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      "statement": "# Hill, Hopkins and Ravenel: high-dimensional Kervaire-invariant-one nonexistence\n\nAn equivariant-bordism construction, detection theorem, 256-fold periodicity and a homotopy gap exclude Kervaire-invariant-one elements in the higher indexed dimensions. Combined with Browder's earlier restriction, the associated framed-manifold dimensions are limited to 2, 6, 14, 30, 62 and possibly 126 in this work.\n\n## Scientific scope\n\nThe result does not settle dimension126; that is a boundary of these sources, not a claim that the case remains open today. Existing low-dimensional constructions and Browder's dimensional restriction are inherited.\n\n## Reading status\n\nThis is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.\n\n## People and systems\n\nMichael A. Hill; Michael J. Hopkins; Douglas C. Ravenel\n\nSource-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.\n\n\n\n## Original sources\n\n- [On the non-existence of elements of Kervaire invariant one](https://arxiv.org/abs/0908.3724v1)\n- [On the non-existence of elements of Kervaire invariant one](https://arxiv.org/abs/0908.3724v4)\n",
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      "title": "Hill, Hopkins and Ravenel: high-dimensional Kervaire-invariant-one nonexistence"
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    "what_changed": "An equivariant-bordism construction, detection theorem, 256-fold periodicity and a homotopy gap exclude Kervaire-invariant-one elements in the higher indexed dimensions. Combined with Browder's earlier restriction, the associated framed-manifold dimensions are limited to 2, 6, 14, 30, 62 and possibly 126 in this work.",
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