Geometric Multi-State Computing Units (GLUs): A Comprehensive Mathematical, Computational, and Architectural Framework Beyond Binary Logic

The figure illustrates a geometric representation of a logical unit based on continuous phase geometry. A triangle is embedded within a circular boundary, representing a single geometric bit whose logical states are defined by regions on a manifold rather than discrete symbolic values. The circular boundary denotes a closed phase space, while the triangular structure encodes constraint relations between multiple logical regions. Points along the edges and interior of the triangle may simultaneously belong to overlapping logical domains, enabling geometric superposition and non-factorizable state representation. This visualization captures the core principle of Geometric Logic Units (GLUs): logical information emerges from spatial relations, overlap, and projection within a continuous geometric structure, rather than from isolated binary states. The model remains entirely classical and is intended as a foundation for analog, neuromorphic, and unconventional computing architectures.