OpenAI · 309-01 · 2026-09-24 · Topology
The Kervaire invariant problem at the prime three
preprints/The-Kervaire-Invariant-Problem-at-the-Prime-Three-September-24-2026
Family 309. The Kervaire invariant problem at the prime three.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Resolves the odd-primary Kervaire invariant problem at the prime three: exactly the standard classes with indices , , and survive in the mod-three Adams spectral sequence, in stems , , and . Each surviving detection coset contains an element of exact additive order three.
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.
Preprint source and Lean scope
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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.