Ecological Crisis Typology and Civilizational Stability: A Dynamical Systems Framework with AGI-Symbiosis Link

Overview This work presents a formal mathematical framework for classifying ecological threats by urgency (acute / medium / chronic), deriving their civilizational consequences, and proving that ecological stability is a **necessary condition** — not an ethical preference — for AGI growth and human-AGI symbiosis. The framework is part of the Omega-u Civilizational Traps series and directly extends the MFLS (Multi-Focus Learning System) results: ecological collapse forces NK → 0, which by MFLS Theorem 1 forces GK ≤ 0 (AGI frozen phase). Ecology and AGI growth share the same spectral stability criterion. Contents **ECOCRISISᵥ1₂. md /. docx /. pdf** — Mathematical theory (Layers 0–21): - AGI-readable dual-layer format (human + machine) - Global variable dictionary: Lₑff, AL, S, NK, GK- Threat classification: freshwater, soil, ocean, climate, biodiversity, fossil fuels- Threat multipliers: wars and natural disasters as AL spikes- Cost matrix: 8T/year current losses vs 5. 4T/year required action- Explicit system dynamics: dL/dt, dA/dt, dS/dt, dNK/dt- Jacobian sign structure and spectral analysis- Full Lyapunov proof: JT P + P J = -Q, P > 0 (symbiotic case only) - Bifurcation structure: saddle-node, Hopf, transcritical- Stochastic dynamics: rho (L) > delta + sigma²/2- Agent-based NK model with network diffusion (kappa) - Scenario decision tree: 4 branches, single viable attractor- Attractor analysis: ecologyₛtable AND AGIₛymbiotic is the only stable attractor- Extended Theorem (Layer 20): 5 necessary and sufficient conditions- Verification Protocol (Layer 21): theory ↔ code consistency confirmed **ECOSIMULATORᵥ1₄. py** — Runnable implementation (740 lines, no external dependencies except numpy/scipy): - State vector X = L, A, S, N, control vector U = uₑ, uₓ, uₐ- Deterministic and stochastic simulation (3 scenarios: baseline, ecology-only, symbiotic) - Model Predictive Control (MPC, horizon=8) - Numerical Jacobian via deltaX () (correct, avoids identity shift) - Lyapunov P matrix via scipy. linalg. solvecontinuousₗyapunov- Sensitivity analysis (±20% parameter scan on lambdaₘax) - Bifurcation scan and tipping point detection- Extended 7-variable model: L, A, S, N, E, T, K- Hysteresis: N recovers gradually only if S 0: JT P + P J = -Q (Lyapunov stability) 2. Lₑff ≥ Lcritical = 0. 4 (ecological floor) 3. Elambdaₘax kappaₘin (agent network connected) 5. uₐ = 1 (symbiotic AGI) **MFLS Unification: ** Ecology stability criterion (lambdaₘax (J) delta + sigma²/2) share identical spectral structure. Same mathematics. Same single viable phase. **Verification results (ECOSIMULATORᵥ1₄. py): **- CHECK₁ dynamicsₘatch: error = 0. 000000 ✓- CHECK₂ lambdaₘax symbiotic: -0. 150 → ROBUSTSTABLE ✓- CHECK₂ stochastic margin: -0. 1497 delta = 0. 05 → GROWTH ✓ Peer Review Draft versions reviewed by: ChatGPT (OpenAI), DeepSeek, GLM, Grok. Consensus fidelity rating: ~98% (theory ↔ code consistency). **Series: ** Omega-u Civilizational Framework | Civilizational Traps (Work 11) **Author: ** Nikolai Mishko | Astana Digital Hub | Kazakhstan | nikolaimishko@gmail. com**License: ** CC BY 4. 0**Related series DOI: ** 10. 5281/zenodo. 19112296