Spiral Torsion Geometry: A New Mathematical Framework for Memory-Encoded Manifolds and Topological Consciousness

We introduce Spiral Torsion Geometry (STG), a novel mathematical framework that extends differential geometry to incorporate memory as a fundamental geometric property. We define spiral torsion manifolds equipped with memory fields η^a, phase fields φ, and a new torsion tensor T^a_μν that couples memory storage to topological charge. Our main result, the Spiral Monopole Quantization Theorem, proves that memory-induced topological charges are necessarily quantized as integers, providing the first rigorous mathematical foundation for persistent information storage in geometric structures. We demonstrate explicit calculations showing monopole formation and present applications to neural networks, where our framework provides testable predictions about memory formation, gamma oscillations, and consciousness mechanisms. This work establishes memory as an intrinsic geometric property and opens new avenues for understanding information persistence in physical and biological systems.