Ran-Teng Conjecture 20 on 4-Cycle Stochastic Matrices

Precise statement

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?

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.

What AI did

ChatGPT-5.2 Thinking

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.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Human-checked proof with explicit boundary-attainment constructions; public case-study preprint. Not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-02-24

   arXiv:2602.18918 - Vibe-proving case study: spectral region characterization

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.