Despite being mentioned everywhere, the term "object" is never really formally defined at all.

What does the brain even consider an "object"? The paper is fundamentally flawed by missing this definition, since their idea is entirely reliant on the definition of an object.

Are there some common things in the physical world that constitute the basic atomic building blocks of objects according to the brain? If so, this needs to specified, otherwise all of this theory is totally vague...

How is the statement that "the cortex is capturing the relative positions of objects" in the slightest bit novel at all? Obviously mammals are capable of navigation, hunting, etc etc. Basically any interaction with your environment requires immediately knowing where all objects are, so obviously this is critically encoded within our learned representations of the world.