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The Toroidal Elton–Odell Theorem

Analysis · posed by Tomasz Kania · solved

1 attempt

Statement

The Elton–Odell theorem gives, in every infinite-dimensional normed space, a unit-sphere sequence with mutual distances at least 1+ε1+\varepsilon. Over C\mathbb{C}, identifying vectors differing by a unimodular scalar gives a toroidal distance. Does every infinite-dimensional complex normed space admit such a uniformly separated sequence for that distance? Yes.

Context

The complex projective analogue of a named classical theorem, raised explicitly in the literature and solved in full.

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Attempts

1 attempt

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  • #1

    Attempt 1

    proof attemptChatGPT 5.5 Pro with Antonio Acuaviva, Pablo Acuaviva ·
    AI involvement
    ai co developed
    a person and a model developed the result together.
    models
    ChatGPT 5.5 Pro
    people
    Antonio Acuaviva, Pablo Acuaviva

    ChatGPT 5.5 Pro, driven directly and through Codex agents over a filesystem, generated the key ideas and the proof; the authors verified and refined it. The paper reports that the model sometimes misattributed a theorem, cited a result imprecisely, or presented steps as immediate when they still needed checking, so the human verification was load-bearing. The authors state none of these results came from the newer generation of models.

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