What was already known
Ball minimality was known for V≤1, and nonexistence had been proved for V≥7.5; the intervening range remained open.
AI involvement
Otis Chodosh and Matilde Gianocca say ChatGPT 5.6 Pro obtained the mathematical results without significant assistance. They checked, reworked and explained the proof.
Primary disclosure says the model obtained the results without significant author assistance and retained the fundamental strategy.
Importance
Gives the sharp fixed-volume minimizer picture for the classical three-dimensional model.
Limitations
The result concerns this perimeter-plus-Coulomb model. The authors’ full proof check is reported by them; no independent complete audit is documented.
Technical verification
The authors explicitly say they checked and reworked the full proof; this is a reported author check, not independent reproduction.
Independent checking
author check and reworking of the model proof
- Checker
- Otis Chodosh and Matilde Gianocca
- Scope
- Theorem 1.1 fixed-volume sharp threshold and Corollary 1.2
- Basis
- Reported by the linked checker
Human understanding
The authors explain the 3D capacitary/Gauss–Bonnet estimate and the one/two-ball comparison proof.
Correction and publication history
The threshold and nonexistence statements belong to one liquid-drop result with a specified energy model.
Read this published revision