Publication v5

Record details

Coverage & review

Coverage of this curation

Original question, distinct results, proof provenance, selected history and an explanatory schematic.

Formal proofs: No formal proof project for these explicit Gaussian identities was located in the selected primary sources. Independent mathematical assessment is pending.

AI-assisted work: Long is the human author. ChatGPT 5.6 Sol Pro and Claude Fable 5 receive distinct, self-reported witness-discovery credits; Derksen, van den Essen and Zhao supplied the original question and reduction.

Search scope & review

Selected primary papers, exact formal declarations, project provenance and official descriptions checked on 13 October 2026.

Checked Oct 13, 2026 · independent review pending.

No linked formal proof of the moment identities was found in the selected sources.
The two-variable case and comprehensive later literature require continued review.

General status observations

Small Counterexamples to the Gaussian Moments Conjecture ↗

Universal conjecture refuted by an explicit polynomial · observed Oct 13, 2026

Source status dated Jul 20, 2026 · observed Oct 13, 2026

Three independent real Gaussian coordinates suffice; the construction extends to every higher dimension.

Source identities & rights

The Gaussian Moments Conjecture and the Jacobian Conjecture ↗

Harm Derksen, Arno van den Essen, Wenhua Zhao · metadata-link · Original source license and document rights apply.

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms

1 cited entry · exact source identity

Version: gaussian-moments:source:original:v1
Revision: 2015-06-17
Content SHA-256: 182136b363b272c1d1221aa2ca5c6603fd52942efe423463f46997f473503660
Source update: Unavailable
Observed: 2026-10-13
Check cadence: 90 days

Conjecture 1.1, Theorem 1.6 and Proposition 4.2 ↗gaussian-moments:entry:original:v1

Small Counterexamples to the Gaussian Moments Conjecture ↗

Christopher D. Long · metadata-link · Original source license and document rights apply.

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms

1 cited entry · exact source identity

Version: gaussian-moments:source:long:v1
Revision: 2026-07-20
Content SHA-256: d568de4b8568f627548eaacb7c65b1b852a52f1017aa5402150250e3d5cf6738
Source update: Unavailable
Observed: 2026-10-13
Check cadence: 90 days

Proposition 4.1, Theorem 5.1, Corollary 5.2, Section 7 and AI disclosure ↗gaussian-moments:entry:long:v1

Publication history

Problem ID: problem-gaussian-moments
Publication checksum: c0adfa54375375f9763ec1e793d2fadc879a987020ad68562416a24f1b2e2b89
Published: 2026-10-14T09:35:12.516081+00:00
Publication reason: Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

Version 1 · Oct 13, 2026
Source-linked pilot import; independent mathematical review remains pending.
Version 2 · Oct 13, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Version 3 · Oct 13, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Version 4 · Oct 13, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Version 5 · Oct 14, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Version 6 · Oct 21, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

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