If you were to ask me, I would say exactly where Will Smith stabs V.I.K.I. with his robot arm at the end of I, Robot.
But I guess Justice Breyer has his own views on this:
In an effort to find a single, more uniform interpretation of the statutory phrase, this Court returns to the “nerve center” approach: “[P]rincipal place of business” is best read as referring to the place where a corporation’s officers direct, control, and coordinate the corporation’s activities. In practice it should normally be the place where the corporation maintains its headquarters—provided that the headquarters is the actual center of direction, control, and coordination, i.e., the “nerve center,” and not simply an office where the corporation holds its board meetings.Seems simple, but I predict application will be trickier in practice -- those corporations are wily beasts.