When the back wheels of Air Force One finally lifted off the tarmac at Joint Base Andrews on Wednesday bound for Mar-a-Lago, Donald Trump’s White House-in-exile in West Palm Beach, cheers erupted in millions of households across America and around the globe.

Four years of screeching tweets and ugly divisiveness were over, and for many it felt like the hope of a calmer, more civil world had swept in.

In one respect, though, the acrid, bitter smell of Trump continues to hang in the air: he left the presidency having never conceded that he lost the election to Joe Biden.

Trump’s decision to shun Biden’s inauguration – the first outgoing president to do so in 152 years – can be explained away as the hissy fit of a sore loser. But there’s a darker side to it. By forgoing the ritual of the peaceful handover of power that has been a pillar of American democracy since the country’s founding, he leaves a black cloud over the incoming administration.

Trump’s refusal formally to pass the baton means that the terrible events of 6 January are unfinished business. The armed mob of Trump supporters and white supremacists who stormed the Capitol Building, fired up by Trump’s lies about the “stolen election” and hunting for members of Congress to lynch, still have their marching orders. It is a legacy, made manifest on inauguration day by the 7ft non-scalable fences and the war zone-like presence of thousands of national guard troops in Washington DC.

As Trump legacies go, this one could prove much harder to unpick than those he left behind on the pandemic, immigration or the climate crisis that Biden tried to reverse with the flick of a pen on day one.

The legacy of the “stolen election”, by contrast, has the potential to endure. Michael Chertoff, the former homeland security secretary under George W Bush, told the Guardian recently that domestic terrorism inspired directly by Trump “is going to be the security challenge for the foreseeable future”.

Current intelligence chiefs agree. They are primed to have to deal with a lasting threat posed by Trump’s ongoing refusal publicly to accept the will of the American people.

An intelligence bulletin obtained by the Washington Post that was written just a week before the inauguration spelled out the intelligence community’s anxieties. The memo concluded that “amplified perceptions of fraud surrounding the outcome of the general election … very likely will lead to an increase in DVE [domestic violent extremist] violence.”

At the center of this new domestic terrorism threat is the seed of doubt that Trump has implanted in the minds of millions of Americans that the 2020 presidential election was “rigged”. It is the “animating lie”, as the former homeland security official Juliette Kayyem has put it, that drove the mob to storm the US Capitol and that now hangs in the air like a toxic gas.

Trump’s campaign to overturn the results of the presidential election amounted to a “big lie” familiar to those who study demagogic propaganda. Embedded within it are many of the core elements of what the Yale historian Timothy Snyder has called Trump’s post-truth, “pre-fascism”.

The lie was simple – able to be repeated and shared on TV and social media in six short words: “They stole the election from me.” That “they” was important too – by signaling a clear enemy, it allowed his supporters to direct their frustration and anger at identifiable targets.

Trump lashed out repeatedly at the media, which he denounced as the “enemy of the people”. He attacked “cowardly” Republican election officials who refused not to do their jobs, his own vice-president, and finally the heart of US democracy, Congress itself.

For Bandy X Lee, a forensic psychiatrist and violence expert, there was another key aspect to the “stop the steal” big lie – it was rooted in paranoia. In her analysis, paranoia, perceiving threat where none exists, is the most common symptom to cause violent behaviour.

“The fact that Trump actually believes himself to have been wronged and persecuted, or has paranoid ideations, spreads and finds resonance in paranoia that already exists in the population. That will increase the chances of violence,” Lee said.

As any student of tyrannies will tell you, for big lies to work they have to be repeated and repeated. Trump certainly fulfilled that requirement. He has been working assiduously to spread his animating lie for years. Consider the headline in the New Yorker, “Trump and the truth: the ‘rigged’ election”. The article beneath it reported that Trump was “trying to delegitimize a national election even while campaigning for the presidency” and that his ploy was working – about half of his supporters thought the election was cooked.

That New Yorker piece was published on 8 October 2016.

Trump’s efforts have paid even greater dividends in this election cycle. The most recent opinion polls suggest that more than a third of the total US electorate still believe that Trump won the November election, a proportion that rises above 70% when you ask Republicans. Nor is there any sign such a stunningly large number of Americans who bought Trump’s make-believe is on the wane. As Snyder wrote in the New York Times, “the lie outlasts the liar”.

Perhaps the most remarkable aspect of Trump’s sleight of hand is that he presented himself in the cloak of the protector of American democracy precisely in order to undermine American democracy. He invoked patriotism in order to legitimize the ultimate act of sedition – overthrowing the electoral will of the American people.

That is what most concerns David Gomez, a former FBI national security executive who spent many years countering domestic terrorism. He fears that Trump, by wrapping his actions in the cloth of patriotism, has given his blessing to violent action that could linger beyond his presidency.

“This is what makes this particular moment in time more dangerous,” he told the Guardian. “Fashioning yourself as a patriot makes it easier to justify, in your own mind, participating in acts that might lead to violence.”

The patriotic rhetoric acts like an ethical get-out clause, Gomez said. “It provides the average person a face-saving scenario to participate. ‘Oh, I’m not a bad guy, I’m a good guy acting as a patriot to save my country.’”

Into this mix has been poured the even more poisonous influence of far-right and white supremacist groups, motivated by racial animus and wielding their Confederate flags inside the Capitol building. Trump made repeated overtures to them throughout his presidency, from his “you had very fine people, on both sides” comment about the 2017 neo-Nazi rally in Charlottesville, to his notorious invitation to the Proud Boys to “stand back and stand by”.

White supremacists have enthusiastically heeded his call. For them, this was the break for which they had long been waiting, the welcome gesture that would usher them into the fold.

Shortly before the storming of the Capitol, the Three Percenters, an extreme anti-government militia network, put out a statement in which they aligned themselves overtly with Trump’s “stolen election”. They name-checked Ted Cruz, the Republican senator from Texas who was complicit in Trump’s big lie, as well as the ever more erratic Rudy Giuliani and the former national security adviser and pardoned criminal Michael Flynn.

“We are ready to enter into battle with General Flynn leading the charge,” the group said.

This all presents the incoming administration with a bilious soup of disaffected Trump supporters and their white supremacist allies hooked on the idea that Biden is an illegitimate president. Given the millions of Americans who have bought into the fantasy, should even a tiny fraction of them harbor violent aspirations or find themselves drawn to the newly elevated white supremacist groups, that would give rise to a national security challenge of monumental proportions.

Biden himself has vowed to tackle the trouble head-on. In his inauguration speech he addressed the threat directly, talking about the “rise in political extremism, white supremacy, domestic terrorism that we must confront and we will defeat”.

But the new president may find himself hamstrung by the relative lack of attention that has been paid up until now to the phenomenon.

Last year Chris Wray, the FBI director who Biden intends to keep in post, told Congress that “racially and ethnically motivated violent extremists” were the main source of ideological killings, overshadowing international jihadism that has dominated US intelligence thinking for 20 years.

Yet the way the FBI dishes out its resources is the exact opposite. Some 80% of its counter-terrorism budget goes on fighting international terrorism, and only 20% on domestic.

Gomez, the former FBI supervisor, said that any residual sluggishness on the part of the FBI in refocusing its sights on far-right violence will have vanished on 6 January. The storming of the Capitol was a “call to action for the FBI as it showed that there are individuals and groups within these political movements that are violent and willing to act out their frustrations and ideations in public”.

The FBI’s immediate priority, Gomez said, was likely to be on identifying the main conspirators behind the attack. “The FBI are going to focus on those groups that wore color-coordinated clothing at the Capitol, used communications and tried to organize specific actions,” he said.

The longer-term ambition will be to flip many of the more than 150 suspected rioters who have already been arrested and turn them into informants who can act as the feds’ eyes and ears. In all, Gomez expects a “paradigm shift” within the FBI away from international terrorism towards far-right and white supremacist domestic terrorism similar in scale and significance to the seismic change that followed 9/11.

As they scramble to make up for lost time, federal agencies will face some daunting obstacles. How do you begin to identify individuals who have the capability of violence when they are embedded in such a vast mass of American citizenry?

As the Atlantic has pointed out, the mob that breached the Capitol was full of “respectable people” – business owners, real-estate brokers, Republican local and state legislators. The only indication that they would take part in a rabble that beat a police officer to death was their shared belief that they have, in the Atlantic’s words, an “inviolable right to rule”.

Also among the mob were current and former law enforcement officers and at least six people with military links, signaling what may become the largest challenge of all – the fact that an unknown number of heavily armed and weapons-trained servants of the federal government are indirectly or even actively engaged in white supremacy. That’s a problem that long precedes Trump, but that has been supercharged by his presidency.

Here, too, what amounts to a crisis in American society has been largely overlooked. Two years ago, the Department of Defense revealed that out of almost 2 million serving military personnel only 18 had been disciplined or discharged for extremist acts over the previous five years.

So when security chiefs in charge of protecting dignitaries at Biden’s inauguration realized they had a fundamental problem, and called in the FBI to vet some 25,000 national guard troops brought to Washington for the event, they were acting exceptionally late in the day.

“The growing threat of rightwing nationalism in the military has been ignored, it hasn’t been emphasized enough,” Jeff McCausland said.

McCausland, a retired army colonel and former dean of the US Army War College, said that only now was the scale of far-right infiltration in the military being properly assessed. “Throughout the Trump administration, there was no focus on this problem because it did not fit their narrative that the threat was coming from the left.”

Asked whether the Pentagon was finally taking the matter seriously, McCausland replied: “Their words suggest they are stepping up the effort. Let’s see how well they have done in a year.”

Working in Biden’s favor will be the hope that with Trump off the scene – banished both from Washington and from social media – the allure of the stolen election myth will fade. “Now that Trump has been removed, much of his impact will dissipate,” said Bandy X Lee.

She added that it would remain important that Trump is discredited and disempowered to curtail his pull. “Prosecution and firm boundaries will be critical to keeping his influence under check.”

On Monday the article of impeachment against Trump for “incitement of insurrection” will be handed to the US Senate, and his second trial will begin in the week of 8 February. But the chances of conviction look slim.

For now at least the nation remains on alert. The big lie outlasts the liar, suspended in air and obscuring Biden’s sun.