What is the test for a constructive amendment claim?

To prevail on a constructive amendment claim, a defendant must demonstrate that either the proof at trial or the trial court's jury instructions so altered an essential element of the charge that, upon review, it is uncertain whether the defendant was convicted of conduct that was the subject of the grand jury's indictment. See United States v. Zingaro, 858 F.2d 94, 98 (2d Cir.1988). In the case before us, the appellants do not claim that the district court permitted the government to introduce any evidence relating to conduct that differed significantly from that described in the indictment. Nor do the appellants claim that the district court's instruction referred to any such evidence. In the absence of any indication that the evidence adduced at trial impermissibly broadened the basis of the appellants' convictions, we cannot accept the argument that the district court's mere use of the "substantially the same" language constructively amended the indictment.