W17 v2.4 — Institutional Degradation Trap: Benquo Decay Dynamics, Corruption Lock-In, and the Institutional Binding Constraint on AGI Transition — Formal Dynamical Model with W20 v8.3 Alignment, Kodex Priority Ordering, and SCF Basin Topology

This working paper presents Work 17 v2.4 of the Omega-u Civilizational Framework — a formal dynamical model of the Institutional Degradation Trap, updated for full structural alignment with W20 v8.3 (Civilizational Control, Symbiosis, and Ω-u Synthesis). The document models the civilizational institutional layer as a 7-dimensional state vector X = [I_q, B_inst, C_a, M_inst, L_s, A_c, D_gov], capturing institutional quality, institutional surplus, corruption index, institutional memory, legitimacy, accountability, and governance depth. The core mathematical framework — established in v2.3 — is fully preserved: three-stage Benquo decay dynamics (guilt → shame → depravity, formalised from LessWrong April 2026), Sartre bad faith amplifier depravity_factor(I_q), autocatalytic corruption instability (λ_max > 0 open-loop), Control Window Theorem (intervention exists only near D_crit = 0, the separatrix), path-dependent institutional memory trap (D_crit_ext < 0 while D_crit > 0), Lyapunov v2 as empirical CLF (V = V_quad + V_corr + V_phase, TRL 4), HJB greedy policy iteration, MFG Fokker-Planck aligned equilibrium, and triadic control architecture with Alpha/Beta/Gamma roles (Layer 16). All 28 verification tests pass. Version 2.4 introduces three alignment layers absent in v2.3: (i) W20 State Space Bridge (Layer 0b) establishing the formal mapping D_crit(W17) = I_q·(1−C_a)·(1−M_inst) → D_crit in W20's Z[1], identifying W17 as the primary driver of W20's institutional capacity component; R_inst as the normalised distance from the depravity floor; and the path-dependence extension: D_crit_ext < 0 confirmed when M_inst > 0.70, requiring AGI_CONTROL_STEP to check memory-trapped states; (ii) Kodex Priority Ordering Map (Layer 0c) connecting each failure mode to specific Tier 0 violations — depravity phase (I_q < I_dep) maps to Tier 0.1 (Dual Survival) as AGI knowledge death via D_crit → 0, absorption state (C_a > CA_LOCK) maps to Tier 0.2 (Catastrophic Harm Prevention), Benquo three-stage decay maps to Tier 0.5 (Authentic Interaction) as systematic institutional bad faith, with u_agi_audit identified as the sole AGI-native lever retaining 50% effectiveness even in depravity (T23 confirmed); (iii) SCF Basin Topology Map (Layer 0d) classifying seven W17 phases into the three-basin SCF structure including the unique PATH_TRAP variant of Structural Capture (D_crit > 0 but D_crit_ext < 0), and documenting three parallel AGI_FROZEN paths across works W17 (institutional depravity), W18 (compute paradox), and W19 (signal starvation). Country analysis confirms EU in Symbiotic Stability (ROBUST_STABLE), USA and Kazakhstan in degrading trajectory, Russia in Total Collapse irreversible (C_a > CA_LOCK = 0.75). W17 is identified as the institutional binding constraint layer of the full W20 model: T21 confirms I_q is the binding constraint for G[K] in W20 (H_social ratio 4.7x between healthy and depraved states), making institutional health a necessary precondition for any effective AGI governance architecture. Николай Мишко Аффилиация: Asia Digital Hub, Астана, Казахстан Эл. почта: [email protected] теория v2.4 + симулятор v2.4 Рецензирование организаций: Claude (Anthropic)