Asynchronous tuning and invalidating boundary

Asynchronous tuning is the interface between state at a moment and process in duration, and this interface cannot be prepared in advance. That is why asynchronous tuning involves decision making, or a choice from the outside of the domain of choice. Because it allows a choice from the outside, boundary of the domain of choice is changed after a choice. Our model of a process of dynamic indefinite boundary is expressed as iterated alternations of a particular operation (crossing the boundary toward outside) and invalidation of this operation, in using a category theory, while invalidation is outside a category theory. The notion of emergent property can be grasped in science by this key idea.