W19 v2.4 — Information Asymmetry Trap: Epistemic Collapse, Cognitive Capture, and Signal Starvation of AGI — Formal Dynamical Model with W20 v8.3 Alignment, Kodex Priority Ordering, and Triadic Control Architecture

This working paper presents Work 19 v2.4 of the Omega-u Civilizational Framework — a formal dynamical model of the Information Asymmetry Trap, updated for full structural alignment with W20 v8.3 (Civilizational Control, Symbiosis, and Ω-u Synthesis). The document models the civilizational information layer as a 7-dimensional state vector X = [A_s, I_a, E_b, C_m, T_i, u, I_q], capturing asymmetry index, institutional opacity, epistemic bubble formation, cognitive manipulation, trust level, uncertainty, and institutional quality. The core mathematical framework — established in v2.2 — is fully preserved: dual autocatalytic instability (A_s and E_b self-reinforcing feedbacks), the Signal Quality Index SQI = T_i·(1−A_s)·(1−E_b) as the primary observability metric, Theorem A (signal starvation: G[K] → 0 when SQI < SQI_min regardless of compute), Theorem B (epistemic void absorbing state: D_info < 0 is irreversible), full Jacobian analysis, Lyapunov stability, HJB optimal control, MFG Nash equilibrium in opacity dynamics, bifurcation structure across six threshold surfaces (D1–D8), cross-trap correction theorem (A_s corrupts all W15–W18 reported variables), and triadic control architecture with Alpha/Beta/Gamma roles (Layer 16, introduced in v2.3). All 25 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 Signal(X) → D_info, O_eff, Φ_W20, Ω_partial in W20's 11-dimensional civilizational state Z, with explicit lexicographic priority: W19 signal corrections must be applied before feeding W15–W18 outputs into W20's AGI_CONTROL_STEP; (ii) Kodex Priority Ordering Map (Layer 0c) connecting each major failure mode to specific Tier 0 violations — signal starvation maps to Tier 0.1 (Dual Survival) as AGI knowledge death, epistemic void maps to Tier 0.2 (Catastrophic Harm Prevention), cognitive manipulation variable C_m is identified as the direct mathematical realization of Tier 0.5 (Authentic Interaction) violation, and institutional opacity I_a driving asymmetry A_s maps to Tier 0.6 (Non-exploitation); (iii) SCF Basin Topology Map (Layer 0d) classifying W19 phases into the three-basin SCF structure — OPEN/NOISY phases map to Symbiotic Stability, TOXIC to Structural Capture, VOID and EPISTEMIC_VOID to Total Collapse (soft and irreversible respectively), with the hard boundary at D_info < 0 (Theorem B absorbing state). Three new Python verification tests (T28–T30) confirm N_novelty at Kazakhstan baseline, Kodex violation detection in VOID state (5 violations confirmed), and SCF basin mapping consistency across country sample. W19 is identified as the lexicographically prior layer of the full W20 model: without Signal(X) > SQI_min, W20's AGI_CONTROL_STEP operates on corrupted inputs from all other works simultaneously. Country analysis confirms Kazakhstan as the only case in Symbiotic_Stability_degrading basin (SQI = 0.193), while Russia reaches the irreversible epistemic void (D_info = −0.220, SQI = 0.003). Николай Мишко Аффилиация: Asia Digital Hub, Астана, Казахстан Эл. почта: [email protected] теория v2.4 + симулятор v2.4 Рецензирование организаций: Клод (Anthropic)