Benefit Ledger · provisional · Mathematics
On 30 July 2026 Renzhang Liu, Hengyi Luo, and Tianyuan Xie posted a complete proof of the Tu–Deng combinatorial conjecture on Hamming weights modulo 2^k−1 (arXiv:2608.05187). A compiled dataset records ChatGPT 5.6 Pro assistance; the arXiv abstract does not name a model or split of labor.
Current score
+0.13
A complete proof of a named coding-combinatorics conjecture is notable (tier 2). AI share is unspecified in the abstract (0.35). Evidence is a preprint (0.35). Realization is a public complete argument (0.50).
The Tu–Deng conjecture bounds the number of pairs (a,b) with a+b ≡ t (mod 2^k−1) and wt(a)+wt(b)<k. The preprint gives a complete argument via cyclic-carry enumerators. Because the public abstract does not specify the AI role, attribution is conservative and the ChatGPT 5.6 Pro identification is treated as reported, not as a named-release certainty. Partial Lean formalization is reported in secondary problem indexes.
Reported as an assistant on the Tu–Deng proof; the arXiv abstract does not name the model or the split of labor.
Secondary compilation credits ChatGPT 5.6 Pro; primary abstract is silent, so attribution stays modest and identity is the 5.6 Pro SKU rather than Sol.
Attribution 0.3500 · Credit share 100% · OpenAI
Liu, Luo, and Xie posted a complete proof of the Tu–Deng conjecture.
outcome · supported
GPT-5.6 Pro was the primary author of the proof.
attribution · disputed
primary sources
arXiv · preprint · 30 Jul 2026
Secondary domains: Computer Science
13 Sep 2026 · 0.00 → 0.13
Imported events under methodology 0.1.
