearly identified themselves, and Ms. Ocasio-Cortez said so on Instagram. She did not claim that they were rioters — only that, from her hiding spot, she initially thought they were.

During the riot, reporters wrote on Twitter that the Cannon building was being evacuated because of credible threats, and that Capitol Police officers were running through the hallways and entering offices just as Ms. Ocasio-Cortez described.

The false claims about her statements have spread widely online, much of the backlash stemming from an article on the conservative RedState blog and a livestream from the right-wing commentator Steven Crowder. On Thursday, Representative Nancy Mace, Republican of South Carolina, tweeted, “I’m two doors down from @aoc and no insurrectionists stormed our hallway.”

But Ms. Ocasio-Cortez never said insurrectionists had stormed that hallway, and Ms. Mace herself has described being frightened enough to barricade her own door. A spokeswoman for Ms. Mace said on Friday that the congresswoman’s tweet had been intended as “an indictment of the media for reporting there were insurrectionists in our hallway when in fact there were not,” and that it “was not at all directed at Ocasio-Cortez.”

“As the Capitol complex was stormed and people were being killed, none of us knew in the moment what areas were compromised,” Ms. Ocasio-Cortez tweeted in response to Ms. Mace’s post. (A spokeswoman for Ms. Ocasio-Cortez said the lawmaker had no additional comment.)

Others have corroborated Ms. Ocasio-Cortez’s account and confirmed that the Cannon building was threatened, even though the rioters did not ultimately breach it.

Ari Rabin-Havt, a deputy manager for Senator Bernie Sanders’s 2020 presidential campaign, tweeted that he was in the Capitol tunnels during the attack. As Mr. Rabin-Havt moved toward the Cannon building, he wrote, members of a SWAT team yelled at him to find a hiding place.

And Representative Katie Porter, Democrat of California, said on MSNBC that after the Cannon building was evacuated, she and Ms. Ocasio-Cortez sheltered in Ms. Porter’s office in another building. She said Ms. Ocasio-Cortez was clearly terrified, opening closets to try to find hiding places and wishing aloud that she had worn flats instead of heels in case she had to run.

Jacob Silver contributed reporting.

Mr. Giuliani regularly stated, falsely, that Dominion “really is a Venezuelan company” and that it “depends completely on the software of Smartmatic,” a company “developed in about 2004, 2005 to help Chavez steal elections.”

As Dominion writes in its lawsuit: “Dominion was not founded in Venezuela to fix elections for Hugo Chávez. It was founded in 2002 in John Poulos’s basement in Toronto to help blind people vote on paper ballots.” The suit later adds that the headquarters for the company’s United States subsidiary are in Denver.

2. Programming Votes

Another often-repeated claim was that Dominion had programmed its machines to flip votes: “In other words when you pressed down Biden, you got Trump, and when you pressed down Trump you got Biden.”

This has been proved false by numerous government and law enforcement officials, including former Attorney General William P. Barr, who said in December: “There’s been one assertion that would be systemic fraud, and that would be the claim that machines were programmed essentially to skew the election results. And the D.H.S. and D.O.J. have looked into that, and so far, we haven’t seen anything to substantiate that.”

Similarly, a joint statement by numerous government and elections officials and agencies, including the National Association of State Election Directors, the National Association of Secretaries of State, and the Cybersecurity and Infrastructure Security Agency, stated that there was “no evidence that any voting system deleted or lost votes, changed votes, or was in any way compromised.”

The hand recount in Georgia also affirmed that the machine recounts were accurate in that state.

3. Antrim County, Mich.

Mr. Giuliani zeroed in on Antrim County, Mich., falsely claiming that a “Dominion machine flipped 6,000 votes from Trump to Biden” there, and that machines in the county were “62 percent inaccurate,” had a “68 percent error rate” and had an “81.9 percent rejection rate.”

Mr. Giuliani’s focus on Antrim County stems from human errors made by the county clerk on election night. According to the lawsuit, the clerk “mistakenly failed to update all of the voting machines’ tabulator memory cards.” But the suit says that “her mistakes were promptly caught as part of the normal canvass process before the election result was made official.” The Michigan secretary of state’s office also conducted a hand audit of all presidential votes in Antrim County that found the machines were accurate.

4. A Problematic Expert

Mr. Giuliani claimed that his accusations, particularly in Antrim County, were backed up by experts. But he largely relied on one man, Russell Ramsland Jr., a former Republican congressional candidate from Texas, who, according to the lawsuit filed by Dominion, had also publicly favored false conspiracy theories.

Dominion spent more than five pages on Mr. Ramsland’s lack of credentials to properly examine equipment, noting that he had a “fundamental misunderstanding of election software.” The suit also quotes the former acting director of the U.S. Election Assistance Commission Voting System Testing and Certification program, saying the report produced by Mr. Ramsland “showed a ‘grave misunderstanding’ of Antrim County’s voting system and ‘a lack of knowledge of election technology and process.’”

Twitter continues to grapple with misinformation on the platform. In the months before the U.S. presidential election, Twitter added fact-check labels written by its own employees to tweets from prominent accounts, temporarily disabled its recommendation algorithm, and added more context to trending topics. Still, false claims about the coronavirus and elections have proliferated on Twitter despite the company’s efforts to remove them. But Twitter has also faced backlash from some users who have argued that the company removes too much information.

Giving some control over moderation directly to users could help restore trust and allow the company to move more quickly to address false claims, Twitter said.

“We apply labels and add context to tweets, but we don’t want to limit efforts to circumstances where something breaks our rules or receives widespread public attention,” Keith Coleman, a vice president of product at Twitter, wrote in a blog post announcing the program. “We also want to broaden the range of voices that are part of tackling this problem, and we believe a community-driven approach can help.”

“The more I think about it, I do think it’s very possible that Biden will be the one who pulls the trigger,” one account wrote in a QAnon channel on the messaging app Telegram.

Others expressed anger with QAnon influencers who had told believers to expect a dramatic culmination on Inauguration Day.

“A lot of YouTube journalists have just lost one hell of a lot of credibility,” wrote a commenter in one QAnon chat room.

Still others attempted to shift the goal posts, and simply told their fellow “anons” to hang on and wait for future, unspecified developments.

“Don’t worry about what happens at 12 p.m.,” wrote one QAnon influencer. “Watch what happens after that.”

And some appeared to realize that they’d been duped.

“It’s over,” one QAnon chat room participant wrote, just after Mr. Biden’s swearing-in.

“Wake up,” another wrote. “We’ve been had.”

Followers hoping for guidance from “Q,” the pseudonymous message board user whose posts power the movement, were bound to be disappointed. The account has been silent for weeks, and had not posted Wednesday.

Ron Watkins, a major QAnon booster whom some have suspected of being “Q” himself, posted a note of resignation on his Telegram channel on Wednesday afternoon.

“We have a new president sworn in and it is our responsibility as citizens to respect the Constitution,” he wrote. “As we enter into the next administration please remember all the friends and happy memories we made together over the past few years.”

Both appeared in videos of the Capitol siege.

Their presence demonstrates how the disinformation networks that drove the spread of Covid-19 falsehoods are integrated with the networks spreading voter fraud disinformation, said Kate Starbird, a University of Washington associate professor studying online disinformation.

Several prominent anti-vaccination activist groups, including the Natural News website as well as several large groups and influencers on Facebook and Instagram with hundreds of thousands of followers, reveled in the events on the Capitol and posted prolifically about it. “Grab some 🍿 and enjoy the show!” said one Instagram post with images of the Capitol being raided. The post collected 2,700 likes.

People connected to those networks, Ms. Starbird said, “are saturated in disinformation and experiencing a very different, grievance-based reality than the rest of us.”

Mr. Willis entered the Capitol building, but said in a Facebook post that he did not go in far and left quickly. In a speech right after the siege, he was captured in a video speaking to a crowd of people and referring to those who had pushed into the Capitol as “compatriots.” He also railed against the left and the “diabolical” and “corrupt tyrants” of the mainstream media. “This is psychological warfare,” Mr. Willis said in the video. “This is what war looks like today.”

In an email, Mr. Willis said he had made plans to attend the rally at the Capitol because he was “deeply concerned about the loss of our civil liberties.” He added that he found out too late that the rally he was meant to attend, called Health Freedom DC, included the “Make America Great Again” tagline associated with President Trump. Mr. Willis said he did not support any political party and his presence in videos had been “terribly distorted.”

In his email, Mr. Willis said, “I’ve only seen the violence on TV and social media.”

Ms. Gold, the doctor who shared misleading information about the coronavirus, appeared in a video on the tiled Rotunda floor at the Capitol, reciting a speech from a sheaf of papers protesting a “massive medical establishment,” according to The Washington Post.

In a separate video that went viral after “Plandemic,” which collected tens of million views in July, Ms. Gold appeared with a group of doctors calling themselves America’s Frontline Doctors, which she founded. The group was sponsored by conservative activists called the Tea Party Patriots Action and the video spread the misleading message that hydroxychloroquine was an effective coronavirus treatment and that masks did not slow the spread of the virus.

Ms. Gold later said, “I do regret being there.” She did not respond to requests for comment.

Facebook said on Thursday that it is identifying people involved in storming the Capitol last week and disabling their accounts.

The rumors may have originated from — and mischaracterized — a popular tweet from the writer Anne Nelson pointing out that Ms. Thomas is on the advisory board of Turning Point USA, a conservative student group.

The founder of Turning Point USA, Charlie Kirk, said in a since-deleted tweet that Turning Point’s political action arm and an affiliated group, Students for Trump, were sending more than 80 “buses of patriots to D.C. to fight for the president” on Jan. 6.

While 80 buses was the number that Turning Point Action had committed to funding, Mr. Kirk’s tweet was “ultimately inaccurate” as the groups ended up sending just seven buses from New Jersey, North Carolina, and other locations, according to a spokesman for Turning Point.

Ms. Thomas did not fund any buses herself, the spokesman said. Ms. Nelson, the author of a book about an influential conservative group whose members include Ms. Thomas, also told The New York Times that the claim that Ms. Thomas “paid for buses” is “far beyond any of the documentation I’ve presented.”

An itinerary provided to The New York Times by Turning Point noted that the buses would arrive at the South Lawn of the White House at 9 a.m. on Jan. 6, and that there was no exact time for the buses to depart because the duration of Mr. Trump’s speech was unclear. It did not provide any instructions about joining the march to the Capitol, and Brian Caviness, a student who traveled with the group, was quoted by The Fort Worth Star-Telegram as saying that he did not do so as “that wasn’t part of the plan.”

Among those pushing the falsehood were Representative Matt Gaetz, a Florida Republican, who said while objecting to the electoral votes for Mr. Biden that people in the mob were “in fact members of the violent terrorist group antifa.” Ken Paxton, the attorney general of Texas, also said antifa was involved.

But even President Trump acknowledged that the people who supported him — not liberal activists — had invaded the Capitol. At one point on Wednesday he told the mob, “we love you.”

An analysis by the media insights company Zignal Labs found that the unfounded rumor had been mentioned 411,099 times across cable television, social media, and in print and online news outlets on Wednesday and Thursday. It was by far the most widely shared false or misleading claim about the Capitol Hill mob, Zignal said.

Adam Goldman contributed reporting.

1. Rioters on the Capitol were actually antifa: 411,099 mentions

The false narrative that antifa supporters were actually behind the unrest at the Capitol peaked at 66,122 mentions on Wednesday evening, according to Zignal’s data. Rep. Matt Gaetz even referenced the false Washington Times article as proof that the mob was “in fact members of the violent terrorist group antifa.”

On Thursday, The Washington Times published a new version of its article, reporting that it was actually “neo-Nazis and other extremists” who were identified in photos of the mob, after BuzzFeed News challenged the outlet’s reporting.

2. The mob’s actions were a “setup” and an “inside job”: 122,287 mentions

The idea that the mob’s work was an inside job spread widely on social media, even though there was no evidence to support the conspiracy theory. People said the setup had been planned by the “deep state,” which is shorthand for the conspiracy theory about Democratic elites secretly exercising political control over the public. The narrative peaked at 12,593 mentions from 6 p.m. to 7 p.m. on Wednesday, according to Zignal’s data.

3. President Trump knew that the mob would happen, and people should “trust the plan” and “hold the line”: 83,990 mentions

The distorted idea that President Trump knew about the mob’s actions in advance and that people should “trust the plan” and “hold the line” was widespread especially among supporters of the conspiracy movement QAnon — which is based upon the false premise that the country is run by a Democrat-led cabal of pedophiles whom President Trump is bringing down.

4. The mob at the Capitol was made up of people “posing as MAGA”: 64,258 mentions

A popular false narrative that people in the mob were simply “posing as MAGA” peaked early on Wednesday, before accusations specifically zeroed in on antifa.

5. President Trump will “declassify” information on how the election was stolen: 63,190 mentions

Some supporters of the president pushed the falsehood that he would soon “declassify” information on how the election was stolen, in spite of overwhelming evidence — and a host of court rulings — that no widespread fraud was found in the election.

In some versions of the baseless rumor, people stated that this was the real reason that Mr. Trump’s opponents in Congress were calling on the president to be stripped of his power from office under the disability clause of the 25th Amendment.

Among the most popular figures pushing the conspiracy theory were the commentator Candace Owens, the Georgia lawyer L. Lin Wood and Juanita Broaddrick, a nursing home administrator who in 1999 publicly accused President Bill Clinton of raping her in 1978. Other prominent figures spreading the rumor included Ken Paxton, the attorney general of Texas; Sarah Palin, the former vice-presidential candidate; and Representative Mo Brooks, an Alabama Republican.

The rumor that supporters of the antifa movement — a loosely organized collective of antifascist activists — had posed as members of the far right on Wednesday was shared more than 150,000 times on Twitter and thousands of times more on Facebook, according to an analysis by The New York Times. Altogether, the accounts pushing the rumor had tens of millions of followers.

“Indisputable photographic evidence that antifa violently broke into Congress today to inflict harm & do damage,” Mr. Wood posted on Twitter. “NOT @realDonaldTrump supporters.”

The “photographic evidence” that Mr. Wood pointed to in his post included a link to phillyantifa.org, where the photo of a bearded man involved in the mob was hosted. But that particular page exposed photos of known individuals in the neo-Nazi movement.

Another popular post, shared at least 39,000 times on Twitter, claimed without evidence that a “former FBI agent on the ground at U.S. Capitol just texted me and confirmed at least 1 ‘bus load’ of Antifa thugs infiltrated the peaceful Trump demonstrators.”

Untrue claims that “busloads” or “planeloads” of antifascist activists infiltrated protests are a common refrain from the far right.

In response to the baseless assertion, a Twitter user said, “Of course they did.” The user attached photos of a man wearing a horned helmet with his face painted in an American flag design as an apparent example of an antifa supporter.

The man was not an antifa supporter. Instead, he is a longtime QAnon supporter who has been a fixture at Arizona right-wing political rallies in recent months, according to The Arizona Republic.

Ben Decker and Jacob Silver contributed research.

Here is a rundown of the false claims about Georgia’s vote-counting that Mr. Trump and his lawyers made on the call and in other venues, and Mr. Sterling’s explanations of what actually happened.

TRUMP’S CLAIM: That, amid the disruption caused by a broken water main at a vote-counting center in Fulton County, election workers brought in “suitcases or trunks” of ballots.

STERLING’S EXPLANATION: Late in the evening, after the water main break had been fixed, election workers prepared to go home for the night and followed standard procedures to store ballots securely: placing them in containers and affixing numbered seals. But when Mr. Raffensperger found out that they were closing up shop, he ordered them to continue counting through the night — so the workers retrieved the containers and resumed counting ballots.

All of this is on video footage that the secretary of state’s office posted publicly.

“This is what’s really frustrating: The president’s legal team had the entire tape,” Mr. Sterling said. “They watched the entire tape. They intentionally misled the State Senate, the voters and the people of the United States about this.”

TRUMP’S CLAIM: That workers scanned some batches of ballots multiple times.

STERLING’S EXPLANATION: When a scanning machine encounters a problem, it stops, but a few ballots get through while it’s stopping. When that happens, workers take the ballots and scan them again so they’re counted properly. This is standard procedure, and the ballots aren’t counted twice — and if they were, the hand recount Georgia conducted would have shown it.

“That audit showed that there was no problem with the machine scanning,” Mr. Sterling said. “If somebody took a stack of ballots and scanned them multiple times, you would have a lot of votes with no corresponding ballots.”

TRUMP’S CLAIM: That tens of thousands of ineligible voters cast ballots.

STERLING’S EXPLANATION: The actual number of ballots cast by ineligible voters is minuscule, and nowhere near enough to change the outcome of the election.

Mr. Sterling also addressed more specific claims about ineligible voters:

• Mr. Trump said that thousands of people voted despite not being registered to vote. This is impossible, Mr. Sterling said: “You can’t do it. There cannot be a ballot issued to you, there’s no way to tie it back to you, there’s nowhere for them to have a name to correspond back to unless they’re registered voters. So that number is zero.”

• Mr. Trump said that thousands of voters died before the election. Mr. Sterling said the secretary of state’s office had found only two who might fit that description.

• Mr. Trump said that hundreds of people voted using P.O. boxes rather than a residential address. Mr. Sterling said that the secretary of state’s office was still investigating, but that everyone it had examined so far had, in fact, used a proper residential address — just one for a multifamily residence or apartment building.

• Mr. Trump’s campaign said that many felons voted. In reality, using records from the state’s corrections and probation departments, the secretary of state’s office identified only 74 people who might fit that category — and Mr. Sterling said the final number would be even lower once the office completed its investigation, because in many cases, the person might have had their voting rights reinstated after completing a sentence or might simply have the same name as a felon.

• Mr. Trump’s campaign said that tens of thousands of people younger than 18 voted. “The actual number is zero,” Mr. Sterling said, “and the reason we know that is because the dates are on the voter registration. There are four cases — four — where people requested their absentee ballot before they turned 18, but they turned 18 by Election Day. That means that is a legally cast ballot.”

• Mr. Trump’s campaign said that hundreds of voters cast ballots in two states. Mr. Sterling said that officials were still investigating, but that if any such cases were confirmed, it would be “handfuls,” and nowhere near enough to change the outcome.

TRUMP’S CLAIM: That machines flipped votes, counting Trump ballots as Biden ones.

STERLING’S EXPLANATION: If this had happened, Mr. Sterling said, the hand recount would have shown it, and it did not show anything of the sort.

Discussing allegations of hacking, he added that ballot machines and scanners aren’t connected to the internet. “Neither one has modems,” Mr. Sterling said. “It’s very hard to hack things without modems.”

TRUMP’S CLAIM: That election officials did not properly verify signatures for mail-in ballots.

STERLING’S EXPLANATION: The secretary of state’s office brought in signature experts, who examined more than 15,000 mail-in ballot envelopes. They found potential problems with only two, and upon investigation, both ballots turned out to be legitimate.

TRUMP’S CLAIM: That, compared with previous election cycles, Georgia rejected a suspiciously low number of mail-in ballots.

STERLING’S EXPLANATION: The decrease in rejections is attributable to a recently passed law that gives Georgians a chance to correct problems, such as a rejected signature, with their ballots. Both parties had teams roaming the state and contacting voters whose ballots were at risk of rejection, but Mr. Sterling said the Democrats were simply more prepared for the task.

TRUMP’S CLAIM: That election officials shredded ballots.

STERLING’S EXPLANATION: “There is no shredding of ballots going on,” Mr. Sterling said with clear annoyance. “That’s not real. It’s not happening.”

Workers did shred secrecy envelopes: the blank envelopes that protect the privacy of a voter’s absentee ballot and go inside an outer envelope. It’s the outer envelope that voters have to sign, and election officials have kept those outer envelopes as required by law. The secrecy envelopes, however, “have no evidentiary value,” Mr. Sterling said, because by definition they have no identifying information on them.

TRUMP’S CLAIM: That employees of Dominion Voting Systems “moved the inner parts” of voting machines “and replaced them with other parts.”

STERLING’S EXPLANATION: “No one is changing parts or pieces out of Dominion voting machines. That’s not real. I don’t even know what that means.”

TRUMP’S CLAIM: That officials improperly counted “pristine” ballots — meaning ballots that weren’t folded, indicating that they hadn’t arrived in an envelope.

STERLING’S EXPLANATION: “Pristine” ballots aren’t unusual, Mr. Sterling said. For instance, many military and overseas voters receive electronic ballots that they print out, complete and mail back. But these printed ballots aren’t the right size for scanners, so election workers have a standard process for transferring the votes to scannable ballots. A ballot that gets damaged and can’t be scanned may be transferred in the same way.

TRUMP’S CLAIM: That Mr. Raffensperger is compromised because he has a brother who works for a Chinese technology company. (Mr. Trump was echoing a conspiracy theory about an unrelated man who happens to be named Ron Raffensperger.)

STERLING’S EXPLANATION: Mr. Raffensperger doesn’t have a brother named Ron.

False. Mr. Trump was most likely referring to debunked claims that a water leak at a vote counting location in Fulton County forced an evacuation and made it possible for trunks full of ballots to be rolled in. Election officials have said and surveillance videos show that this did not happen.

A water leak caused a delay for about two hours in vote counting at the State Farm Arena, but no ballots or equipment were damaged. Georgia’s chief election investigator, Frances Watson, testified that a “review of the entire security footage revealed that there were no mystery ballots that were brought in from an unknown location and hidden under tables.”

Throughout the phone call, Mr. Trump also repeatedly suggested that an election worker seen in the surveillance videos “stuffed the boxes” and “they thought she’d be in jail” — referring to a baseless conspiracy theory promoted on social media.

[Read more about the voting in Georgia so far.]

What Mr. Trump Said

“There were no poll watchers there. There were no Democrats or Republicans. There was no security there.”

This is misleading. Election observers and journalists were present at State Farm Arena when the water leak occurred. They were not asked to leave, Ms. Watson said, but simply “left on their own” when they saw one group of workers, who had completed their task, leave.

What Mr. Trump Said

“So dead people voted. And I think the number is close to 5,000 people.”

False. The actual number was two, Brad Raffensperger, Georgia’s secretary of state, told the president in the call.

What Mr. Trump Said

“You had out-of-state voters — they voted in Georgia but they were from out of state — of 4,925.”

This is misleading. Ryan Germany, the chief counsel for Mr. Raffensperger’s office, refuted this description in the call.

“Everyone we’ve been through are people that lived in Georgia, moved to a different state, but then moved back to Georgia legitimately,” he said. “They moved back in years ago. This was not like something just before the election. So there’s something about that data that, it’s just not accurate.”

What Mr. Trump Said

“In Fulton County and other areas — and this may or may not be true, because this just came up this morning — that they are burning their ballots, that they are shredding ballots, shredding ballots and removing equipment. They are changing the equipment on the Dominion machines, and you know that’s not legal.”

False. Mr. Trump was likely referring to images of Fulton County ballots that circulated on social media and posted by a supporter, Patrick Byrne, the former chief executive of Overstock.

The photos showed piles of ballots that were visibly not filled out and wrapped in plastic. Mr. Byrne characterized the ballots as “counterfeit” and said they were later shredded.

But those images were simply of emergency backup ballots, said Gabriel Sterling, a Republican official who is the voting system implementation manager in Georgia. State law requires counties to prepare additional paper ballots in case voting machines cannot be used.

Dominion Voting Systems, which has been the subject of countless conspiracy theories and false rumors, did not remove any machinery from Fulton County, Mr. Germany told the president.

What Mr. Trump Said

“In Detroit, we had 139 percent of the people voted. That’s not too good. In Pennsylvania, they had well over 200,000 more votes than they had people voting.”

False. About 51 percent of registered voters and 38 percent of the entire population cast a ballot in Detroit.

The figure for Pennsylvania was a reference to faulty analysis conducted by state Republican lawmakers. The analysis relied on a voter registration database that Pennsylvania’s Department of State said was incomplete as a few counties — including Philadelphia and Allegheny Counties, the two largest in the state — had yet to fully upload their data. The department called the analysis “obvious misinformation.”

What Mr. Trump Said

“She got you to sign a totally unconstitutional agreement, which is a disastrous agreement. You can’t check signatures. I can’t imagine you’re allowed to do harvesting, I guess, in that agreement.”

False. This was an inaccurate reference to a settlement between Georgia and the Democratic Party. Under the March settlement, officials must notify voters whose signatures were rejected within three business days and give them the chance to correct issues. It does not bar officials from verifying signatures and does not allow “harvesting,” or collecting and dropping off ballots in bulk.

“Harvesting is still illegal in the state of Georgia. And that settlement agreement did not change that one iota,” Mr. Raffensperger said in the call.

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This week, Jack Stollsteimer, the district attorney of Delaware County, accused Bruce Bartman of Marple Township, Pa., of illegally voting in place of his deceased mother in the general election. In addition to his mother, Mr. Bartman registered his mother-in-law, Elizabeth Weihman, who died in 2019, as a voter, according to the district attorney’s office, but is not accused of voting for her. He also cast a ballot under his own name.

“This is the only known case of a ‘dead person’ voting in our county, conspiracy theories notwithstanding,” Mr. Stollsteimer said in a statement. “The prompt prosecution of this case shows that law enforcement will continue to uphold our election laws whenever presented with actual evidence of fraud and that we will continue to investigate every allegation that comes our way.”

Samuel Stretton, a lawyer for Mr. Bartman, said: “He’s admitted everything. He’s cooperated.” Mr. Stretton added that he was negotiating a guilty plea, and that Mr. Bartman had no criminal record.

“He’s a good man,” Mr. Stretton said. “He did something very stupid under some misguided theory that this was his form of protest.”

In an interview with The New York Times in November after the Trump campaign first made its claims, Mr. Bartman said he did not recall seeing a mail-in ballot for his mother. “Oh, no, no, I haven’t gotten anything,” he said. “Occasionally I would get some junk mail for her. But not in several years.”

He added that he did not hear of the Trump campaign’s allegation because he did not use social media much and only infrequently logged on to Facebook to see pictures of his grandchildren.

Asked whether he knew why a vote for his mother would have been recorded despite her having passed away, he said the state’s governor, Tom Wolf, “doesn’t know anything or what’s going on in the city of Philadelphia, or the surrounding counties in the middle part of the state.”

“Some of the stuff that has gone on in Philadelphia is just atrocious,” Mr. Bartman added.

Mr. Stretton, his lawyer, said, “He was wrong in saying that, he admits he was wrong, and since he was approached by the detectives, he has cooperated and told the truth.”

The claim that a vote was fraudulently cast using Elizabeth Bartman’s name and that it was emblematic of systemic voter fraud helping Mr. Biden spread widely online. On Facebook, articles with the claim from the conservative websites ZeroHedge and The Epoch Times were shared 1,800 times and reached up to 61 million followers, according to data from CrowdTangle, a Facebook-owned social media analytics tool.