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the claim

The Jacobian conjecture states that a polynomial map with a nonzero constant Jacobian determinant has a polynomial inverse.

the verdict
SUPPORTED
the evidence backs this
Recorded sources
8 sources for · 0 against

Counts group repeated records of the same source within each side. They do not measure evidence strength or source independence.

Is it true that the Jacobian conjecture states that a polynomial map with a nonzero constant Jacobian determinant has a polynomial inverse?

Yes. Multiple reference and peer-reviewed sources state the Jacobian conjecture as the proposition that a polynomial map with a nonzero constant Jacobian determinant has a polynomial inverse. The claim accurately reports the conjecture's content.

Verdict: SUPPORTED · 8 sources for, 0 against · Last checked

The private library was unavailable for some searches in this check. Missing library results are not evidence against the claim.

Evidence for · 8
Jacobian matrix and determinant
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Jacobian matrix and determinant. (n.d.). en.wikipedia.org. https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant

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More for · 7
Determination of Inverse Maps Related to the Jacobian Conjecture
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Determination of Inverse Maps Related to the Jacobian Conjecture. (n.d.). cir.nii.ac.jp. https://doi.org/10.11346/cstj.2017.138_11

Formal inverse expansion and the Jacobian conjecture
1987
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Formal inverse expansion and the Jacobian conjecture. (1987). doi.org. https://doi.org/10.1016/0022-4049(87)90109-5

Structured Resolution Framework for the Jacobian Conjecture via Druzkowski Reduction and Operator Descent
2025
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Structured Resolution Framework for the Jacobian Conjecture via Druzkowski Reduction and Operator Descent. (2025). doi.org. https://doi.org/10.5281/zenodo.15070006

A Hierarchical Algebraic Framework for Analyzing Polynomial Automorphisms and the Jacobian Conjecture
2025
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liu, d. & liu, s. (2025). A Hierarchical Algebraic Framework for Analyzing Polynomial Automorphisms and the Jacobian Conjecture. doi.org. https://doi.org/10.33774/coe-2025-js9lx

A Complete Proof of the Jacobian Conjecture via Hierarchical Methods
2025
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A Complete Proof of the Jacobian Conjecture via Hierarchical Methods. (2025). doi.org. https://doi.org/10.33774/coe-2025-9nt0j

Homological structures and computational verification of a proposed three-dimensional counterexample to the jacobian conjecture
2026
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Sergio, L. R. (2026). Homological structures and computational verification of a proposed three-dimensional counterexample to the jacobian conjecture. zenodo.org. https://doi.org/10.5281/zenodo.21538118

The Jacobian Conjecture, a Reduction of the Degree to the Quadratic Case
2016
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The Jacobian Conjecture, a Reduction of the Degree to the Quadratic Case. (2016). hal.science. https://doi.org/10.1007/s00023-016-0490-9

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