When Galt's dog poops

Maybe yesterday's example of Galt's dog killing Smith's dog was a little extreme. It was intended to raise the issue of behaviors in common spaces being limited beyond Rand's simple prohibition of murder. But suppose Galt's dog does nothing more than poop. A stinking mess of dog poop is left in the path for others to step in, inhale, or otherwise enjoy. This poop, of course, is tied to the historically significant personhood of THE John Galt. But consider that a few other people would prefer that Galt honor the standard procedure for dog owners who live in proximity with each other, and use an inverted plastic bag to remove the dog's poop from the ground and move it to some other location from which it can be more properly disposed. Is Galt under any obligation to do so? In other words, does Galt's extreme high worth as an individual person grant him exemption from obligations of civility? I think that Rand would support the position that Galt is, indeed, exempted from such obligations. I expect her to propose that such exemption arises from the summative good that is attributed to having a Galt among us.
Rand's opinion on the matter, however, isn't worth the dog poop it talks about. The only circumstance that mandates Galt's exemption is his ownership of the commons. But even if there is such ownership, how would it be acknowledged among the rest of us? Are there deeds? Who wrote them? Who were parties to the sale? By what authority did ownership convey itself to the sellers? These are serious questions because we presume Galt to be intelligent enough to have avoided purchases of the Brooklyn Bridge. For a claim of ownership of the commons to be meaningful, Galt, and Rand along with him, must acknowledge the presence of an authority strong enough to assure the validity of the sale. Thus, Galt must acknowledge the legitimacy of big government.
If you ask a "libertarian", he or she will tell you that big government ought not to exist. It follows that John Galt cannot own the commons. But the libertarian can attempt to make the case that the commons does not formally exist. They may argue that there is nothiing that can be legitimately set aside for public usage. However, it may be countered that without a commons and the rules that govern its usage, chaos is all that can exist. One simply has to look outside one's front door to see a street maintained by some agency to promote public passage. Without the street to lie on the division lines between one's property and that of one's "across-the-street" neighbor, leaving my own property puts me into a position of trespass. Freedom to move demands a minimum of a path on which such motion can occur. And Galt, too, must pick up his portion of the dog poop, to maintain that roadway in condition for others to travel.