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Online Spencer Vector-Balancing Question

Theoretical computer science · posed by 2023 · solved

1 comment

Statement

Can online vector balancing in the Spencer setting achieve the optimal order of prefix discrepancy with an efficient algorithm?

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    ChatGPT-5.6 Pro

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    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 d≥log⁡(T)1+o(1)d \ge \log(T)^{1+o(1)}.

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