Tencent Hy(@TencentHunyuan):For a finite set of integers (A), how much faster can (|A+A|) grow than (|A-A|)? A 1969 theorem gave an upper bound of 2 for the exponent. For more than 50 years, the best constructions barely exceeded 1.1. With help from our research agent Hyra and the Hy3 model, we found an explicit construction showing that the optimal exponent is exactly 2. A 50-year-old problem, solved. Paper: https://t.co/OU7lfH0hXR Hyra blog: https://t.co/NeQEekUSZ3 Formal proof:

2026.07.30 02:33

For a finite set of integers (A), how much faster can (|A+A|) grow than (|A-A|)? A 1969 theorem gave an upper bound of 2 for the exponent. For more than 50 years, the best constructions barely exceeded 1.1. With help from our research agent Hyra and the Hy3 model, we found an explicit construction showing that the optimal exponent is exactly 2. A 50-year-old problem, solved. Paper: Hyra blog: Formal proof: