Warped Semantic Manifolds: A Geometric Framework for Deterministic AI Reasoning (Preliminary Memo)

We introduce the Noetic Geodesic Framework, a novel geometric approach to AI reasoning, where semantic mass warps cognition space into Cognition Wells, enabling deterministic Geodesic Traversals to Noetic Singularities, which are truth-aligned endpoints. A Noetic Geodesic is a straight-to-the-point journey in the mind’s landscape, guided by this curvature to eliminate probabilistic drift and hallucinations, showing promising improvements in benchmark performance (e.g., outperforming baselines on ARC-like and MMLU tasks with reduced hallucination rates). This framework addresses the ‘it works, but we don’t know why’ enigma by making wrong trajectories geometrically unstable, demonstrated via a toy simulation showing shortened paths and unstable deviations. Warped Semantic Manifolds serve as the overarching space, Semantic Mass as the curving agent, and Cognition Wells as localized basins housing Noetic Singularities. This preliminary memo claims priority on these concepts; stay tuned for comprehensive updates on empirical validation, mathematical rigor, and LLM integration.