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Optimal Vector Balancing for Zonotopes

Probability & statistics · posed by vector balancing literature, 2002 · solved

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Statement

For every zonotope Z⊂RdZ \subset \mathbb{R}^d and vectors v1,…,vn∈Zv_1,\ldots,v_n \in Z, there are signs with ∑ixivi∈Cd Z\sum_i x_i v_i \in C\sqrt{d}\,Z for a universal constant CC. This resolves a 2002 conjecture on vector balancing in zonotopes.

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

  1. proof attempt · #1

    Victor Reis, using GPT-5.5 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

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    ai assisted
    — a person led the work and used a model along the way.

    The acknowledgement says the model was used during development to explore proof strategies and to translate between formulations. No single step is attributed, so the lowest tier applies.

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