The nightmarish scenario of widespread doubt and denial of the legitimacy of the election would cap a period in American history when truth itself has seemed at stake under a president who has strayed so far from the normal bounds that he creates what allies call his own reality. Even if the election ends with a clear victory or defeat for Mr. Trump, scholars and players alike say the very concept of public trust in an established set of facts necessary for the operation of a democratic society has eroded during his tenure with potentially long-term ramifications.

“You can mitigate the damage, but you can’t bring it back to 100 percent the way it was before,” said Lee McIntyre, the author of “Post-Truth” and a philosopher at Boston University. “And I think that’s going to be Trump’s legacy. I think there’s going to be lingering damage to the processes by which we vet truths for decades. People are going to be saying, ‘Oh, that’s fake news.’ The confusion between skepticism and denialism, the idea that if you don’t want to believe something, you don’t have to believe it, that’s really damaging and that’s going to last.”…

Mr. Trump has spent four years telling Americans not to trust anyone other than him, whether it be public health experts, scientists, journalists, judges, career government officials, investigators, generals, intelligence agencies, election officials and even mail carriers. “Just remember,” he told a crowd one summer, “what you are seeing and what you are reading is not what’s happening.”

Trust, once lost, is hard to restore. “We know a lot about the delegitimation of democratic institutions over the last two centuries,” Ms. Rosenblum said. “But we know nothing about how you relegitimate institutions that have lost their main value and authority for an awful lot of people. That’s the real question.”