Gaussian Completely Monotone Conjecture

Along the heat flow, do the successive time derivatives of the entropy of $X + \sqrt{t}\,Z$ alternate in sign, as conjectured by Cheng and Geng? An explicit measure on $\mathbb{R}$ has a fifth derivative with the forbidden sign.

Result

Disproved(see note)

Status

Resolved

AI contribution

AI-discovered

Method

Construction

Field

Entropy & heat flow

Posed by

Fan Cheng & Yanlin Geng

Year posed

2015

Years open

11y

Solved

2026-05-12

Model

GPT-5.5 Pro

Vendor

OpenAI

Collaborators

Yuzhou Gu, Mark Sellke

Verification

Unreviewed

Publication

Preprint

Significance

15 / 100*

Disclosed cost

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Wikipedia

No dedicated article