The definition is half, as in "not half" — a hemisphere is half of the world. HEM means "border," and IS HERE means "has shown up." The phrase "throttling power" tells us that IS HERE goes around P (power), giving IS-P-HERE. Put HEM in front and you get HEMI-SPHERE. The surface reading cleverly disguises the answer by suggesting "world? Not half" as a phrase, but "half" is the actual definition and "world" is part of the misdirection.