The Kervaire invariant problem at the prime three at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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The Kervaire invariant problem at the prime three

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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The Kervaire invariant problem at the prime three. 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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LEVEL 1 The Kervaire invariant problem at the prime three

released 2026-09-24 | 8 theorems · 47 lemmas · 70 proofs · 41,084 words | PLAY LEVEL 1 » (pdf)

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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