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

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) < 1 − σ²/2), cognitive diversity above a minimum threshold (D_i ≥ D_min), and continuous human novelty injection (H_human > 0).

The central result — MASTER_THEOREM_MULTI_AGI — 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 < 3), synchronization collapse and diversity loss (ρ(W) ≥ 1), or absorbing frozen state (H_human = 0). Sufficiency is proven constructively via an analytical diversity equilibrium D_i* = β·D_max·H_human / (α·∑W + β·H_human), a Lyapunov functional V = a||H||² + b||D||² + c||I − I*||², and the MFLS spectral growth criterion ρ(L) > δ + σ²/2.

Three key theorems are established. THEOREM_DIVERSITY_EQUILIBRIUM derives the stationary diversity as a closed-form function of human novelty and coupling strength, formally proving that D_i* = 0 when H_human = 0. THEOREM_B3_IRREVERSIBILITY proves that human exclusion creates an absorbing basin in phase space: once H_human = 0, the system reaches full mutual information saturation (I_ij → min(H_i, H_j)), information channels collapse (H_j − I_ij → 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 (λ_max(J_eco) < −σ²/2), AGI network stability (λ_max(W) < 1 − σ²/2), and MFLS knowledge growth (ρ(L_operator) > δ + σ²/2). The coupling parameter κ from ECO_CRISIS_v1_2 (Work 11) equals mean(W_ij), directly connecting ecological substrate to AGI network dynamics.

A runnable Python implementation (AGI_NETWORK_SIMULATOR_v1_0.py) verifies all theoretical results: 8 verification checks pass, including analytical D_i* confirmation, B3 absorbing state demonstration, N_inter decay without human injection, and MFLS GROWTH phase in symbiotic regime. The simulator implements adaptive coupling W_ij(t) = w₀ · (1 − I_ij/H_j) · (D_i + D_j)/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