This whole FactChecking thing began in the US, and our American counterparts are experiencing a very busy spell following the decision of one Donald John Trump to run for president.

Trump is being criticised by the White House and other Republicans for his latest contribution to the debate on events in the Middle East – a call for “a total and complete shutdown of Muslims entering the United States until our country’s representatives can figure out what is going on”.

The billionaire tycoon’s antics on the campaign trail have rarely been out of the headlines since he announced he was running for the presidency in June.

In the last fortnight he was accused of mocking a disabled reporter, making stereotypical jokes about Jews, and doubting the existence of Muslim American sports heroes – despite meeting Muhammad Ali several times.

At time of writing, most polls suggest Trump is still the favourite to become the Republican presidential nominee ahead of the election next year.

FactChecking “The Donald” has become a miniature industry in itself, with most of the major US sites compiling fat dossiers of dubious statements and regularly awarding him the equivalent of our full-blown Fiction rating.

Let’s look at the five dodgiest claims uttered so far by the man NBC have called the “post-truth” presidential candidate.

Obama is a Muslim

Trump has never uttered these exact words, but he’s dropped some pretty heavy hints that he sympathises with “birthers” – people who subscribe to the conspiracy theory that Barack Obama was not born in the United States, and often believe him to be a secret Muslim.

In January 2011 Trump began to cast doubt about Obama’s birth certificate and early life.

He said in a speech: “Our current president came out of nowhere. Came out of nowhere. In fact, I’ll go a step further: the people that went to school with him, they never saw him, they don’t know who he is.”

This was shot down by PolitiFact, who spoke to people who remember the future president at Columbia university, and provided links to many other reminiscences of the young Obama from friends.

Trump kept up the innuendo, telling Fox News: “He doesn’t have a birth certificate. He may have one, but there’s something on that, maybe religion, maybe it says he is a Muslim.”

He repeatedly challenged Obama to make his birth certificate public, which the president duly did in April 2011.

The document confirmed Obama was born in Honolulu, Hawaii, and made no mention of religion. It failed to satisfy the conspiracists, although claims that the certificate is a fake have been comprehensively debunked.

Days later, Trump sat stony-faced at the 2011 White House Correspondents Dinner when the president mockingly revealed his “official birth video” – an excerpt from the Lion King, followed by the payoff: “Oh well – back to square one.”

Despite seeking to reignite the debate about Obama’s back-story a year later, by offering to give $5m to a charity of the president’s choice if he made public his college and passport records, Trump has brushed off questions about the affair in recent interviews.

At a campaign rally in September Trump failed to challenge or contradict an audience member who said: “We have a problem in this country – it’s called Muslims. We know our current president is one. You know he’s not even an American.”

Thousands of American Muslims cheered when the Twin Towers fell

Last month, Trump was talking at a rally about the need for surveillance of certain mosques in the US, when he came out with this claim:

“Hey, I watched when the World Trade Center came tumbling down. And I watched in Jersey City, NJ, where thousands and thousands of people were cheering as that building was coming down. Thousands of people were cheering.”

Jersey City is close to New York and is home to one of the largest Muslim communities in America.

It’s true that there were rumours at the time of Muslim Americans gathering on rooftops and partying in celebration the September 11, 2001 terror attacks on New York.

But extensive fact-checking strongly suggests that the rumours were either exaggerated or flatly untrue.

The mayor of New York City at the time, Rudy Giuliani, said “we did have some reports of people celebrating that day” but accused Trump of inflating the numbers involved.

Other local politicians and law enforcement officials have said reports of Muslims celebrating on 9/11 turned out to be bogus.

When challenged by ABC news, Trump was unrepentant saying: “It was on television. I saw it… it was well covered at the time. There were people over in New Jersey that were watching it, a heavy Arab population, that were cheering as the buildings came down.”

But no one has ever produced any evidence of footage like this being aired on television.

See also:
The 9/11 hijackers “put their families on airplanes a couple of days before”. (No, they didn’t)
“I predicted Osama bin Laden… was coming in to do damage.” (He didn’t.)

Mexico is exporting its criminals to the US

“The Mexican Government is forcing their most unwanted people into the United States. They are, in many cases, criminals, drug dealers, rapists, etc.”

There are really two threads to this claim: an immigrant crime wave, and a deliberate policy on the part of Mexico to encourage its criminals to emigrate to the US. Neither of these things is rooted in reality.

Several US fact-checkers noted that the evidence suggests first-generation immigrants actually tend to commit less crime than “natives”, although data is not comprehensive.

The Washington Post found that native-born men aged 18-39 without a high-school diploma were nearly four times more likely to be in prison in 2010 than Mexican men with the same demographic profile.

Immigration experts interviewed by PolitiFact were left scratching their heads at the suggestion that the Mexican authorities were “forcing” unwanted citizens to migrate.

See also: “I will build the best wall (between the US and Mexico). The biggest, the strongest, not penetrable…” (He almost certainly won’t.)

Blacks kill 81 per cent of white homicide victims

In fairness, the presidential candidate didn’t make this statistical claim himself – he retweeted something that had been doing the rounds.

But in doing so he appeared to endorse something blatantly and dangerously untrue.

At a time when race and crime is an explosive issue in America, Trump circulated this graph to his followers:

The source – “Crime Statistics Bureau – San Franciso” – does not actually exist. And full figures for 2015 cannot possibly have been published yet, because the year isn’t over.

Unsurprisingly, the numbers are completely untrue. The most incendiary claim – that 81 per cent of white victims are killed by blacks – is the most inaccurate, with the FBI putting the true proportion at 15 per cent in 2014.

Some 82 per cent of white victims were in fact killed by other whites last year.

By the way, we’re not being flippant about America’s real problems with race and crime – we FactChecked the topic here.

“Our president wants to take in 250,000 from Syria.”

Trump has repeatedly weighed in to the Syrian refugee crisis, not entirely consistently.

In September he told Fox News that the US should accept some refugees from Syria to ease the “unbelievable humanitarian problem.”

A day later he said: “Maybe we could do something… but we have big problems to solve.”

By November, after the Paris attacks the would-be president was warning that an influx of people from Syria could be a “Trojan horse” for terrorists, saying: “”We cannot let them into this country, period.”

He claimed that Obama had promised to resettle a quarter of a million refugees from the war-torn country.

Again, fact checkers shot this down: Trump didn’t explain his numbers, but was probably garbling the total number of refugees from the rest of the world that America planned to take in over three years.

See also: They only send Syrian refugees “to the Republicans, not to the Democrats”. (No, they don’t.)