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 Rₜotal = Rwar + Rᵥpk + Rₒver + Rₐgents + Rₙatural demonstrates that Rₙatural (physical scarcity) is the smallest term, while Rwar + Rᵥpk 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 ucrit, 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 > ucrit even with fully rational actors; a formal game-theoretic proof that the Price of Anarchy Ωₒpt/ΩNash >> 1, establishing that rational self-coordination to u → 0 is mathematically impossible without external coordination; and mechanism design solution τ (u) = k· (u − uₒpt) 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 Z0 (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 > ucrit drives GK → 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 AGIFROZEN path (allocation channel: u → 1 → C·I → 0 → Nₙovelty → 0, parallel to but distinct from W18 Compute Paradox) ; (iv) Triadic Control Architecture with τ (u) as the single AGI lever (rank (Gₐgi) = 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 ucrit = 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).
Nikolai Mishko (Thu,) studied this question.