The Kinoshita Conjecture and Kirby Problem 4.37
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Statement
Kinoshita conjectured that every embedded projective plane in is reducible. False: an irreducible embedded projective plane exists in . The construction also answers both parts of Problem 4.37 of the Kirby problem list.
Context
A named conjecture plus a numbered problem from the Kirby list, the standard catalogue of open questions in low-dimensional topology.
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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.
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