What is the test for a claim of fraud under the Federal Fraud Act?

Although the Government was not always clear as to what theory of fraud applied in this case, see, e.g., J.A. 486164, the record shows that the jury was charged only as to a theory of fraud through an affirmative misstatement, i.e., a statement that was either an outright lie or partially true but omitt[ed] information necessary to correct [a] false impression. J.A. 5219. Thus, we review the proof at trial only by reference to this charged theory, see Yates v. Evatt, 500 U.S. 391, 409, 111 S.Ct. 1884, 114 L.Ed.2d 432 (1991), and we do not address whether other situations, such as silence without any affirmative statement while under a duty to disclose material information, can constitute fraud under the federal statutes, particularly in the context of a breach of contract, cf. United States v. Gallant, 537 F.3d 1202, 1228 (10th Cir.2008) (nondisclosure is actionable under the federal fraud statutes where there is a duty to speak); United States v. Altman, 48 F.3d 96, 102 (2d Cir.1995) (failure to disclose material information while in a fiduciary relationship constituted a scheme to defraud).¹⁴