Problem detail · source-aware
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Given online vectors $v_t \in \mathbb{R}^d$ with $\|v_t\|_2 \le 1$, can signs $\varepsilon_t \in \{-1, 1\}$ be chosen in $O(dT)$ total time so that every prefix has $\ell_\infty$ discrepancy $O(\sqrt{\log T})$ with high probability? The previous optimal algorithm ran in time exponential in $T$ and $d$.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
The algorithm and main proof were discovered in a GPT-5.5 Pro Extended conversation prompted by the author; every prefix sum is written as a sum of three coupled Gaussian vectors.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Author-checked arXiv preprint. Not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.