An approach to the mathematical theory of perception-based information

In the paper we approach the mathematical theory of perception-based information by using a theory that captures a new type of processes. These processes are the formations of integer relations with the integers as the ultimate building blocks. The theory of integer relations and their formations stands out remarkably because it is irreducible, i.e., the theory can not be explained in terms of deeper principles. It is suggested that the optimal functioning of a complex system may be a law of the integer formations and perception-based information plays a key role in the use of this law.