In the FrontierMath, a globally recognized top-tier AI mathematical benchmarking test, a significant mathematical conundrum concerning the 'emptiness of the core' in approval committee elections, a problem initially proposed in 2017, has been successfully resolved through a collaborative effort between GPT-6 Astra and three human researchers. The original challenge was to identify a counterexample where the 'core' is devoid of any elements. However, GPT-6 Astra demonstrated that no such counterexample can exist, thereby establishing that an absolutely equitable committee is achievable under all circumstances. Furthermore, it developed a novel voting rule grounded in 'harmonic entropy' and presented a polynomial-time algorithm to verify that locally optimal solutions align with the 'core' requirements. In this synergy between humans and machines, humans offered guidance and logical scrutiny, while AI supplied extensive knowledge repositories, computational capabilities, and innovative insights. This achievement marks the inaugural instance of AI resolving a major mathematical problem at the progress level, heralding the transformation of large models from mere 'problem-solving entities' to 'pioneers of mathematical principles'. It also spurred Epoch AI to introduce a new 'Human + AI' status designation on the leaderboard.