The Cognitive Geometry of High‑Structure Belief Systems: A Carlo‑Mathematical, Psychological, and Information‑Theoretic Analysis with a Case Study of Jehovah's Witnesses

This deposit presents a full interdisciplinary analysis of high‑structure belief systems using a unified Carlo‑hybrid framework that integrates cognitive psychology, sociology of religion, information theory, and dynamical systems modelling. The work introduces *Carlo Attractor States* to describe belief‑system stability, *Carlo Drift Equations* to model controlled organisational evolution, and an information‑theoretic treatment of doctrinal compression, transmission fidelity, and entropy regulation. The paper examines mechanisms of cognitive load reduction, identity stabilisation, epistemic closure, cognitive boxing, dissonance management, boundary‑maintenance, ritual reinforcement, and outreach‑based entropy management. A detailed case study of Jehovah’s Witnesses illustrates how organisational architecture, communication topology, ritual practice, and outreach interact to produce predictable cognitive and behavioural patterns. The Carlo‑hybrid model demonstrates that high‑structure belief systems behave as dynamic cognitive‑mathematical entities governed by identifiable attractors, drift parameters, and entropy‑regulation mechanisms. This framework provides a generalisable foundation for analysing belief‑system stability, divergence, and long‑term evolution across religious, ideological, and socio‑cultural domains. Core Carlo Equation (Stability Model) \[\frac{dX}{dt} = F(X, P) + D(t)\] \[F(X, P) = 0 \quad \text{at attractor equilibrium}\] \[J = \frac{\partial F}{\partial X}\] \[\text{Stability condition: } \lambda_i(J) < 0\] This work engages with high‑structure belief systems, cognitive architecture, identity stabilisation, epistemic closure, cognitive load reduction, cognitive boxing, dissonance management, doctrinal reinforcement loops, boundary‑maintenance mechanisms, organisational drift, privatisation dynamics, outreach‑based entropy management, information‑theoretic modelling, doctrinal compression, transmission fidelity, noise‑reduction, redundancy, attractor dynamics, Carlo Attractor States, Carlo Drift Equations, entropy regulation, social network topology, ritual reinforcement, communication topology, structured religious organisations, sociology of religion, cognitive psychology of belief, mathematical modelling of social systems, dynamical systems theory, stability analysis, schism formation, belief‑system evolution, doctrinal coherence, high‑structure religious groups, Jehovah’s Witnesses (neutral case study), interdisciplinary systems theory, cognitive‑mathematical modelling, and the geometry of belief‑system stability. Includes a browser-based 3D cognitive geometry visualizer that renders belief-system stability, attractor basins, and dynamic parameter drift using Three.js and real-time differential math. Contact: For enquiries or research questions related to this work, email [email protected]