Disproved
Universal conjecture refuted by an explicit polynomial ↗
Three independent real Gaussian coordinates suffice; the construction extends to every higher dimension.
Source dated Jul 20, 2026 · Observed Oct 13, 2026
Conjecture · version 1
Eventual mixed-moment vanishing in every dimension
Statement
For every n ≥ 1 and every , if for every m ≥ 1, then for each there is M such that for every m ≥ M.
Assumptions
- X consists of n independent standard real Gaussians.
- Positive integer powers; the threshold may depend on P and Q.
Scope
The all-dimensional assertion fails already at n = 3.
Evidence
Source reports
Connections
In this problem · publication v5 · Selected context
Gaussian moments conjecture →
Primary formulation · Disproved
Relationship not independently reviewed. This concerns its use in this problem.
In this problem · publication v6
Gaussian moments conjecture →
Primary formulation · Disproved
Relationship not independently reviewed. This concerns its use in this problem.
Sources
Small Counterexamples to the Gaussian Moments Conjecture →
- Proposition 4.1, Theorem 5.1, Corollary 5.2, Section 7 and AI disclosure → · Original passage ↗
Recorded wording
Gives a cubic four-variable witness and a quartic three-variable witness, both with zero pure moments and nonzero mixed moments of every order.
paraphrase · OpenMath supplies its own mathematical paraphrases and links; proof text is not republished.
Christopher D. Long · Preprint · Publication date Jul 20, 2026
Revision & attribution
Source revision: 2026-07-20. Observed Oct 13, 2026.
Long credits ChatGPT 5.6 Sol Pro with the four-variable polynomial, Claude Fable 5 with the three-variable reduction and checks, and ChatGPT with editing. Long is the paper’s author and responsible for its mathematical claims.
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.
Disproved
Universal conjecture refuted by an explicit polynomial ↗
Three independent real Gaussian coordinates suffice; the construction extends to every higher dimension.
Source dated Jul 20, 2026 · Observed Oct 13, 2026 · Source passage →
Record details
- Claim ID
- claim-gaussian-moments-universal
- Statement version
- 1
- SHA-256
- 998941b01f0779341f53431aa406bf86dca0d9ac27d370ad8a4e60fc75330431