Online sleuths believe the use of a particular word – “lodestar” – in the explosive article points to the Republican’s seemingly loyal vice president, Mike Pence, though he has forcefully denied authoring it.
The unnamed author, who the Times said was a senior member of the Trump administration, cites the late senator John McCain as an example to follow in the “chaotic era” Mr Trump has ushered in; a “lodestar for restoring honour to public life and our national dialogue”.
“Americans should know that there are adults in the room. We fully recognise what is happening. And we are trying to do what’s right even when Donald Trump won’t,” they add.
A lodestar is either, literally, a star used as a reference point by navigators, or a metaphorical guide or inspiration.
The term has been used a number of times by Mr Pence in past speeches, leading to speculation the former Indiana governor and congressman was behind the op-ed Mr Trump has condemned as “gutless”.
Late-night television host Jimmy Kimmel presented a supercut video of Mr Pence using the word in media interviews and speeches over a number of years.
But penning an op-ed so embarrassing to Mr Trump would be a serious change of tack for the vice president, who has defended his running mate through thick and thin over the past few years.
Mr Pence’s office issued a fierce denial on Thursday morning, with his communications director Jarrod Agen tweeting: “The Vice President puts his name on his Op-Eds. The @nytimes should be ashamed and so should the person who wrote the false, illogical, and gutless op-ed. Our office is above such amateur acts.”
Mike Pompeo, the secretary of state, has also denied authoring the piece and called it “sad”.
Others online suggested the use of “lodestar” may have been an attempt at misdirection, drawing attention to Mr Pence while obscuring the article’s true source.
Earlier this year, in a story examining how leaks emerged from the White House, Axios quoted one Trump administration official as saying: “To cover my tracks, I usually pay attention to other staffers’ idioms and use that in my background quotes. That throws the scent off me.”
Mr Trump has called for the source of the article to be handed over to the government for “national security” reasons, and has ordered aides to track them down.
In a tweet, the Times used the pronoun “he” to refer to the writer, leading to speculation a woman was not behind the op-ed.
The newspaper later said the Twitter post referring to “he” had been “drafted by someone who is not aware of the author’s identity, including the gender, so the use of ‘he’ was an error”.
Other names floated by commentators speculating on the author’s identity included the president’s daughter, Ivanka Trump, her husband, Jared Kushner, and – mainly in jest – the leader’s wife, Melania Trump.
In a Thursday morning tweetstorm Mr Trump suggested the piece represented a floundering “deep state” and a crisis of confidence among his opponents.
“The Deep State and the Left, and their vehicle, the Fake News Media, are going Crazy – & they don’t know what to do. The Economy is booming like never before, Jobs are at Historic Highs, soon TWO Supreme Court Justices & maybe Declassification to find Additional Corruption. Wow!,” he said.
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