Non-Euclidean Logic: 4D Dynamic System Modeling

This paper proposes a departure from static Boolean logic in Artificial General Intelligence, introducing a dynamic, four-dimensional Riemannian manifold architecture. By treating logical relationships as a physical geometry that warps under systemic stress, we demonstrate a method for enforcing ethical and fiduciary adherence through spatial exclusion rather than algorithmic filtering. We define the Fiduciary Repulsion Vector as a non-linear geometric force that ensures logical convergence within a positively curved manifold, mathematically barring incoherent or anti-fiduciary propositions from the system's decision-making core. Using system stress as a Lyapunov function candidate, we provide a formal proof of structural stability, ensuring the manifold remains self-correcting under extreme operational pressure. This framework offers a robust alternative to current high-dimensional modeling failures, establishing a "virtual physics" for safe, scalable human-machine teaming. Please Note: The paper is specifically structured so that the mathematical notation remains in its raw, semantic form (LaTeX), making it exceptionally easy for others to port and compile. Additionally, there are two document files for two different readers. HUM_ is a PDF for human usage, while SYS_ is a markdown file for machines. And, most importantly: 9x - 7I > 3 (3x - 7U) ♥