How have the courts interpreted the doctrine of "beyond a reasonable doubt" in an assault case?

When the predicate facts relied upon in the instruction, or other facts necessarily found by the jury, are so closely related to the ultimate fact to be presumed that no rational jury could find those facts without also finding that ultimate fact, making those findings is functionally equivalent to finding the element required to be presumed. The error is harmless because it is "beyond a reasonable doubt," Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 828, 17 L.Ed.2d 705 (1967), that the jury found the facts necessary to support the conviction.

109 S.Ct. at 2433.