Source authenticated

The Tu-Deng Conjecture

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.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Jul 30, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: preprint. AI contribution: ai-assisted. Imported under CC BY 4.0.

Canonical aliases: The Tu-Deng Conjecture · Tu-Deng conjecture

Confidence: Not scored

Registry verification: lean checked · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Renzhang Liu
human · human collaborator

Hengyi Luo
human · human collaborator

Tianyuan Xie
human · human collaborator

ChatGPT 5.6 Pro
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: The Tu-Deng Conjecture

specialist registry · passed

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.

Source ↗

The Tu-Deng Conjecture

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Lean formalization of the proof

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Artifacts and verifiers

Lean formalization of the proof

lean artifact · pending