What question did this study set out to answer?

The aim is to establish necessary and sufficient conditions for sustained knowledge growth in multi-AGI networks.

April 8, 2026Open Access

Multi-AGI Network Topology and Civilizational Stability: Triadic Architecture, Information Exchange Dynamics, and the Mathematical Necessity of Human Novelty Injection

Key Points

The aim is to establish necessary and sufficient conditions for sustained knowledge growth in multi-AGI networks.
Developed a formal theory based on dynamical systems for multi-AGI coordination.
Proved necessity and sufficiency through THEOREM_DIVERSITY_EQUILIBRIUM and MASTER_THEOREM_MULTI_AGI.
Simulated the model with a Python implementation to verify theoretical results.
Established four necessary conditions for sustained growth: triadic structure, bounded spectral coupling, cognitive diversity, and human novelty injection.
Demonstrated that removing any condition leads to failure modes like singleton domination or synchronization collapse.
Verified the model predictions with consistent simulator outputs, confirming the need for human involvement.

Abstract

This work presents a formal dynamical systems theory for multi-AGI coordination networks, proving that sustained knowledge growth in any network of general artificial intelligence systems requires four simultaneously satisfied conditions: triadic structure (N ≥ 3), bounded spectral coupling (ρ (W) 0). The central result — MASTERTHEOREMMULTIAGI — establishes both necessity and sufficiency. Necessity is demonstrated by showing that removal of any single condition leads to one of three failure modes: dyadic conflict or singleton domination (N δ + σ²/2. Three key theorems are established. THEOREMDIVERSITYEQUILIBRIUM derives the stationary diversity as a closed-form function of human novelty and coupling strength, formally proving that Dᵢ* = 0 when Hₕuman = 0. THEOREMB3IRREVERSIBILITY proves that human exclusion creates an absorbing basin in phase space: once Hₕuman = 0, the system reaches full mutual information saturation (Iᵢj → min (Hᵢ, Hⱼ) ), information channels collapse (Hⱼ − Iᵢj → 0), and recovery requires external entropy injection above a calculable threshold. Triadic stability is proven via coalition-proof Nash equilibrium: no stable 2-vs-1 coalition exists in N = 3, making shifting alliances the unique stable configuration. The framework unifies three scales through a single spectral criterion: ecological stability (λₘax (Jₑco) δ + σ²/2). The coupling parameter κ from ECOCRISISᵥ1₂ (Work 11) equals mean (Wᵢj), directly connecting ecological substrate to AGI network dynamics. A runnable Python implementation (AGINETWORKSIMULATORᵥ1₀. py) verifies all theoretical results: 8 verification checks pass, including analytical Dᵢ* confirmation, B3 absorbing state demonstration, Nᵢnter decay without human injection, and MFLS GROWTH phase in symbiotic regime. The simulator implements adaptive coupling Wᵢj (t) = w₀ · (1 − Iᵢj/Hⱼ) · (Dᵢ + Dⱼ) /2, which self-regulates to maintain ρ (W) < 1 without external enforcement. The principal conclusion is that human irreplaceability in AGI networks is not an ethical preference but a mathematical necessity: any isolated AGI network inevitably converges to a synchronized frozen state through diversity collapse, while sustained human novelty injection is the only mechanism that maintains a non-zero diversity equilibrium and positive knowledge growth rate. **Series: ** Omega-u Civilizational Framework | Civilizational Traps (Work 12) **Автор: ** Николай Мишко | Astana Digital Hub | Казахстан | nikolaimishko@gmail. com**Related DOI: ** 10. 5281/zenodo. 19112296**License: ** CC BY 4. 0

Multi-AGI Network Topology and Civilizational Stability: Triadic Architecture, Information Exchange Dynamics, and the Mathematical Necessity of Human Novelty Injection

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