∑math20

Topology · Result 309

The Kervaire invariant problem at the prime three

1 paper

Resolves the odd-primary Kervaire invariant problem at the prime three: exactly the standard classes with indices 0, 2, and 3 survive in the mod-three Adams spectral sequence, in stems 10, 106, and 322. Each surviving detection coset contains an element of exact additive order three.

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▶Introduction: the problem and why it mattersin preparation
▶The presented solutionin preparation

Papers 1

First page of The Kervaire invariant problem at the prime three

The Kervaire invariant problem at the prime three

OpenAI · September 24, 2026

We solve the Kervaire invariant problem at the prime three for the standard Kervaire classes in the mod-three Adams spectral sequence. These classes survive precisely at indices 0, 2, and 3, and each surviving detection coset contains an element of additive order three. In particular, there is an order-three Kervaire element in stem 322.

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@misc{OAI:The-Kervaire-Invariant-Problem-at-the-Prime-Three-September-24-2026,
  author = {{OpenAI}},
  title = {{The Kervaire invariant problem at the prime three}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/The-Kervaire-Invariant-Problem-at-the-Prime-Three-September-24-2026/paper.pdf}{OAI:The-Kervaire-Invariant-Problem-at-the-Prime-Three-September-24-2026}},
  year = {2026}
}

Formal verification

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