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.
Kinoshita conjectured that every embedded projective plane in $S^4$ is reducible. False: an irreducible embedded projective plane exists in $S^4$. The construction also answers both parts of Problem 4.37 of the Kirby problem list.
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.
Deliberately bounded, and the authors draw the boundary themselves: they acknowledge using ChatGPT, Cursor and Gemini during initial exploration and computation, and state that all final computations were performed and verified by the authors without the use of AI. So the models were exploratory instruments and none of the standing mathematics rests on them.
Provider: unknown · Prompt public: unknown · Independence: unknown
The authors state they performed and verified all final computations themselves without AI. The result is an explicit construction plus a $\pi_1$ computation, so it is checkable by hand. arXiv preprint, not peer-reviewed.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.