Solving the Hodge Conjecture through Collaborative Intelligence.pdf

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-Khler manifolds; ultraprecise algebraic quantum algorithms (such as AQA v3.0) with topological