Does the government have to prove that a violation of Rule 43 is harmless beyond a reasonable doubt?

Whether the government must prove that a violation of Rule 43 is harmless beyond a reasonable doubt or to some lesser degree of certainty has not been specifically addressed in this circuit. Cf. United States v. Reynolds, 489 F.2d 4 (6th Cir.1973), cert. denied, 416 U.S. 988, 94 S.Ct. 2395, 40 L.Ed.2d 766 (1974) (error reversible if any reasonable possibility of prejudice); United States v. Freed, 460 F.2d 75 (10th Cir.1972) (standard is clear prejudice). Few of our cases have had reason to explore that area of the Rule 43 presence right that is outside constitutional protection. Given our prior finding that the defendants' due process rights were violated by proceeding in their absence without determining whether the absence was voluntary, we need only assess the prejudice in this case under a "harmless beyond a reasonable doubt" standard.