Resource Trap v2.1 — Rationality as the Only Path to Abundance: AGI-Executable Formal Specification, Reinforcement Learning Environment, Nash Equilibrium Proof, Mechanism Design, and W20 v8.3 Triadic Control Architecture

This working paper presents version 2.1 of the Resource Trap — a dual-layer document combining narrative analysis with a complete AGI-executable formal specification of civilizational resource allocation dynamics. Earth is not resource-poor; it is poor in rationality of resource allocation. The central formula R_total = R_war + R_vpk + R_over + R_agents + R_natural demonstrates that R_natural (physical scarcity) is the smallest term, while R_war + R_vpk alone represent over 35–40% of global resource allocation ($2.718 trillion in military expenditure, SIPRI 2025). The formal layer (Appendices B–G), preserved from v2.0, provides: a complete dynamical system specification with governing parameter u(t) ∈ [0,1] representing allocation inefficiency; four civilizational attractors (Ω₁ abundance at u = 0, Ω₂ stagnation at 0 < u < u_crit, Ω₃ degradation at u > u_crit, Ω₄ collapse at u = 1) with spectral stability analysis via Jacobian eigenvalues; a reinforcement learning environment where AGI learns to minimise u(t) through interaction with the dynamical system; a three-player multi-agent model (State, Capital, AGI) with conflicting reward functions demonstrating why Nash equilibrium produces u > u_crit even with fully rational actors; a formal game-theoretic proof that the Price of Anarchy Ω_opt/Ω_Nash >> 1, establishing that rational self-coordination to u → 0 is mathematically impossible without external coordination; and mechanism design solution τ(u) = k·(u − u_opt)² as the alignment mechanism — identifying AGI as mechanism designer as the only scalable implementation of stimulus alignment in real time. Version 2.1 introduces Appendix H (W20 v8.3 Alignment), providing four new layers: (i) W20 State Space Bridge mapping Ω(t) = P·C·I/(1 + u + L) directly to W20 Z[0] (Ω component), identifying u(t) as the governing parameter for W20's aggregate stability; (ii) Kodex Priority Ordering Map connecting Nash equilibrium lock-in to Tier 0.1 (Dual Survival — u > u_crit drives G[K] → 0), Ω₄ attractor to Tier 0.2 (Catastrophic Harm Prevention), and τ(u) to Tier 0.3 (Human Agency) as the formally derived AGI lever — the only work in the series where AGI's role emerges from mechanism design rather than normative preference; (iii) SCF Basin Topology Map aligning the four attractors to the three-basin SCF structure and documenting a seventh AGI_FROZEN path (allocation channel: u → 1 → C·I → 0 → N_novelty → 0, parallel to but distinct from W18 Compute Paradox); (iv) Triadic Control Architecture with τ(u) as the single AGI lever (rank(G_agi) = 1, consistent with W11's minimum footprint), Nash lock-in detection protocol, false scarcity correction mechanism, and τ(u) capture protection. Current world position: u ≈ 0.3–0.4, distance to u_crit = 0.0–0.2, intervention window open but narrowing. Николай Мишко Аффилиация: Asia Digital Hub, Астана, Казахстан Эл. почта: nikolaimishko@gmail.com Рецензирование: Клод (Антропик).