"The end of that subsection brings up corporations but the argument is terrible."

Which subsection? I did a search to find where is mentions corporations and it nothing came up. Group property is illegitimate because it's a stolen concept fallacy. property(rights) are a system to determine who gets to decide how something is used without aggression and for avoiding conflict(NAP violations). Contracting about how property is used it contract theory. It's a misuse of a contract. Contracts are for transfer and for letting people use your property. a and b are merely stand ins dude.

Dave and Jim buy a car together. Dave wants to pain the car green and Jim wants to not paint it. Who gets to decide? This is the issue with collective property. it does not solve the issue it intended to solve. who gets to decide how it is used. Flipping a coin, court, or making up some system is contract theory. Contract theory is about property. It is not property. It's an illegitimate contract.

"For most of human history marriages were considered a form of property---and things not considered property (by law) are not necessarily not property (by nature)."

People steal historically too. That doesn't make it legitimate. He is talking of objective law. Not what the illegitimate law states. What you said is not logical as it does not do what property is supposed to do and is an easily bendable and subjective way to view property.

"Property is a formalization (via contract) of control, which may be sold, i.e., monetized. Since control admits of group control then it is natural."

Contract theory and property theory are separate and property theory has to come before contract theory. The reasons I stated above. Group control does not avoid conflict. It's a nonsensical use of the word property.

"Certainly group ownership requires a hierarchy of control."

Group property does not make sense and what you described does not solve the issues with it. You are applying contract theory instead of property rights. You can contract it out to form group organizations involving an individuals property but it can not be group owned and be a legitimate contract. Use is not control. Mixing your labor is not a magical thing that creates ownership over someone elses property nor does it make group property make sense.

Your logic leads to things like involuntary contract theory. (social contract, slave contracts, extortion all are implied from group property theory). I consider those illegitimate as well because it is other people contracting other peoples property against their will. This is another topic though.

"It is like the author is stuck on this A or B thing, when relationships do have a first among equals. Within that hierarchy you can also establish orthogonality (e.x., it is both of our house, but you get to decorate the kitchen and I get to decorate the den)."

This is what I am talking about. Only the owner can contract it as if they both own it and if they can't agree it does not solve the conflict. That is the sole purpose of property. Do you understand what I am saying?

Lets say she wants to decorate the den in a way you don't want. Figuring a way out to get along is contract theory. Then someone will end up getting to decide and it will be them who gets to decide how it is used. That is why it is illegitimate. I have literally no say in public property. It is not even remotely used how I would like. There is no point in even using words like property under your definition. It's subjective and really is just a rejection of property.

"The most silly thing about that subsection is that it does not consider cooperative labour mixed with property. Only a miniscule of buildings are built by one man alone---"

Paying someone to build a house literally can not make it their property. You are exchanging voluntarily for their labor. That is the trade.

"when I help my buddy hold a sheet of plywood in place we both have claim to the improvement on the property."

If you have already homesteaded the land. Your friend "HELPING" you with your stuff does not make it become his stuff. He may homestead an area but it can only be one of yours. There is even a section on determining how to deal with two people homestead the same item at the same time and how it is dealt with. You also realize people trade things other than money right? They trade socially as well.

I understand your position. It's the most common position but as far as I can tell it is wrong. Property is for determining how something is used. Your theory on property does not resolve this issue. I am moving on though from this, no offense. I'm not going to convince everyone and I am no longer trying to in life.