Former President Donald Trump is basing a significant chunk of his currently unfolding attempt at returning to power on complaints about migrants to the U.S., arguing in a debate held on Thursday night in Georgia that pitted him against incumbent President Joe Biden that individuals arriving to the U.S. have been destroying it.

But there are large gaps in the narrative that he presents, some say.

“Trump has presented zero proof for his regular claims about countries emptying prisons and mental institutions under Biden to somehow turn prisoners into migrants; his campaign has cited only a vague, unverified Breitbart article about Venezuela,” wrote Daniel Dale, a fact-checker with CNN, on X (formerly Twitter) this Thursday.

Trump’s rhetoric during the debate got extreme. Per CNN transcripts, he claimed that Americans “are living right now in a rat’s nest. They’re killing our people in New York, in California, in every state in the union because we don’t have borders anymore. Every state is now a border. And because of his ridiculous, insane and very stupid policies, people are coming in and they’re killing our citizens at a level that we’ve never seen. We call it migrant crime.”

Though individual tragedies do continue, the apparent implication that the U.S. is experiencing a surge in violent crime — specifically, murder — is undercut by the evidence. Details spotlighted by sources including the Pew Research Center suggest a significant decline in the murder rate in 2023, well into Biden’s presidency that brought supposed chaos at the southern border that Republicans have claimed. And by the way, attestations from figures personally involved in federal efforts at border security are clear and consistent: the southern border is not “open,” no matter how many times that Trump claims otherwise. It’s just not. Border enforcement continues apace!