Selected research history · publication v1

Gaussian moments conjecture

Follow the ideas, results and limitations over time. This is a selected history, not a complete literature survey or a measure of how close the problem is to being solved.

Current state & remaining question →

Viewing the timeline from pinned publication v1.

2 selected milestones · Source coverage checked 2026-10-13 · Historical annotation and mathematical review remain separate.

Jun 17, 2015 preprint
Foundation
Gaussian vanishing and polynomial inversion
Derksen, van den Essen and Zhao formulate the conjecture and prove its one-variable case.
Scope & review: Their implication to the Jacobian conjecture is global, rather than an equivalence in matching dimensions.
Statements & sources
- Eventual mixed-moment vanishing in every dimension →
- The one-variable case →
- The Gaussian Moments Conjecture and the Jacobian Conjecture ↗Conjecture 1.1, Theorem 1.6 and Proposition 4.2
Historical annotation review: pending. The date refers to the preprint, with the precision supported by the source.
Jul 20, 2026 preprint
Related result
Two explicit polynomial witnesses
Long publishes the cubic four-variable and quartic three-variable constructions.
Scope & review: Publication date records the source; the paper describes discovery order without providing separate calendar dates.
Statements & sources
- A quartic witness in three real variables →
- A cubic witness in four real variables →
- Small Counterexamples to the Gaussian Moments Conjecture ↗Proposition 4.1, Theorem 5.1, Corollary 5.2, Section 7 and AI disclosure
Historical annotation review: pending. The date refers to the preprint, with the precision supported by the source.

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Gaussian vanishing and polynomial inversion

Two explicit polynomial witnesses