The Supreme Court on Tuesday turned down conspiracy theorist Alex Jones’s appeal of a roughly $1.4 billion defamation judgment he owes for falsely claiming the Sandy Hook Elementary School shooting was a hoax.

The brief order ends Jones’s bid to stave off the staggering sum, which has plunged him into bankruptcy and could force him to give up airing his Infowars show.

Jones’s Supreme Court petition called it “financial death penalty by........

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