Ran-Teng Conjecture 20 on 4-Cycle Stochastic Matrices
Is the exact nonreal spectral region of the four-cycle family of row-stochastic nonnegative matrices determined by the Karpelevich constraint, as Ran and Teng conjectured in 2024?
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Matrix analysis
- Posed by
- Ran & Teng
- Year posed
- 2024
- Years open
- 2y
- Solved
- 2026-02-24
- Model
- ChatGPT-5.2 Thinking
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 5 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
Resolved across seven documented ChatGPT-5.2 Thinking threads in a generate-referee-repair loop; the model drove high-level proof search while human experts closed the correctness-critical steps.
Verification
Human-checked proof with explicit boundary-attainment constructions; public case-study preprint. Not yet peer-reviewed.
Source
arXiv:2602.18918 - Vibe-proving case study: spectral region characterization