This example of an implicit contract is really interesting.  I agree with your example above that if Caveden doesn't leave your house he is implicitly agreeing to follow your rules.  But what if your rules were "If you don't leave my house by Monday next week, you agree to be my slave for life" ?  Furthermore, if Caveden then replies: "No. I am a self-owner and will not agree to be yours or anyone's slave."  But then he stays on past Monday.  Is he then your slave?  I'm not trying to lead you into a trap, I just want to clarify my understanding of your point.

The other thought I had was that while I agree with your example, I don't agree with the analogy you draw to living under The State.  You, presumably, own your house.  Therefore it is YOUR private property and you get to set the rules for it.  By saying that The State can set the rules for everyone in its jurisdiction, you are saying that it OWNS ALL of it.  This necessarily negates all private property.  From previous posts it seems that you are not against private property, so I'm not sure how you could agree with the concept of an implicit social contract with the State.  Am I not understanding your point?
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I think that there are some contracts that are unenforceable, like slave contracts. I think that the UN declaration of human rights has it mostly right. In the example above a contract which sais that he will be my slave is is void. A contract has to be "reasonable". Lifetime slavery for housing isn't. I do however think that I have the right to use "force" to either evict or "extract wealth" if he doesn't leave. What reasonable is should be set by the market, limited by certain basic human rights.

I don't think that the state owns everything, I think that "we" own everything, but that it is governed by the state. That way someone can buy something from us, through the state, and use it as their private property. And "we" set the rules, by proxy.
I'm absolutely not against private property, quite the contrary, but I also don't subscribe to the idea that "every man is an island" and that there has to be rules to be followed, even with regards to your private property.