The evidence that no one has successfully contested Norfolk Southern is evidence that it's a natural monopoly. The burden is on you to show that it's possible and there's some other reason it hasn't happened (and why it's okay that the free market is allowing a monopoly to exist).
>If even the monopoly on violence, the core characteristic of a state
Not sure why you brought this up. Can you explain how this relates to your argument?
If you search for Norfolk Southern competitors the following names come up, Union Pacific, Canadian National Railway Company, CSX Corp, Canadian Pacific Railway and Kansas City Southern[0]. Whatever that is it isn’t a natural monopoly.
Violence has high fixed costs and relatively low marginal costs. If the efficient number of states, violence monopolists, is so much greater than one why would we expect anything else to be a natural monopoly?
[0]http://financials.morningstar.com/competitors/industry-peer....
Norfolk Southern from a cursory look at its Wikipedia page may have a local monopoly on rail transport of coal on North Anerica’s East Coast. This will enable it to charge slightly higher than competitive prices. It will not enable it to charge profit maximising monopolist prices because other companies can build their own rail lines and coal can be transported by truck. Local monopolies are contestable. You may have no actual competition but the price you can charge is limited by the fact that if you charge enough potential competition will become actual competition.
The concept of natural monopoly does not depend on government or private companies. It depends on minimum efficient scale being more than half of a market. If even the monopoly on violence, the core characteristic of a state, is not a natural monopoly, what is?