As Donald Trump reminded the world Tuesday morning, the Republican Party is on the verge of nominating a conspiracy theorist who regularly uses debunked Internet and tabloid rumors to smear his enemies.

In the latest case, Trump seized on a ludicrously thin-sourced National Enquirer story to insinuate Sen. Ted Cruz’s father, Rafael Cruz, was involved in the 1963 assassination of President John F. Kennedy.

“His father was with Lee Harvey Oswald prior to Oswald’s being, you know, shot,” Trump told Fox News over the phone. “I mean, the whole thing is ridiculous. What is this, right prior to his being shot, and nobody even brings it up. They don’t even talk about that. That was reported, and nobody talks about it.”

Trump’s evidence? A photo, disseminated in fringe circles online and then by the National Enquirer, that conspiracy sleuths claim shows the elder Cruz near Oswald. There is zero evidence the person in question is Rafael Cruz.