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Two Counterexamples in the Geometry of Numbers

Number theory · posed by J. W. S. Cassels and Chuanming Zong; Peter Sarnak, formulated by Chiu · disproved

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Statement

The paper gives counterexamples in dimensions eight and nine to two problems: the Cartesian-product problem posed by Cassels for critical determinants and formulated by Zong for lattice packings, and a question raised by Sarnak, formulated as a conjecture by Chiu, on whether height among unit-volume flat tori is minimized by a lattice maximizing its shortest nonzero vector.

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

  1. construction · #1

    ChatGPT 5 + Codex, with Nihar Gargava

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

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    — the result was found by a model.

    The acknowledgements state the counterexamples were found using ChatGPT, and that the final paper is partly the author's own writing and partly written with the help of Codex.

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