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An explicit three-variable polynomial map has constant determinant −2 and a fiber containing three distinct rational points.
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An explicit three-variable polynomial map has constant determinant −2 and a fiber containing three distinct rational points.
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Passage ID: jacobian-conjecture:entry:witness:v2
Source item: witness
Source record: jacobian-conjecture:source:witness:v2
Replaces passage: jacobian-conjecture:entry:witness:v1
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Problem publication v8
Source assessment
Disproved
Explicit three-variable counterexample
The all-dimensions complex Jacobian conjecture.
Observed Oct 13, 2026
Construction
Exact polynomial map and repeated fiber
Formal declaration
Lean: the three-point fiber
History
Explicit three-variable counterexample
Question
Jacobian conjecture
Further reading
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Complete formal proof reported externally
The polynomial witness is source-reported complete; OpenMath has not built it. The project also proves jacobian_det and not_injective.
Statement match: Linked by OpenMath · independent review separate · checked Oct 13, 2026
Alpoge.three_point_fiberCommit b8eec94711a9b73151929b78cbd7cb999a008590
Recorded authorship
ULAM research manuscript (no author named)
The manuscript cites Levent Alpöge’s announcement, credits Akhil Mathew for asking the question and Fable for the work leading to the example. No named author is printed on this verification manuscript; these discovery credits are not its bibliographic authorship.
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A Counterexample to the Jacobian Conjecture
An explicit Jacobian counterexample
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