What is the test for an improper amendment to the original indictment for perjury?

Bernesser contends that he was convicted upon an improper amendment to the indictment because the perjury count in the indictment referred to the "second phase" of the Shea Stadium job and the evidence at trial regarding the rigged bidding concerned "Phase Three" of the project. ⁵ See Stirone v. United States, 361 U.S. 212, 217, 80 S.Ct. 270, 273, 4 L.Ed.2d 252 (1960) (where "new basis for conviction" added by theory not presented in indictment, cannot assume jury convicted on original indictment theory); see also United States v. Zingaro, 858 F.2d 94, 98 (2d Cir.1988) (constructive amendment of indictment is per se violation of grand jury clause of Fifth Amendment).