How do you verify that x owns the watch he claims y stole from him? You collect and evaluate the evidence, and make as best a decision as you can. If you can’t figure it out, you refer it to someone who can.
There is always someone who can.
I would predict that among other things beyond my ken as a mere economics student and warehouse rat, this would involve:
Testing the contestants’ knowledge of particular marks on the property that would prove their prior claim;
Hearing the testimony of witnesses (neighbors, business partners, et al);
Tracking the history of title and testing its validity, etc.
And also, the contestants may have conflicting claims of varying degrees of strength - x may have planted a garden and let it go fallow in later years, whereupon y built a house on that spot. Does the prior claim of x extend over a period of time sufficient to sustain it beyond the building of y’s house? Or does y have the stronger claim because he used land for an obviously productive purpose, where x’s claim was based on dubious and tenuous productive use?
That’s a question for x and y to work out through their respective advocates. As more and more of those situations are resolved, the theory is refined.
It’s not a problem if you or I or the folks here are unable to conceptualize how private land management might work. Market entreprenuers can, that’s all that matters.
It is a much easier issue concerning land that has already been platted and titled by previous statist land bureaus. Successor private defense agencies are pretty much bound by existing records.
The problem will be with all the unclaimed land held by the government by fiat that will all of a sudden be opened to homestead, as per Rothbard’s theory of initial acquisition of vacant land. This land is completely unplatted. Thankfully all of it is divided by townships, so there will be a reference point for private defense agencies to recognize land claims.
Loggers will be able to secure pretty quick title to their existing lease lands from the government. Same with ranchers and mineral leasee’s. I think privately funded interests will move fast to grab the national parks before anybody would have a chance to homestead and possibly try to develop said parks. The main problems will develop in fiat land that currently has no use.
All in all, there will be a lot of troubles in the beginning, but I think the market will figure them out.
Even today there is no “central archive”. In Arizona (where I live) and in most other states that I know, all land ownership records are maintained at the county level, not at the state or federal level.
When we are finally rid of government rulers, I image that the numerous Title Insurance agencies will homestead the county records, probably thru a mutually owned subsidiary. Title Insurance agencies would then probably continue to insure land titles and utilize and update (for a fee as they do today) the “central” database maintained by the subsidiary.
That problem exists today, and the solution under anarchy would probably be the same as it is now. Hire a Title Insurance agency to validate and insure the title to the property.
I owned some mountain property in Arizona that had overlapping claims. These claims arose from mining claims that were quickly made and not accurately established. (Rugged terrain is especially prone to inaccurate boundary lines). When the minining claims were converted to “regular”, surveyed property, the overlapping claims were resolved by earliest registration date.