The Gunshots Rang Out. Then the Conspiracy Theories Erupted Online.

Four minutes after the first report of a shooting at a rally for Donald J. Trump on Saturday, an anonymous account on X posted, “Joe Biden’s antifa shot President Trump.”

Within half an hour, another account on X with links to the QAnon conspiracy theory claimed without proof that the attack against Mr. Trump had most likely been ordered by the Central Intelligence Agency. Shortly after that, the far-right activist Laura Loomer posted on X about some recent remarks that President Biden made about Mr. Trump and then wrote, “They tried to kill Trump.” She did not provide evidence.

An hour later, with official details of the assassination attempt still scant, the narrative that President Biden and his allies had engineered the attack on Mr. Trump was being amplified by Republican lawmakers, Russian sympathizers and even a Brazilian political scion. By the time 24 hours had elapsed, posts about the unverified claim had been viewed and shared millions of times.

The idea that President Biden was behind the shooting of Mr. Trump was perhaps the most dominant conspiracy theory to emerge after the attack in Butler, Pa., on Saturday. The unproven conjecture surfaced almost instantly, hardened into a narrative and then catapulted between platforms large and small, even as information about the incident was limited. It was a striking example of the speed, scale and stickiness of rumors on social media, which often calcify into accepted truth far more efficiently than efforts to debunk or pleas for restraint.

That the subject this time was Mr. Trump, who frequently claims to be victimized by powerful forces while demonizing his enemies, only helped fuel the conspiracy theory. Its acceleration was also enabled by years of distrust