General Theory of Relational Primacy

Ngueuleweu Tiwang Gildas

Papers from arXiv.org

Abstract: This paper presents the General Theory of Relational Primacy (GTRP), a conceptual and formal framework for understanding stability, crisis, and transition in complex systems. The central thesis is that systems are not defined by their variables but by the relations that organize them. Variables are merely late manifestations of deep relational mechanisms. Crises arise from the silent reorganization of these relations, not from changes in the variables themselves. We formalize three axioms (relational primacy, antecedence of relations, and universality of coupling) and derive from them a complete hypothetico-deductive framework (hypotheses H1-H5, validity conditions C1-C6, and properties P1-P5 of the observable beta). We prove a foundational theorem establishing that every complex system possesses an irreducible relational level, introduce an invariant of the theory analogous to the conservation of energy, and propose universal definitions of crisis, relational causality, and relational information. The parameter beta(t) = d log y / d log x, estimated via a time-varying Kalman filter in the log-log space, measures this reorganization with an O(delta theta) sensitivity, one order of magnitude faster than classical O((delta theta)^2) signals. The empirical evidence (NASA AIRS data, 2002-2026) and validations on six simulated systems confirm that beta precedes classical early warning signals by 14 to 24 months and 39 to 153 time steps. The theory is designed to be universal, applicable to climate, biology, economics, artificial intelligence, and sovereignty of systems.

Date: 2026-07
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