I mean, the definition is a little vague. If your meaning is something like “It goes in A if it is more accurately described as controlled by the viscera, and it goes in P if it is more accurately described as controlled by the environment,” then I guess you can get a bijection by definition, but it is not obvious these are natural categories. I think there will be parts of the boundary that feel like they are controlled by both or neither, depending on how strictly you mean “controlled by.”
I mean, the definition is a little vague. If your meaning is something like “It goes in A if it is more accurately described as controlled by the viscera, and it goes in P if it is more accurately described as controlled by the environment,” then I guess you can get a bijection by definition, but it is not obvious these are natural categories. I think there will be parts of the boundary that feel like they are controlled by both or neither, depending on how strictly you mean “controlled by.”