Online Spencer Vector-Balancing Question
Can online vector balancing in the Spencer setting achieve the optimal order of prefix discrepancy with an efficient algorithm?
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Discrepancy theory
- Posed by
- —
- Year posed
- 2023
- Years open
- 3y
- Solved
- 2026-07-18
- Model
- ChatGPT-5.6 Pro
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The compactly supported Metropolis fixed-point walk at the heart of the algorithm was proposed by ChatGPT-5.6 Pro; the authors manually checked and rewrote the proof. The result also extends the offline Beck-Fiala bound to sparsity .
Verification
Author-rewritten and checked arXiv preprint. Not yet peer-reviewed.
Source
arXiv:2607.14238 - Online Beck-Fiala down to logarithmic sparsity