Singularization Framework: Structural Compression, Resonance Collapse, and Adaptive Capacity in Complex Systems

2026/03/16 by Bernd von Mallinckrodt · 1 voice
Computer Science · Physics and Astronomy · Environmental Science · #Chaos, Complexity, and Education #Complex Systems and Dynamics #Ecosystem dynamics and resilience

paper · doi:10.5281/zenodo.19047459

openalex publication_date 2026/03/16 · openalex created_date 2026/03/17 · openalex updated_date 2026/07/01

Abstract

This paper introduces Version 3 of the Singularization Framework, a formal theoretical model proposing that collapse in complex adaptive systems is driven primarily by endogenous structural compression and the progressive loss of adaptive resonance. Version 3 substantially extends previous versions with: (1) Formal definitions — configuration space C(t), Structural Compression Comp(t), Adaptive Resonance Res(t) via Recurrence Quantification Analysis (RQA), and Systemic Tension T(t) as demand-capacity mismatch. (2) Complete CRTI formalization — the Compression–Resonance–Tension Index as a three-dimensional diagnostic vector CRTI(t) = (Comp(t), Res(t), T(t)) with explicit phase-assignment criteria and collapse region Ω_c. (3) Mallinckrodt Cycle — five-phase lifecycle model (Expansion, Integration, Compression, Brittleness, Collapse/Singularization) with CRTI-based phase boundaries and Holling mapping. (4) Cybernetics integration — explicit alignment with Ashby's Law of Requisite Variety, Beer's Viable System Model, and Ulanowicz's ascendency-overhead balance. (5) Falsifiability conditions — four explicit testable predictions specifying disconfirming observations. (6) Toy ODE model (Appendix B) — three coupled differential equations illustrating the compression-driven collapse mechanism, with numerical simulation and embedded figure. (7) Scaling hypothesis E = S · S_max² — reformulated as an explicit falsifiable scaling hypothesis. The framework is positioned against Holling's Panarchy, Scheffer's critical transitions theory, Taleb's antifragility, Kauffman's NK models, Truong et al.'s entropy collapse (arXiv:2512.12381), and Gosme's sociotechnical phase transition model (arXiv:2512.09352). All claims are framed as falsifiable theoretical proposals. Empirical validation is identified as future work. Version history:v1 (Positioning paper): 10.5281/zenodo.19046702v2 (Full conceptual paper): 10.5281/zenodo.19046970v3 (This version — formal definitions, ODE model, simulation): current complex adaptive systemsstructural compressionadaptive resonanceresonance collapsesingularizationMallinckrodt CycleCRTICompression-Resonance-Tension Indexcollapse dynamicsconfiguration spacetipping pointsearly warning signalsresilience theorypanarchycritical transitionsentropy collapsephase transitionbrittlenessantifragilityNK modelscomplexity sciencecyberneticsrequisite varietyviable system modelrecurrence quantification analysisODE modelnonlinear dynamicsfalsifiability

Discussions

• If collapse in complex systems … is preceded by structural compression and loss of adaptive resonance, early warning may already be visible in system dynamics. Preprint: doi.org/10.5281/zeno... 🖖 [bsky, 3 points, 0 comments]

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