Petty’s conjecture in dimension 5: proof by Tencent’s hyprover agent
Awaiting review
Importance: major (4 of 5)The takeaway
Petty conjectured that every n-dimensional normed space contains n + 1 points at equal distances. Petty proved dimension 3 and Makeev dimension 4. On 29 Oct Kaiwen Yang (Tongji University and Tencent Hunyuan) posted a proof for dimension 5. Its AI declaration says the proof ‘was generated by Tencent Hunyuan’s AI agent hyprover on September 29, 2026’, and that the author organised, verified and rewrote it. The paper prints the full prompt, which points the agent to Lu–Yang’s solution of Banach’s isometric conjecture. Few research results in our dataset credit a Chinese lab’s agent. It is a preprint, not refereed.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Preprint only
- Importance
- Major (4 of 5)
- Last verified
- 30 October 2026
Your AI and this story
- GPT-6 Astra182 days after its cutoff
- Claude Opus 5.5121 days after its cutoff
- Gemini 4 Argon212 days after its cutoff
- Grok 4.7151 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 121 days before it.
Key facts
- Claim (abstract): ‘Petty conjectured that every n-dimensional real normed space contains n+1 equidistant points. The conjecture was proved in dimensions three and four by Petty and Makeev, respectively. We prove the five-dimensional case.’
- AI declaration (verbatim): ‘The proof was generated by Tencent Hunyuan’s AI agent hyprover on September 29, 2026. The author organized, verified, and rewrote the proof. The prompt was written by the author and is reproduced in Appendix A.’
- The prompt (Appendix A) asks the agent to ‘Prove that every five-dimensional real normed vector space contains six equilateral points’, hints at ‘an appropriate differential-topological reformulation’ and to ‘consult Lu–Yang’s A Solution to Banach’s Isometric Conjecture for methodological inspiration, not a ready-made argument’, and demands that the agent ‘Distinguish proved statements, conjectures, failed approaches, and unresolved gaps. Never replace a missing argument with a claim of verification’
- Author: Kaiwen Yang, with two affiliations, Tongji University and Tencent Hunyuan; a Kaiwen Yang co-authored the Lu–Yang solution of Banach’s isometric conjecture in August (arXiv 2608.13536), which used ChatGPT 5.5/5.6 Pro
- No public description of ‘hyprover’ found on 30 Oct (no Tencent blog, model card or GitHub repository); we know it only from this paper
- Verification status: preprint, not refereed, no formal proof; no reaction found on HN on 30 Oct
What happened
In a normed space, distances are measured by an arbitrary norm instead of the Euclidean one. Petty asked whether such a space of dimension n always has n + 1 points that are all at the same distance from each other, as the vertices of a regular simplex are in ordinary space. It was proved for dimensions 3 and 4.
Kaiwen Yang, of Tongji University and Tencent Hunyuan, posted a proof for dimension 5 on 29 Oct. The paper says Tencent’s AI agent hyprover produced the proof a month earlier from a prompt the author wrote and printed in full, and that the author verified and rewrote it.
Why it matters
Most AI-maths results so far name OpenAI, Anthropic or Google models. This one names a Tencent agent that has no public documentation yet, which suggests Chinese labs run similar research agents. The prompt is published, which is rare. The result itself awaits checking.
What is disputed or not yet verified
| Verification | Preprint; not refereed |
|---|
Sources
1 source from 1 site. Numbers match the chips in the text.
1 source: 1 primary
Primary
Changes
- Filed (science agent; arXiv abstract and PDF read, AI declaration and prompt quoted)