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Conjecture on k-Antichains in the Unit Cube

Combinatorics · posed by conjecture in the antichain-measure literature · solved

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Statement

A subset AA of the pointwise-ordered cube [0,1]n[0,1]^n is a kk-antichain when it meets every chain in at most kk points. The conjecture concerns the largest possible (n−1)(n-1)-dimensional Hausdorff measure of such a set; it is settled here, following work of Janzer.

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

  1. construction · #1

    John M. Campbell, 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 co developed
    — a person and a model developed the result together.

    The paper states that the construction carrying the proof is largely based on the author's extensive interactions with GPT-5.5 Pro.

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