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A few weeks back, the Boston Herald ran a story on “speculation” that Boston Mayor Michelle Wu would step down for a job at Harvard University, where she attended both college and law school. Wu, according to the rumor, had been offered a job at Harvard because school leaders knew she was thinking about not serving out her full term as mayor. The piece also quoted Wu’s response when asked about the rumor, which was squishier than might have been wise. “No, not that I would share it with you,” Wu said when queried — and then, laughing, “I’m always honest.”

About a week later, Wu was far more emphatic when asked about the rumor on GBH’s Boston Public Radio. “There is absolutely no chance I would abandon this role for any other job, at any organization, any other level of government,” Wu said, adding: “Boston deserves a mayor who’s not eyeing the next big thing. This is the big thing.”

It seemed like that unequivocal denial would put the speculation to rest. And yet, days after Wu’s direct denial, the notion that a Wu-to-Harvard jump was imminent was still circulating in some quarters of Boston’s political world. Which raises an obvious question: why?

The answer may lie in just how versatile the rumor in question is for people who don’t like the mayor. If you’re a detractor, murmuring about Wu decamping for Harvard does several things at once. It provides a reminder to anyone listening that Wu, unlike any mayor in recent memory, is not originally from Boston, but came to Massachusetts to attend Harvard College — a detail that simmered below the surface in her 2021 contest with Annissa Essaibi George. It also paints Wu as an elitist, at least among people for whom “Harvard” functions as a pejorative.

The suggestion that Wu is ready to jump ship now, so early in her term, also hearkens back to earlier speculation — convincingly debunked by the Boston Globe’s Emma Platoff in March 2022 — that Wu had suffered one or more panic attacks as mayor, and been taken by ambulance to a local hospital as a result. And, while the Harvard rumor didn’t keep Enrique Pepén — who Wu endorsed and helped campaign — from advancing in last week's Boston preliminary election, it could undercut her efforts on the campaign trail between now and November if it keeps circulating and enough people give it credence. And if it keeps circulating and enough people give it credence, it could foster a broader perception that she’s governing as a lame duck, diminishing her ability to effectively make policy and lead the city.

It is, in short, a potent political weapon, even if it’s not true. And it’s materialized at a moment when Wu’s detractors, particularly on the conservative end of the local political spectrum, seem to be gearing up for some type of sustained effort aimed at weakening her before the next mayoral campaign. Think of that abortive “Save Our City” campaign linked to PR magnate George Regan, which was predicated (while it lasted) on the idea that, under Wu, Boston has lost its way and needs to be rescued.

Perhaps, as time passes and Wu doesn’t hold a press conference announcing that she’s headed to Harvard, the rumor will finally fade out. If so, though, brace yourself for another one to take its place.