False Statements. The principal federal statute criminalizing false statements to government investigators is 18 U.S.C. § 1001. As relevant here, under Section 1001(a)(2), it is a crime to knowingly and willfully “make[] any materially false, fictitious, or fraudulent statement or representation” “in any matter within the jurisdiction of the executive . . . branch of the Government.” An FBI investigation is a matter within the Executive Branch’s jurisdiction. United States v. Rodgers, 466 U.S. 475, 479 (1984). The statute also applies to a subset of legislative branch actions—viz., administrative matters and “investigation[s] or review[s]” conducted by a congressional committee or subcommittee. 18 U.S.C. § 1001(c)(1) and (2); see United States v. Pickett, 353 F.3d 62, 66 (D.C. Cir. 2004). Whether the statement was made to law enforcement or congressional investigators, the government must prove beyond a reasonable doubt the same basic non-jurisdictional elements: the statement was false, fictitious, or fraudulent; the defendant knew both that it was false and that it was unlawful to make a false statement; and the false statement was material. See, e.g., United States v. Smith, 831 F.3d 1207, 1222 n.27 (9th Cir. 2017) (listing elements); see also Ninth Circuit Pattern Instruction 8.73 & cmt. (explaining that the Section 1001 jury instruction was modified in light of the Department of Justice’s position that the phrase “knowingly and willfully” in the statute requires the defendant’s knowledge that his or her conduct was unlawful). In the D.C. Circuit, the government must prove that the statement was actually false; a statement that is misleading but “literally true” does not satisfy Section 1001(a) (2). See United States v. Milton, 8 F.3d 39, 45 (D.C. Cir. 1993); United States v. Dale, 991 F.2d 819, 832-33 & n.22 (D.C. Cir. 1993). For that false statement to qualify as “material,” it must have a natural tendency to influence, or be capable of influencing, a discrete decision or any other function of the agency to which it is addressed. See United States v. Gaudin, 515 U.S. 506, 509 (1995); United States v. Moore, 612 F.3d 698, 701 (D.C. Cir. 2010). Perjury. Under the federal perjury statutes, it is a crime for a witness testifying under oath before a grand jury to knowingly make any false material declaration. See 18 U.S.C. § 1623. The government must prove four elements beyond a reasonable doubt to obtain a conviction under Section 1623(a): the defendant testified under oath before a federal grand jury; the defendant’s testimony was false in one or more respects; the false testimony concerned matters that were material to the grand jury investigation; and the false testimony