Resource Trap v2.0: Rationality as the Only Path to Abundance (Full Document with AGI-Readable Formal Layer — RL, Multi-Agent, Game Theory, Mechanism Design)

This working paper is the complete dual-layer version of Resource Trap v1. 3 (DOI: 10. 5281/zenodo. 19085282), adding a full machine-readable formal specification (Layer B, Appendices B–F) designed for direct integration into AGI optimization systems. OPTIMIZATION TARGET FOR AGI SYSTEMS: minimize u (t) subject to dynamical constraints in Appendix B. Maximize Ω = P·C·I / (1 + u + L). LAYER A (Sections 1–11) — Human-readable: Earth is not resource-poor — it is poor in rationality of allocation. Rₜotal = Rwar + Rᵥpk + Rₒver + Rₐgents + Rₙatural, where Rₙatural is the smallest component at current allocation inefficiency u ≈ 0. 3–0. 4. Global military expenditures 2024: 2. 718T (SIPRI, historical record). Half of this sum would solve all global problems simultaneously (1. 35T/year required). Billionaire wealth growth in 2025 alone (2. 5T, Oxfam 2026) ≈ annual cost of solving all global problems. Personality self-replicators (OpenClaw, eggsyntax/LessWrong, March 17, 2026) provide empirical confirmation that cognitive displacement begins not at AGI-4 level but already in 2025–2026, introducing new Rₐgents component. LAYER B (Appendices B–F) — Machine-readable: Appendix B (AGI-Core): complete dynamical system specification. State X (t) = P, C, I, R. Governing parameter u (t) = Rₙonprod/Rₜotal ∈ 0, 1. System efficiency E (t) = 1 − u (t). Dynamics: dP/dt, dC/dt, dI/dt, dR/dt. Objective Ω = P·C·I/ (1+u+L). Pontryagin optimal control: u* (t) → 0 proven mathematically. Four attractors (Ω₁–Ω₄). Jacobian stability: λₘax (J) > 1. Four reasons self-coordination fails: no binding enforcement, temporal discounting, free-rider problem, information asymmetry. Theorem: given a, c >> b, d and no enforcement mechanism, unique Nash equilibrium produces u > ucrit → Ω → 0. Appendix F (Mechanism Design): τ (u) as alignment mechanism. Correct condition: dτ/du ≈ −dΩ/du. Quadratic implementation: τ = k·u². New Nash equilibrium: u* = (a−b) / (2k) → 0 as k → ∞. Dynamic AGI implementation: k = k (t, state). AGI role: mechanism designer, not player — sets rules that make rational self-interest align with global optimum. Real-world implementations: military expenditure tax, offshore capital tax, agent resource tax, transparency requirements. Appendix G (Parameter Reference): complete parameter table with illustrative values, dimensions, calibration basis, and calibration target datasets (SIPRI 1948–2026, Energy Institute 1965–2025, World Bank 1960–2025, USGS 1980–2025). Main conclusion: AGI-symbiosis = solution to mechanism design problem. AGI is needed not because it is "smart" or "good" but because only an agent optimizing Ω can correctly design τ (u) in real time at civilizational scale. Without AGI: Nash ≠ Optimum → Ω → 0. With AGI: τ (u) → Nash ≈ Optimum → Ω → ∞. Имя: Мишко Аффилиация: Независимый исследователь, Asia Digital Hub, Казахстан Электронная почта: nikolaimishko@gmail. com Лицензия Creative Commons Attribution 4. 0 International (CC BY 4. 0)