Tencent Open Sources Hy3 Model, Solving Half-Century-Old Math Problem, Full Proof Validated by Machine

According to Dynamic Beating monitoring, Tencent's quantum research AI Hyra, using its proprietary Hy3 open-source model, assisted two researchers in solving a long-standing combinatorial math problem that has been unresolved for over 50 years.

The problem is: For a set of integers, how much faster can the "sum set" grow compared to the "difference set"? The mathematical community had previously proved that the relevant index would not exceed 2, but it was unknown whether 2 was the optimal answer.

Hyra had Hy3 first search for specific sets and then attempt a general construction. Approximately 24 hours later, the AI found the core solution eventually adopted in the paper. The researchers then verified, corrected, and organized the proof, with the assistance of GPT-5.6 Sol for conversion to Lean 4 verification.

The final paper proved that this index can approach 2 indefinitely, making the upper bound of 2 the optimal solution. Although the AI did not single-handedly write the entire paper, the most crucial construction was indeed found by Hy3.