Problem detail · source-aware
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Does every globally asymptotically stable homogeneous polynomial vector field admit a homogeneous polynomial Lyapunov function? No. A planar homogeneous cubic vector field with integer coefficients is globally asymptotically stable yet admits no positive definite homogeneous polynomial with nonpositive Lie derivative, and no real-analytic Lyapunov function even locally, though it does have exponential and rational strict Lyapunov functions.
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.
The acknowledgement is direct: the authors used GPT-5.6-Sol Pro to discover the counterexample and to produce initial versions of the mathematical arguments in Sections II to IV. Codex assisted with drafting and with the Lean 4 formalization. The authors independently verified all AI-generated content.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
A Lean 4 development covering the four items of the main theorem accompanies the paper at the linked repository, following the proof architecture of the text. We have not compiled it. arXiv preprint, not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.