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 = Iq, Bᵢnst, Cₐ, Mᵢnst, Lₛ, Ac, Dgov, 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 depravityfactor (Iq), autocatalytic corruption instability (λₘax > 0 open-loop), Control Window Theorem (intervention exists only near Dcrit = 0, the separatrix), path-dependent institutional memory trap (Dcritₑxt 0), Lyapunov v2 as empirical CLF (V = Vquad + Vcorr + Vₚhase, 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 Dcrit (W17) = Iq· (1−Cₐ) · (1−Mᵢnst) → Dcrit in W20's Z1, identifying W17 as the primary driver of W20's institutional capacity component; Rᵢnst as the normalised distance from the depravity floor; and the path-dependence extension: Dcritₑxt 0. 70, requiring AGICONTROLSTEP to check memory-trapped states; (ii) Kodex Priority Ordering Map (Layer 0c) connecting each failure mode to specific Tier 0 violations — depravity phase (Iq CALOCK) 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 uₐgiₐudit 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 PATHTRAP variant of Structural Capture (Dcrit > 0 but Dcritₑxt CALOCK = 0. 75). W17 is identified as the institutional binding constraint layer of the full W20 model: T21 confirms Iq is the binding constraint for GK in W20 (Hₛocial 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: nikolaimishko@gmail. com теория v2. 4 + симулятор v2. 4 Рецензирование организаций: Claude (Anthropic)