Proved
Conditional mathematical implication in the cited source ↗
Observed Oct 13, 2026
Theorem · version 1
The global implication to polynomial inversion
Statement
If the Gaussian Moments Conjecture holds in every positive dimension, then every polynomial map F: ℂⁿ → ℂⁿ in every n ≥ 1 with nonzero constant Jacobian determinant has a polynomial inverse.
Assumptions
- The premise is the all-dimensional Gaussian conjecture, not one fixed dimension.
- Complex polynomial maps with nonzero constant Jacobian determinant.
Scope
This is a one-way implication. Refuting the Gaussian premise does not logically refute the Jacobian conclusion; the small Gaussian witnesses are not themselves Keller maps.
Evidence
Source reports
Connections
In this problem · publication v3 · Selected context
Gaussian moments conjecture →
Conditional implication · Proved
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v6
Gaussian moments conjecture →
Conditional implication · Proved
Relationship not independently reviewed. This concerns its use in this problem.
Sources
The Gaussian Moments Conjecture and the Jacobian Conjecture →
- Conjecture 1.1, Theorem 1.6 and Proposition 4.2 → · Original passage ↗
Recorded wording
Introduces Gaussian moment vanishing, proves the one-variable case and gives a global implication to the Jacobian conjecture.
paraphrase · OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
Harm Derksen · Arno van den Essen · Wenhua Zhao · Preprint · Publication date Jun 17, 2015
Revision & attribution
Source revision: 2015-06-17. Observed Oct 13, 2026.
No specific AI contribution is attributed by this source record.
History
Statement versions
Statement versions and problem publication versions are separate. A new publication can update context or sources while retaining the same statement.
Assessment history · 1
Assessments retained in these publication records. Earlier statement versions retain their own source histories.
Proved
Conditional mathematical implication in the cited source ↗
Observed Oct 13, 2026 · Source passage →
Record details
- Claim ID
- claim-gaussian-moments-consequence
- Statement version
- 1
- SHA-256
- 0ec587633bd34140ae3341669c49671a4ad8112afb0c5bef4d259afd6763dc7f