FPRAS for mixed volumes, ideas from GPT-6 Astra
Awaiting review
Importance: major (4 of 5)Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Preprint only
- Importance
- Major (4 of 5)
- Last verified
- 3 November 2026
Your AI and this story
- GPT-6 Astra187 days after its cutoff
- Claude Opus 5.5126 days after its cutoff
- Gemini 4 Argon217 days after its cutoff
- Grok 4.7156 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 126 days before it.
Key facts
- Claim: first FPRAS for mixed volumes of arbitrary compact convex sets given by weak membership oracles; ‘This disproves a longstanding conjecture of Gurvits [Gur09a, Section 4, item 2]’
- AI disclosure (verbatim): ‘The main ideas were generated entirely by GPT 6 Astra. The purpose of this paper is to provide a human-written exposition of the algorithm.’
- Running time: GPT-6 Astra estimated about n^900 ε^-220 · poly(L); the authors say they have not verified it and ‘do not claim it as a proved bound’
- Verification status: unrefereed preprint, rewritten and checked by the authors; no formalization
What happened
Chen and Liu posted an algorithm that approximates mixed volumes to any relative accuracy in randomized polynomial time. They credit the main ideas entirely to GPT-6 Astra and present the paper as their human-written exposition. The polynomial is very large (an unverified model estimate puts it near n^900).
Why it matters
Mixed volumes generalize permanents and volumes; Gurvits had conjectured that no such scheme exists. The result is theoretical, and refereeing has not started.
What is disputed or not yet verified
| Verification | Preprint, author-checked |
|---|
Sources
1 source from 1 site. Numbers match the chips in the text.
1 source: 1 primary
Primary
- arXiv 2611.01368: An FPRAS for Mixed Volumes (Chen, Liu)arxiv.org, paper
Changes
- Filed