But they do not have to prove the material is false.

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Courts have concluded that no one should be convicted of perjury without demonstrating that the testimony in question was in fact false, that the person testifying knew it to be false, and that the testimony involved an issue that is material to the case, one that could influence the outcome of the matter one way or the other.

CNN

The plaintiff, Abdullah Al-Kidd, alleges that prosecutors never had any intention of calling him as a witness and submitted a false affidavit for the purpose of persuading a federal magistrate to issue a material witness warrant.

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