Given our understanding of neuroanatomy, we can confirm that the left cerebral hemisphere controls the muscles on the right side of the body and vice versa due to the motor decussate of the cortical spinal pathway.
A decussate in regards to the nervous system is described as when the nerve fibers cross from one side of the central nervous system to the other. The decussate in question corresponds to the cortical spinal motor decussate.
The cortical spinal pathway is the nerve pathway that is in charge of muscular control and therefore is the pathway that is responsible for the phenomenon described in the question.
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