What's to stop them from using it, but your force?No one was claiming it before, so you're not violating anyone's rights, you're not aggressing against anyone, by appropriating for yourself.
If you actually remove something from nature, you've created a product, and established a property right. By removing it, you have removed the opportunity others have to use it. Locations cannot be removed from nature. There's no way to make a location into a product. Any claim to a location is nothing more than a demand others not use it, with no just basis.There are limits to how much you can claim, the whole "mixing your labor" in thing helps to solidify your claim, also marking the borders if the matter is fairly immobile, or moving the matter into a place you already possess if it's transportable.