Problem detail · source-aware
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With $N = 2^k - 1$ and $\mathrm{wt}(n)$ the binary Hamming weight, Tu and Deng conjectured that for every $1 \leq t \leq N-1$ at most $2^{k-1}$ pairs $(a,b)$ satisfy $a + b \equiv t \pmod N$ and $\mathrm{wt}(a) + \mathrm{wt}(b) < k$. Proved in full.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
"The authors thank ChatGPT 5.6 Pro for assistance with some of the mathematical work presented in this paper. The authors subsequently verified the argument and take full responsibility for the final content." No individual step is attributed, so the lower tier applies.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
The authors provide an accompanying Lean formalization described as an end-to-end machine-checked proof, including the intermediate results and the reduction to the original statement. Nobody independent has audited whether the formal statement faithfully expresses the conjecture, so this sits on the unaudited Lean rung.
Correctness: supported · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.