  The recent financial crisis has sharply revealed that current understanding
of the global financial system is more than limited. In the recovery plan the
confidence in the underlying theory is crucial. To address the problem we
propose the description of complex systems in terms of self-organization
processes of prime integer relations. The description suggests to consider the
global financial system through the hierarchical network built by the totality
of the self-organization processes. To make the description operational we
propose an integration principle and support it by computational experiments
using a multi-agent system. Remarkably, based on integers and controlled by
arithmetic only the description raises the possibility to develop an
irreducible theory of complex systems. These may open a fundamentally new
perspective for the modeling of the global financial system.
