What was already known
Feige conjectured the unit-slack e⁻¹ guarantee. The cited calibration and centroid inequalities existed, but their combination into this sharp range was new in the assessed paper.
AI involvement
The paper credits ChatGPT 5.6 Pro with the initial proof combining the calibration and centroid inequalities. The six human authors checked, revised and explained the argument.
The source expressly credits the model with the initial proof; humans checked and reworked the retained argument.
Importance
Settles the longstanding unit-slack conjecture and proves a sharp finite-n bound throughout δ≥1.
Limitations
The 0<δ<1 estimate is not claimed sharp. The six authors report checking and rewriting the model’s proof; a later independent unit-slack proof does not check this paper’s full δ range.
Technical verification
The authors explicitly report checking the initial proof and rewriting the final argument; this is a source-reported author check.
Independent checking
Authors report checking, revising and rewriting the model proof.
- Checker
- Fu, Han, Wang, Yan, Zhang and Zhou
- Scope
- Theorem 1.1 across the stated δ ranges
- Basis
- Reported by the linked checker
Human understanding
The authors explain the Dirichlet-calibration and convex-geometric proof route in §§1.2–2.
Correction and publication history
The authors checked and rewrote the model-found proof across the stated δ ranges.
Read this published revision