Quantum-Pattern Calculus: A Cross-Domain Framework for Information Exchange Mathematics

This paper introduces Quantum-Pattern Calculus (QPC), a novel mathematical framework that combines quantum information theory with 5-dimensional pattern space to model and transform information across domains. We demonstrate how meaning emerges at the intersection of information exchange through three key innovations: 1. A 5-dimensional pattern space (S, T, C, E, M) capturing structural, temporal, contextual, emergent, and meta-property aspects of information 2. Quantum information principles (superposition, entanglement, contextual collapse) applied to meaning formation, showing that meaning is not inherent to information but emerges through quantum-like interactions 3. Transformation operators enabling systematic cross-domain solution transfer with quantifiable success probabilities Theoretical contributions include:- Solution Invariance Theorem: Mathematical proof that solutions with sufficient transferability can be systematically transformed across domains- Information-Meaning Duality: Meaning emerges through quantum superposition, entanglement, and contextual collapse—not as inherent property of symbols- Pattern Conservation Principle: Patterns transform but cannot be created or destroyed in closed systems Applications include cross-domain problem solving, conversational intelligence enhancement, computational creativity, and quantum-entangled knowledge management systems. This framework provides the first rigorous mathematical formalism for how meaning emerges from information exchange, extending Shannon's quantification of information to address qualitative aspects of understanding and knowledge transfer. Status: Preprint, available for community reviewCode implementation: Python reference implementation included in appendicesContact: [bitsabhi@gmail.com