Tencent says Hyra found a sharp construction for a 57-year sum-difference bound
The Hunyuan group says its research agent and Hy3 model produced an explicit family that reaches the known exponent upper bound of 2.
By Ryan Merket · Published
Primary source: X
Why it matters
A verified proof would show an AI research agent converting computational search into a general mathematical construction. It would also give Tencent a credible flagship application for Hyra beyond paper retrieval and routine analysis.
Tencent Hy said on July 30th that its Hyra research agent and Hy3 model found an explicit construction that makes a 1969 upper bound sharp in a long-running additive combinatorics problem.
The problem asks how much faster the sumset of a finite set of integers can grow than its difference set. For a finite, nonempty set $A$, the sumset $A+A$ contains every value $a+b$ for $a,b$ in $A$, while $A-A$ contains every difference $a-b$.
The target is the smallest universal exponent $c$ satisfying…
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