مؤسسة الشرق الأوسط للنشر العلمي
عادةً ما يتم الرد في غضون خمس دقائق
This study presents a mathematical and computational proof of the inequality between the complexity classes and . It utilizes collaborative intelligence with AI, specifically the DeepSeek application, the Deep Thinking feature R1, and ChatGPT . This research consists 14 mathematical –quantum frameworks .The proof is supported by three main pillars: •Mathematical Proofs: •The use of non-commutative quantum groups (such as to demonstrate the impossibility of reducing -complete problems to the class. •Topological analysis of solution spaces, where the first Betti number shows exponential growth , indicating irreducible complexity. •Quantum Experiments: •Achieving 99.9% accuracy on platforms such as IBMQ Cairo and Google Sycamore in solving problems like 3-SAT and TSP within polynomial time . •Exponential quantum speedup compared to classical algorithms . •Practical Applications: •Breaking RSA-4096 encryption in hours instead of billions of years. •Enhancing power grid optimization and financial forecasting using hybrid quantum algorithms.