Who has the greater claim to property, is it not arbitrary?

Who has a right to own the space around us, that is to say, who should be allowed to exclude all others from space, if they so wish? If we assume that some particular space cannot be utilised by more than one person at a time and that to prosper we must use space, such as land to farm or a place to live, then we must devise a methodology to determine who has the most high claim to the space.

Can we argue that to use the space effectively will yield the best outcome and is therefore the metric under which to determine ownership?

Clearly there is utility in preserving ownership through time, if we plant a field of crops we do not expect that someone else will plant another crop directly on top of our crop a day later. We also do not expect our ownership of the space encapsulated by the walls of our home to be threatened each night, before we go to sleep. So we assume that, one derived, we can expect ownership to continue, at least for while...

The space contained within a home is put to more effective use by the person residing there, for they have built the home and know how everything works, they also derive greater pleasure, which has utility, since they have everything just as they want it.

The barometer against which relative utility is measured is not against the one making the challenge, it is against the population as a whole. We are not required to give up our space to every challenger who has sold their assets, presuming it is possible to sell space, only to justify it against the wider population. This is how we measure whether we have left enough land (or space) to the commons.

Is it even legitimate to defend space? Perhaps not but if it is possible to defend our labour then we can say that we have planted grass on all of the land, which is our labour and walking on it will be damaging, or that we have perfumed the air with our breath. So then we can be said to have built the space, in effect.

...but to what extent has the intruder damaged these items, or prevented the use of them, surely enough has been left for the original creator?

Is it a risk to be near other people, or for them to be allowed to be near you? If we assume there is no risk of being violently attacked then what reason is there to keep others out of your house? What is it that you are being prevented from doing by their presence? What does a violation of your property prevent you from doing, what is it preventing? So does a crime of property violation actually exist or can we say that only preventing others from doing what they (legitimately) want is a crime?

What have you been prevented from doing by their presence?

So then we have no arbitrary claim to (spacial) property, only that we cannot, might not be prevented from doing actions which we would legitimately like to do, specifically to use what we have made. To be prevented from using property the defendant (defending property) must show that they have been, or are, being prevented from doing something, which they have a legitimate right and claim to engage in. So we can use anything (and go anywhere) so long as we do not hurt other people.

What is the harm if we sleep in an unoccupied house undiscovered for many years?

Harm can take a different form to that of the conventional use of the word, in Law, so we can harm someone not only by being aggressive but by preventing them from using something, so if we take up too much land, this is aggressive, if we sit on someone's toilet, preventing them from doing the same, this will harm them, if they either purchased, or created the toilet. We harm others by occupying (or using) their (any) property to the extent that it prevents them from using it when they would like to do so.

The use of any property harms others, for it prevents them from the use of it, when they might want to do so, but the judgement (to be made) is to work out who has the more legitimate claim.