AI research agent cracks Komlós conjecture, proves 3√(2πt) Beck-Fiala bound
basedjensen · x · 2026-09-12
A new arXiv paper, Vector Balancing via Directional Total Variation by Shengtao Guo, Ethan X. Fang and Junwei Lu, reports a proof discovered autonomously by the Odin Automatic AI Research Agent:
- Komlós signing problem: any finite family of real vectors with Euclidean norm ≤ 1 admits a signed sum with ℓ∞-norm below 3√(2π), independent of dimension and family size.
- Beck-Fiala conjecture: any set system where each element belongs to at most t sets admits a two-coloring with imbalance below 3√(2πt), matching the conjectured square-root dependence.
The proof uses directional total variation bounds and the Banaszczyk transform. If it survives scrutiny, this would be a landmark case of an AI agent making a genuine mathematical discovery.
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