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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.
Passage ID: jacobian-conjecture:entry:witness:v1
Source item: witness
Source record: jacobian-conjecture:source:witness:v1
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Problem publication v2
Source assessment
Disproved
Explicit three-variable counterexample
The all-dimensions complex Jacobian conjecture.
Observed Oct 13, 2026
Formal declaration
Lean: the three-point fiber
History
Explicit three-variable counterexample
Question
Jacobian conjecture
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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
Levent Alpöge
Discovery is attributed to Levent Alpöge working with Claude Fable 5; mathematical authorship and the model contribution are separate roles.
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A Counterexample to the Jacobian Conjecture
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An explicit Jacobian counterexample
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