MONTEREY, Calif.—When federal prosecutors can’t muster enough evidence to bring charges against a person suspected of a crime, they can still use a controversial law to get a conviction anyway: They charge the person with lying.

The law against lying—known in legal circles simply as “1001”—makes it a crime to knowingly make a material false statement in matters of federal jurisdiction. Critics across the political spectrum argue that 1001, a widely used statute in the federal criminal code, is open to abuse. It is charged hundreds of times a year, according to court records and interviews with lawyers and legal scholars.

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