Geometric Foundations of Consciousness: Soliton Theory, Möbius Symmetry, and the Global Workspace Principle Incorporating Dual-Temporal Global Connectivity

Abstract Consciousness is widely theorized as an emergent property of neural information flow, yet existing models lack a geometric foundation and fail to explain the global unity of reasoning, feeling, and memory. Here, we derive the structure of conscious moments directly from cortical conformality and Möbius invariance, demonstrating that these constraints uniquely select the Sol geometry among possible Thurston geometries. By applying the Akivis decomposition, we identify three orthogonal components—reasoning (H), feeling (K), and memory (Q)—that govern distinct temporal dynamics. Conscious events correspond to Sol–Akivis solitons that project onto the cortical sphere S², enforcing a unique global workspace as a mathematical necessity. Our Global Workspace Principle (GWP) differs from previous heuristic or architectural accounts by deriving the workspace as the necessary intersection of all possible update trajectories in dual temporal regimes, rigorously dictated by Möbius invariance and the Sol geometric structure. Memory retrieval is formalized as a geometric dislocation, while subjective flow emerges from dual orthogonal time directions. Our model yields eight explicit, testable predictions, including mechanical signatures of recall and non-temporal memory distortions, providing a unified and falsifiable geometric theory for the fundamental structure of consciousness.