What is the test for a constructive amendment claim?

Because defendants raise their constructive amendment claim for the first time on appeal, we review it for plain error. United States v. Bastian, 770 F.3d 212, 219 (2d Cir.2014). To prevail on a constructive amendment claim, a defendant must demonstrate that the terms of the indictment are in effect altered by the presentation of evidence and jury instructions which so modify essential elements of the offense charged that there is a substantial likelihood that the defendant may have been convicted of an offense other than that charged in the indictment. United States v. D'Amelio, 683 F.3d 412, 416 (2d Cir.2012) (emphasis in original, quotation marks omitted). A variance occurs when the charging terms of the indictment are not changed, but the evidence at trial proves facts materially different from those alleged. However, the proof at trial need not, indeed cannot, be a precise replica of the charges contained in an indictment [and] this court has consistently permitted significant flexibility in proof, provided that the defendant was given notice of the core of criminality to be proven at trial. United States v. Heimann, 705 F.2d 662, 666 (2d Cir.1983).