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 contrary to such oath states or subscribes any material matter which he does not believe to be true; or

(2) in any declaration, certificate, verification, or statement under penalty of perjury as permitted under section 1746 of title 28, United States Code, willfully subscribes as true any material matter which he does not believe to be true;

is guilty of perjury …. 18 U.S.C. § 1623(a) provides that: "Whoever under oath (or in any declaration, certificate, verification, or statement under penalty of perjury as permitted under section 1746 of title 28, United States Code) in any proceeding before or ancillary to any court or grand jury of the United States knowingly makes any false material declaration or makes or uses any other information, including any book, paper, document, record, recording, or other material, knowing the same to contain any false material declaration, shall be fined under this title or imprisoned not more than five years, or both."

The Department’s Criminal Resources Manual states that sections 1621 and 1623 share four common elements. The government must prove each element beyond a reasonable doubt. The Manual summarizes these elements as follows:}} "The first element of a perjury offense is that the defendant must be under oath during his testimony, declaration or certification, unless the perjurious statement is an unsworn declaration permitted by 28 U.S.C. § 1746.

The second essential element … is that the defendant must have made a false statement.

The third element … is proof of specific intent, that is, that the defendant made the false statement with knowledge of its falsity, rather than as a result of confusion, mistake or faulty memory.

The false statement must be material to the proceedings."

In addition to the text quoted above, the Manual explains each of the requirements in more detail as well as the differences among the statutory provisions.

4.&emsp;Falsification of records

18 U.S.C. § 1519 imposes criminal liability on any person who:

knowingly … falsifies [] or makes a false entry in any record, document, or tangible object with the intent to impede, obstruct, or influence the investigation or proper administration of any matter within the jurisdiction of any department or