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Algebraic analysis of the three-variable counterexample, including its non-injectivity; the two-dimensional complex case remains open.
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Algebraic analysis of the three-variable counterexample, including its non-injectivity; the two-dimensional complex case remains open.
Passage ID: jacobian-conjecture:entry:analysis:v1
Source item: analysis
Source record: jacobian-conjecture:source:analysis:v1
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Problem publication v1
Source assessment
Open
Dimension two remains open
Complex dimension two.
Observed Oct 13, 2026
Source assessment
Proved
Algebraic witness analyzed
The explicit non-injective map.
Observed Oct 13, 2026
Formal declaration
Lean: the three-point fiber
History
Separate algebraic analysis
History
Keller’s global invertibility question
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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
Shuhong Gao
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Counterexamples to the Jacobian conjecture in dimensions greater than two
On a counterexample to the Jacobian conjecture
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