مؤسسة الشرق الأوسط للنشر العلمي
عادةً ما يتم الرد في غضون خمس دقائق
This research consists of seven mathematical frameworks fully developed through collaborative intelligence with AI, using the DeepSeek application with the Deep Reasoning (R1) feature. The system generated new equations, mathematical functions, and hybrid solutions. Additionally, ChatGPT was used for suggestions, recommendations, and result evaluation. These frameworks aim to provide a comprehensive solution to the Hodge Conjecture by integrating advanced tools from algebraic geometry, numerical analysis, dynamical systems, and quantum computing. The frameworks are based on: enhanced mixed Hodge structure theories to generalize results to non-Kähler manifolds; ultra-precise algebraic quantum algorithms (such as AQA v3.0) with topological error correction, achieving precision up to ; closed-form mathematical proofs using Galois representations, the extended Lefschetz theory, and Grothendieck's representability theorems; and theoretical physics applications, such as connecting Hodge classes to superstring states and Higgs fields in the Standard Model. Together, these frameworks offer a rigorous solution to the conjecture, bridging pure mathematics with modern physics through revolutionary quantum tools.