This essay is part of a series The New Yorker will be running through the election titled “Trump and the Truth.”

It is no surprise that, by feverishly indulging conspiracy theories of many kinds, Donald Trump would end up reintroducing America to the master conspiracy theory of them all, the first of the modern kind, and still the biggest and strangest: the one surrounding the assassination of J.F.K.

The primary campaign was all but over when Trump first suggested—against all evidence except that provided in the Trump-loving tabloid the National Enquirer—that Ted Cruz’s Cuban father, Rafael, had been somehow in concert with Lee Oswald (the “Harvey” belongs to his birth certificate and to the papers and networks; no one who knew him ever called him that) in plotting the murder of the President. The first time Trump brought it up, the smear came out garbled. “His father was with Oswald prior to Oswald being, you know, shot,” Trump announced on “Fox & Friends,” on May 3rd, the day of the Indiana primary. “I mean, the whole thing is ridiculous. What is this—prior to his being shot? And nobody even brings it up. . . . What was he doing with Lee Harvey Oswald shortly before the death? Before the shooting. It’s horrible.” Trump repeated the notion over the next few days, at rambling length, in various interviews, including with “Good Morning America” and Fox News’s Bret Baier. Trump made it plain that the accusation was specifically vengeful, payback for insults, imagined or real, to Trump’s vanity. “He said, you know, very nasty things about me,” Trump said on May 4th, on NBC’s “Today” show. “And then I just asked about stories that were appearing all over the place, not just in the National Enquirer, about the fact that a picture was taken of him with Lee Harvey Oswald. They didn’t deny the picture”—Cruz’s campaign had in fact denied the story, in April—“and I just asked, what was that all about? So this was just in response to some very, very nasty—I mean, honestly very nasty—remarks that were made about me.” Trump couldn’t have been clearer; criticize him, and no family member was safe from being accused of murder, or at least of appearing in the same photograph as a murderer. He never did bother to properly learn the facts of his own accusations. At a press conference in July, he revisited the topic, and described the photograph that ran in the Enquirer as “an old picture” of Cruz’s father “having breakfast with Lee Harvey Oswald.”

Even granting that Trump’s weird first phrasing was intended to mean “before Oswald shot J.F.K.,” rather than “before Oswald himself was shot”—Oswald, too, was killed by gunfire, of course, on November 24, 1963, by Jack Ruby—there is no evidence of any kind that Rafael Cruz was involved with Oswald, overwhelming evidence to suggest he wasn’t, and in any case the figure identified as Cruz in the National Enquirer photograph has no demonstrable connection of any sort to the assassination in Dallas.

The photograph in question was taken on the morning of August 16, 1963—not “shortly before the assassination” by any standard—in New Orleans, where Oswald had gone to search for work and stay with an aunt and uncle who lived there. Oswald, who had by then transferred his obsessive need for an idealized utopia from the Soviet Union, which had disappointed him upon his defection there, in 1959, to Fidel Castro’s Cuba, had been asking the organizers of the pro-Castro Fair Play for Cuba Committee in New York for permission to “open a chapter” of the organization in New Orleans. He had received extremely lukewarm and cautious responses. Nonetheless, on his own initiative, he had at least twice before passed out pamphlets in support of Castro in New Orleans, alarming the local police and (deliberately) outraging the city’s anti-Castro Cuban-exile community.

On August 16th, during what would seem to have been the third occasion of his pamphleting, Oswald was joined by two confederates. One was later identified as Charles Hall Steele, Jr., recruited by Oswald at an employment office with an offer of two dollars for fifteen or so minutes of “work.” As Vincent Bugliosi writes, in “Reclaiming History: The Assassination of President John F. Kennedy**,**” by far the most encyclopedic study of the assassination (and hated by those who still believe in a conspiracy), the other leaflet distributor was a “a short, young Cuban” who passed out only a few of the leaflets that Oswald gave him, according to a local TV reporter and cameraman named Johann Rush, who was there that day. “The short man, who has never been identified, seemed embarrassed by the entire affair, grinning a lot, and soon left with his companion, who seemed to purposefully keep his back to Rush’s camera through the entire incident,” Bugliosi writes. It is Rush’s footage of the incident, turned into still frames, that the Enquirer seized on, and it is the short, embarrassed man who has been identified, originally by the conspiracy theorist Wayne Madsen, and then in the Enquirer, as Rafael Cruz.

Two things need to be emphasized. First, there is no evidence of any kind that the apparently reluctant confederate was Cruz. And, second, even if it had been Cruz in the photograph, there would be no more reason to associate him with the assassination than there is to associate Charles Hall Steele, Jr., with it. As far as anyone knows or has shown, Steele and the other man’s association with Oswald began and ended on that August morning. There is, by the way, something like pan-spectrum agreement on the part of Kennedy-assassination specialists on this point. The veteran journalist Jefferson Morley, who is a passionate skeptic about the standard model of the assassination (he is persuaded that the C.I.A. had a more intense interest in and placed greater scrutiny on Oswald than it later admitted), shares doubts about the identification of Cruz’s father with those who do accept the standard Warren Commission account. “There is no evidence that the man is Rafael Cruz,” he wrote on his Web site, JFK Facts, in April.

It is typical of the pathological nature of Trump’s dishonesty that it sweeps from a simple lie to a more damning one, and manages thereby to rest a wholly absurd claim on the back of a testable (and not in itself ridiculous) one. There is some evidence that Rafael Cruz was in New Orleans around the time the photograph was taken, and so it is impossible to rule out completely that, by chance, he was one of the men Oswald hired to pass out pamphlets. Bending over backward, there is speculation that Oswald chose to associate with anti-Castro exiles at the time, in a kind of self-willed counterespionage program, designed to impress his fantasized contacts in Cuba or among American communists. (The “Odio incident,” in which a Cuban exile later claimed to have seen Oswald in the company of anti-Castro exiles shortly before the assassination, has never been entirely debunked, and even Bugliosi thinks that it has “the ring of truth.”) It isn’t impossible, in other words, that Oswald had some kind of engagement with anti-Castro activists along with his pro-Castro activities, or that, in his confused way, he might have asked an anti-Castro activist like Cruz’s dad to assist him.