A Structural Argument for the Minimal Organization of Local Full Self-Representation

Abstract

This paper investigates the minimal functional organization required for local full self- representation, understood as the capacity of a local configuration to determine its own relational state without reference to anything external. Rather than presupposing a tri- adic structure, we begin from three explicit ontological commitments adopted within the OTWOFDN framework: (i) the defining property of local full self-representation, (ii) the Representational Independence Principle, and (iii) the Ontological Minimality Principle. Through structural case analysis we show that, within these commitments, configurations with fewer than three irreducible functional roles are insufficient, while a configuration with three mutually independent roles satisfies all identified requirements. This result is for- mulated as the Minimal Self-Representation Principle. The argument is structural rather than formal-mathematical and remains conditional upon the stated ontological principles. Assuming, in addition, that irreducible functional roles admit a faithful complex linear rep- resentation, the minimal triadic carrier motivates a natural passage to C 3 , U(3), and SU(3).