That is not what I meant by the question, not how you technically record ownership, but what ownership means and who gets to decide.

ownership is an abstract concept, it doesn't really exist outside of the actions that create the idea. basically, i get to decide what is mine. if there is a conflict (multiple claims to a single resource) it has to be resolved in some way. this is where record keeping systems and other types of agreements come into play.

All present private property was expropriated from somebody else by violence, conquest, enclosure, and subjugation. How can a system of land ownership ever be just or fair if it rests on the historical development of the forceful dispossession of communal and indigenous land?

so you're saying i'm responsible for the actions of my ancestors? lmao my property was all obtained though voluntary exchanges. it would appear that we have learned something from history because at least i can't obtain whatever i need through voluntary means, which is an improvement over the past. if we want to go back to the "original claims" (whatever that means) it would take another series of violent authoritarian actions to "reset" the world back to whatever primitive state you are alluding to.