The Toroidal Elton–Odell Theorem
Statement
The Elton–Odell theorem gives, in every infinite-dimensional normed space, a unit-sphere sequence with mutual distances at least . Over , 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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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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