“Open your eyes,” the online post began, claiming, “Many in our govt worship Satan.”

That warning, published on a freewheeling online message board in October 2017, was the beginning of the movement now known as QAnon. Paul Furber was its first apostle.

The outlandish claim made perfect sense to Mr. Furber, a South African software developer and tech journalist long fascinated with American politics and conspiracy theories, he said in an interview. He still clung to “Pizzagate,” the debunked online lie that liberal Satanists were trafficking children from a Washington restaurant. He was also among the few who understood an obscure reference in the message to “Operation Mockingbird,” an alleged C.I.A. scheme to manipulate the news media.

As the stream of messages, most signed only “Q,” grew into a sprawling conspiracy theory, the mystery surrounding their authorship became a central fascination for its followers — who was the anonymous Q?

Now two teams of forensic linguists say their analysis of the Q texts show that Mr. Furber, one of the first online commentators to call attention to the earliest messages, actually played the lead role in writing them.

Sleuths hunting for the writer behind Q have increasingly overlooked Mr. Furber and focused their speculation on another QAnon booster: Ron Watkins, who operated a website where the Q messages began appearing in 2018 and is now running for Congress in Arizona. And the scientists say they found evidence to back up those suspicions as well. Mr. Watkins appears to have taken over from Mr. Furber at the beginning of 2018. Both deny writing as Q.

The studies provide the first empirical evidence of who invented the toxic QAnon myth, and the scientists who conducted the studies said they hoped that unmasking the creators might weaken its hold over QAnon followers. Some polls indicate that millions of people still believe that Q is a top military insider whose messages have revealed that former President Trump will save the world from a cabal of “deep state” Democratic pedophiles. QAnon has been linked to scores of violent incidents, many of the attackers who stormed the Capitol last year were adherents, and the F.B.I. has labeled the movement a potential terrorist threat.

The forensic analyses have not been previously reported. Two prominent experts in such linguistic detective work who reviewed the findings for The Times called the conclusions credible and persuasive.

In a telephone interview from his home near Johannesburg, Mr. Furber, 55, did not dispute that Q’s writing resembled his own. Instead, he claimed that Q’s posts had influenced him so deeply that they altered his prose.

Q’s messages “took over our lives, literally,” Mr. Furber said. “We all started talking like him.”

Linguistic experts said that was implausible, and the scientists who conducted the studies noted that their analyses included tweets by Mr. Furber from the first days Q emerged.

Mr. Watkins, in a telephone interview, said, “I am not Q.”

But he also praised the posts. “There is probably more good stuff than bad,” he said, listing as examples “fighting for the safety of the country, and for the safety of the children of the country.” His campaign signs in the Republican primary refer to the online name he uses in QAnon circles, CodeMonkeyZ, and he acknowledged that much of the initial support for his campaign came from the movement. Relying mainly on small donors, Mr. Watkins, 34, trails the primary’s front-runners in fund-raising. (Two other Republicans who have expressed support for QAnon were elected in 2000 — Representative Marjorie Taylor Greene of Georgia and Representative Lauren Boebert of Colorado.)

The two analyses — one by Claude-Alain Roten and Lionel Pousaz of OrphAnalytics, a Swiss start-up; the other by the French computational linguists Florian Cafiero and Jean-Baptiste Camps — built on long-established forms of forensic linguistics that can detect telltale variations, revealing the same hand in two texts. In writing the Federalist Papers, for example, James Madison favored “whilst” over “while,” and Alexander Hamilton tended to write “upon” instead of “on.”

Instead of relying on expert opinion, the computer scientists used a mathematical approach known as stylometry. Practitioners say they have replaced the art of the older studies with a new form of science, yielding results that are measurable, consistent and replicable.

Sophisticated software broke down the Q texts into patterns of three-character sequences and tracked the recurrence of each possible combination.

Their technique does not highlight memorable, idiosyncratic word choices the way that earlier forensic linguists often did. But the advocates of stylometry note that they can quantify their software’s error rate.

The Swiss team said its accuracy rate was about 93 percent. The French team said its software correctly identified Mr. Watkins’s writing in 99 percent of tests and Mr. Furber’s in 98 percent.

Machine learning revealed that J.K. Rowling, the creator of Harry Potter, had written the 2013 mystery “Cuckoo’s Calling” under another pen name. The F.B.I. used a form of stylometry to show that Ted Kaczynski was the Unabomber. In recent years, such techniques have helped detectives in the United States and Britain solve murder cases involving a forged suicide note and faked text messages.

The teams studying Q got in touch with each other after the Swiss scientists released an earlier, preliminary study showing that the writing had changed over time. Each team applied different techniques. The Swiss scientists used software to measure similarities in the three-character patterns across multiple texts while comparing the complexity of vocabulary and syntax. The French team used a form of artificial intelligence that learns the patterns of an author’s writing in roughly the same way that facial-recognition software learns human features.

The teams shared text samples, including more than 100,000 words by Q and at least 12,000 words by each of the 13 other writers they analyzed.

Gerald McMenamin of the University of Nevada, Reno, a renowned forensic linguist critical of the machine-learning techniques, said he doubted that software could pick out the telltale individual variations from the quirks of the distinctive voice assumed in the Q messages — full of short sentences, cryptic statements, military jargon and Socratic questions.

To counter the danger that texts spanning different forms or genres might confuse the software, the scientists said, they compared other writing samples that were all of the same type: social media posts, primarily tweets. And the writings by Mr. Furber and Mr. Watkins stood out over all the others in similarity to Q’s.

David Hoover, an English professor at New York University and an expert in author identification, said the scientists seemed to effectively address the potential problem of Q’s distinctive voice. He found the work “quite persuasive,” he said.

“I’d buy it,” said Patrick Juola of Duquesne University, a mathematician who identified Ms. Rowling as the author of “Cuckoo’s Calling.”

“What’s really powerful is the fact that both of the two independent analyses showed the same overall pattern,” Dr. Juola added.

Neither team ruled out the possibility that other writers had contributed to Q’s thousands of messages, especially during what appears to have been a period of collaboration between Mr. Furber and Mr. Watkins around late 2017.

But the scientists relied on other facts to narrow the list of feasible writers to test. That evidence, the scientists said, increased their confidence that they had unmasked the main authors.

Some QAnon followers had begun to suspect as early as mid-2018 that one or more of the commentators who first claimed to stumble onto the Q messages had actually written them. Without prior knowledge, how could anyone have plucked those almost nonsensical postings out of the online torrent? An NBC news report that summer identified Q’s earliest boosters as Mr. Furber (known online as Baruch the Scribe) and three others. The report emphasized that the three others had possible financial motives for stoking the craze because they had solicited donations for Q “research.” (Mr. Furber did not.)

The Swiss team studied writings by those four, as well as by Mr. Watkins and his father, who owns the message board.

In addition to examining those six potential authors, the French scientists added seven more to the mix. They tested tweets by another online Q booster close to the Watkinses as well as by Mr. Trump, his wife, Melania, his son Eric, and three others close to the former president who had publicly encouraged QAnon: Michael T. Flynn, his onetime national security adviser; the political consultant Roger Stone; and Dan Scavino, a Trump White House deputy chief of staff.

“At first most of the text is by Furber,” said Mr. Cafiero, who works at the French National Center for Scientific Research. “But the signature of Ron Watkins increased during the first few months as Paul Furber decreased and then dropped completely.”

Mr. Furber said in an interview that he had inherited his passion for American politics from his parents, who had taught in Canada and traveled around the United States. He visited often while building a career in software development and writing for trade publications.

His fascination with conspiracy theories, he said, began with questions about President John F. Kennedy’s assassination. Then, around 1996, he found a site spinning alternative stories about the suicide of Vincent Foster, the Clinton White House counsel, and other deaths said to be connected to the Clintons. “That sort of kicked off my interest,” he said.

The early Q messages, which the scientists say resemble Mr. Furber’s writing, lay out the core QAnon myths and slogans that later messages repeat. That was also when Mr. Furber and a few other early promoters helped attract the interest of entrepreneurial YouTube creators who amplified the messages.

But at the start of 2018, both studies found, the writing changed conspicuously. Where the 2017 posts were filled with Socratic questions, the later posts were more declarative and expository, with heavy use of exclamation points and words written in all capital letters. Sometimes, Q shared internet memes.

The Q messages had recently jumped from an older message board to the one run by Ron Watkins and owned by his father, Jim — the site known then as 8chan and now as 8kun. Jim Watkins, a former U.S. Army helicopter repairman who had settled in the Philippines, also owned pig and honey farms and dabbled in the online pornography business. Around the 2016 election, he had created a conspiracy-minded pro-Trump website, with his son overseeing the technical side.

The evident change in writing style at the start of 2018 coincided with an unusual exchange between the Q account and Ron Watkins. After a period of confusion, whoever was writing as Q publicly asked Mr. Watkins to confirm that the messages were still coming from the original Q. Mr. Watkins immediately did, and then Q declared all future posts would appear exclusively on Mr. Watkins’s platform.

Mr. Furber began complaining that Q had been “hijacked” and that Mr. Watkins was complicit.

From then on, the scientists said, the messages very closely matched the writing of Ron Watkins alone. “When QAnon started to be successful, one of them took control,” said Mr. Roten of OrphAnalytics.

In a podcast interview in 2020, Fredrick Brennan, who started the message board that the Watkinses now own, asserted without proof that Q was the invention of Mr. Furber. An HBO documentary released last year, “Q: Into the Storm,” built a case that Ron Watkins was behind the messages, and in it Mr. Watkins briefly seemed to admit that he had written as Q. He then smiled, laughed and resumed his denials.

Q has now gone silent, without posting a message since December 2020.

Mr. Furber, in an interview, said he believed that QAnon was “an operation that has run its course.” He said he was still convinced that it was orchestrated by a true insider “to awaken people to this massive secret war against the cabal,” and that “the next phase is coming.”

In an online memoir he posted about the QAnon movement, he writes wistfully about the early days before “the hijacking.” Q’s messages, he says, seemed to validate conspiracy theories he had subscribed to for years — tying the Clintons and George Soros to the Rothschilds and the Illuminati.

“Like a child being taken around his father’s workshop for the first time,” Mr. Furber writes, “we were being given a behind-the-scenes look into the ugly and corrupt world of geopolitics.”