Question

other than that the external physical criminal act occurred, what must the state or federal government also prove beyond a reasonable doubt before an offender can be convicted of a crime?
that the criminal act was accompanied by a state of mind required by the criminal statute
that the offender had real and tangible motive to commit the criminal act
that the criminal act was one of a particularly heinous nature or exceptionally violent
that the victim of the criminal act was not deserving of the action taken

Explanation:

In criminal law, for a conviction, besides the actus reus (the physical act), mens rea (the required state of mind) must be proven. Motive is not always necessary, and the nature of the act or victim - deservability are not elements the prosecution must prove for a basic conviction.

Answer:

that the criminal act was accompanied by a state of mind required by the criminal statute