Former President Donald Trump’s supporters have made inaccurate claims about the judge presiding over his case and misleadingly compared his conduct to that of other politicians.Allies of former President Donald J. Trump have rushed to his defense since he was charged on Tuesday in connection with his efforts to overturn the 2020 election.They inaccurately attacked the judge assigned to oversee the trial, baselessly speculated that the timing of the accusations was intended to obscure misconduct by the Bidens and misleadingly compared his conduct to that of Democratic politicians.Here’s a fact check.What Was Said“Judge Chutkan was appointed to the D.C. District Court by Barack Obama, and she has a reputation for being far left, even by D.C. District Court standards. Judge Chutkan, for example, has set aside numerous federal death-penalty cases, and she is the only federal judge in Washington, D.C., who has sentenced Jan. 6 defendants to sentences longer than the government requested.”— Senator Ted Cruz, Republican of Texas, in a podcast on WednesdayThis is exaggerated. Mr. Cruz is correct that Judge Tanya S. Chutkan, the trial judge overseeing Mr. Trump’s prosecution in the case, was appointed by President Barack Obama. While she has gained a reputation for handing down tough sentences to people convicted of crimes in the Jan. 6 riot, she is not the only federal judge who has exceeded prosecutors’ sentencing recommendations.Of the more than 1,000 people who have been charged for their activities on Jan. 6, 2021, about 561 people have received a sentence, including 335 in jail and another 119 in home detention, as of July 6, according to the Justice Department. Judges have largely issued sentences shorter than what prosecutors sought and what federal sentencing guidelines recommend, data compiled by NPR and The Washington Post shows.Senator Ted Cruz described Judge Tanya S. Chutkan’s appointment as “highly problematic,” but in the Federal District Court in Washington, cases are randomly assigned.Haiyun Jiang/The New York TimesJudge Chutkan ordered longer penalties in at least four cases, according to NPR, and appears to have done so more frequently than her peers. But other judges in Federal District Court in Washington have also imposed harsher sentences.Those include Judge Royce C. Lamberth, appointed by President Ronald Reagan, who sentenced a man to 60 days in prison while the government had asked for 14 days. He sentenced another to 51 months, rather than 46 months, and another to 60 days, rather than 30.Judge Amy Berman Jackson, an Obama appointee, sentenced another defendant to 30 days, twice as long as the government recommendation. Judge Reggie B. Walton, nominated by President George W. Bush, sentenced a defendant to 50 days compared with the recommended 30 days. And Judge Emmet G. Sullivan, appointed by President Bill Clinton, sentenced a man to 60 days rather than 45 days.Moreover, Mr. Cruz described Judge Chutkan’s appointment as “highly problematic” given her political leanings. But it is worth noting that in the Federal District Court in Washington, cases are randomly assigned — similar to how Judge Aileen M. Cannon, a Trump appointee, was randomly assigned to preside over the case involving Mr. Trump’s handling of classified documents after he left office.What Was Said“All of these indictments have been called into question because they come right after massive evidence is released about the Biden family. On June 7, the F.B.I. released documents alleging that the Bidens took in $10 million in bribes from Burisma. The very next day, Jack Smith indicted Trump over the classified documents kept at Mar-a-Lago. And then you go to July 26. That’s when Hunter Biden’s plea deal fell apart after the D.O.J. tried giving him blanket immunity from any future prosecutions. The very next day, Jack Smith added more charges to the Mar-a-Lago case. And now, just one day after Devon Archer gave explosive testimony about Joe Biden’s involvement in Hunter Biden’s business deals, Smith indicts Trump for Jan. 6.”— Maria Bartiromo, anchor on Fox Business Network, on WednesdayThis lacks evidence. Mr. Trump and many of his supporters have suggested that the timing of developments in investigations into his conduct runs suspiciously parallel to investigations into the conduct of Hunter Biden and is meant as a distraction.But there is no proof that Mr. Smith, the special counsel overseeing the cases, has deliberately synced his inquiries into Mr. Trump with investigations into the Bidens, one of which is handled by federal prosecutors and others by House Republicans.Attorney General Merrick B. Garland appointed Mr. Smith as special counsel in November to investigate Mr. Trump’s role in the Jan. 6 riot at the Capitol as well as the former president’s retention of classified documents. After Republicans won the House that same month, lawmakers in the party said they would begin to investigate the Bidens. (The Justice Department separately began an inquiry into Hunter Biden’s taxes and business dealings in 2018.)Over the next few months, the inquiries barreled along, with some developments inevitably occurring almost in tandem. In some cases, Mr. Smith has little control over the developments or when they are publicly revealed.The first overlap Ms. Bartiromo cited centered on an F.B.I. document from June 2020 that contained an unsubstantiated allegation of bribery against President Biden and his son, and on charges filed against Mr. Trump over his handling of classified documents.Jack Smith was appointed in November 2022 to investigate Mr. Trump’s role in the Jan. 6 riot.Doug Mills/The New York TimesRepresentative James R. Comer of Kentucky, the Republican chairman of the House oversight committee, issued a subpoena in May for the document. The F.B.I. allowed Mr. Comer and the committee’s top Democrat access to a redacted version on June 5. That same day, Mr. Comer said he would initiate contempt-of-Congress hearings against the F.B.I. director on June 8, as the agency was still resisting giving all members access to the document.Two days later, on June 7, Mr. Comer announced that the F.B.I. had relented and that he would cancel the contempt proceedings. Members of the committee viewed the document on the morning of June 8, and Representative Marjorie Taylor Greene, Republican of Georgia, held a news conference that afternoon describing the document.That night, Mr. Trump himself, not the Justice Department, announced that he had been charged over his mishandling of classified documents, overtaking any headlines about the Bidens. The department declined to comment, and the indictment was unsealed a day later, on June 9.In the second overlap, on July 26, a federal judge put on hold a proposed plea deal between Hunter Biden and the Justice Department over tax and gun charges. Ms. Bartiromo is correct that a grand jury issued new charges against Mr. Trump in the documents case on July 27.The timing of the latest developments in Ms. Bartiromo’s third example, too, was not entirely in Mr. Smith’s hands.Hunter Biden’s former business partner Devon Archer was first subpoenaed on June 12 to testify before the committee on June 16. Mr. Comer told The Washington Examiner that Mr. Archer rescheduled his appearance three times before his lawyer confirmed on July 30 that he would appear the next day. Mr. Archer then spoke to the House oversight committee in nearly five hours of closed-door testimony on July 31. Republicans and Democrats on the committee gave conflicting accounts of what Mr. Archer said.Mr. Trump announced on July 18 that federal prosecutors had informed him he was a target of their investigation into his efforts to stay in office, suggesting that he would soon be indicted. Mr. Trump’s lawyers met with officials in the office of Mr. Smith on July 27. A magistrate judge ordered the indictment unsealed at 5:30 p.m. on Aug. 1.What Was Said“All of the people who claim that the 2016 election wasn’t legitimate, all of the people who claimed in 2004, with a formal objection in the Congress, that that election wasn’t legitimate, and in fact, objected to the point where they said that the voting machines in Ohio were tampered with and that President Bush was selected, not elected — and not to mention former presidents of the United States and secretary of states, Hillary Clinton, Jimmy Carter and a whole slew of House Democrats who repeatedly led the nation to believe — lied to the nation, that they said Russia selected Donald Trump as president, that the election was completely illegitimate — all of that was allowed to pass, but yet, once again, we see a criminalization when it comes to Donald Trump.”— Representative Michael Waltz, Republican of Florida, on CNN on WednesdayThis is misleading. Mr. Trump’s supporters have long argued that Democrats, too, have objected to election results and pushed allegations of voting malfeasance. None of the objections cited, though, have been paired with concerted efforts to overturn election results, as was the case for Mr. Trump.Democratic lawmakers objected to counting a state’s electors after the elections of recent Republican presidents in 2001, 2005 and 2017. In 2001 and 2017, objecting House members were unable to find a senator to sign on to their objections, as is required, and were overruled by the vice president. In 2005, two Democrats objected to counting Ohio’s electoral votes. The two chambers then convened debate and rejected the objections.In each case, the losing candidate had already conceded, did not try to overturn election results and did not try to persuade the vice president to halt proceedings as Mr. Trump is accused of doing in 2020.Mrs. Clinton has said repeatedly that Russian interference was partly to blame for her defeat in the 2016 presidential election. But she is not accused of trying to overthrow the results of the election. Prosecutors have not detailed any involvement on her part in a multifaceted effort to stay in power, including by organizing slates of false electors or pressuring officials to overturn voting results.What Was Said“Indicting political opponent candidates during a presidential election is what happens in banana republics and Third World countries.”— Representative Andy Harris, Republican of Maryland, in a Twitter post on TuesdayThis is exaggerated. Mr. Trump is the first former U.S. president to be indicted on criminal charges, but he is not the only presidential candidate to face charges in the United States and certainly not in the world.Rick Perry, the former governor of Texas, was indicted in August 2014 and accused of abusing his power. Mr. Perry, who ran for president in 2012, had hinted that he would run again and set up a political action committee the same month he was indicted. He officially announced his presidential bid in 2015 but dropped out before a court dismissed the charges against him in 2016.Eugene V. Debs, the socialist leader, ran for president behind bars in 1920 after he was indicted on a charge of sedition for opposing American involvement in World War I. He was sentenced in 1918 to 10 years in prison.It is also not unheard-of for political leaders in advanced economies and democracies to face charges while campaigning for office. In Israel, Prime Minister Benjamin Netanyahu was indicted in 2019 on charges of fraud and bribery. After losing power, he returned to his post in November 2022 while still facing charges. In Italy, Silvio Berlusconi faced numerous charges and scandals over tax fraud and prostitution while he served as prime minister in the 2000s.And in Taiwan, prosecutors said in 2006 that they had enough evidence to bring corruption charges against the president at the time, Chen Shui-bian. Mr. Chen remained his party’s chairman through parliamentary elections in 2008 as the investigation loomed over him, and he was arrested and charged that November. More