What was already known
The conjecture was known in restricted dimensions, exponent ranges or covariance classes; the general positive-exponent case remained open.
AI involvement
Greaves credits ChatGPT 5.6 Sol with the early complete proof. Greaves formalized it with Codex; Ouimet rewrote the exposition and added separate equality results.
A specific, complete early proof of the central inequality is expressly attributed to ChatGPT 5.6 Sol; Greaves supplied the prompt and the later authors reworked it.
Importance
Proves the general strong Gaussian product inequality.
Limitations
The reported Lean theorem checks the main inequality, not Ouimet’s later equality characterization. The published record reports the Lean build; an independent replay is not documented.
Technical verification
The authors report a Lean formalization of the early inequality proof, and its repository names a complete main theorem and build. This covers the positive-exponent inequality, not Ouimet’s later equality characterization; the build was not independently replayed here.
Independent checking
complete Lean main theorem GaussianProduct.gaussian_product_inequality and project build
- Checker
- Lean through Greaves’s Codex-assisted GaussianProduct project
- Scope
- positive-exponent Gaussian product inequality for centered Gaussian vectors
- Basis
- Reported by the linked checker
Human understanding
Ouimet reworked the proof and the paper explains the branch-averaging kernel inequality and integral recovery of moments; the equality analysis is credited to him separately.
Correction and publication history
The assessed result is the main positive-exponent inequality; equality conditions retain separate credit.
Read this published revision