Systemic Tau and Hierarchical Ordinal Conjunctions: A Relational Theory of Critical Transitions

Abstract

Foundations paper (English, ~30 pp.) for a dual relational account of critical transitions in complex systems. Systemic Tau (τs) is an ordinal, multivariate measure of cross-variable coupling: sliding-window Kendall-type rank concordance tracks relational coherence rather than the amplitude of any single observable. Hierarchical ordinal conjunctions are operationalized through the Discrete Extramental Clock (RECD): three levels of structural claim—coincidence (Φ1), persistent relational structure (Φ2), and the irreducible residual beyond pairwise models (Respair)—plus the scalable hybrid proxy excess3 (not identical to Respair). Weighted advances use admissible aggregation weights αℓ(λ); aggregation share is distinct from abundance. Early warning is cast as a change in hierarchical ordinal structure, not merely a rise in fluctuation size. Claims, estimators, and aggregation policy are kept on separate planes. Includes synthetic validation on coupled logistic maps and a working hypothesis for the excess3 peak near the Feigenbaum accumulation point. v1.1.1 micro-release: title-page footnote with version DOI, concept DOI, and source repository. Concept DOI remains stable across versions. Contents: PDF + TeX source + bibliography; key figures.