{"id":"openai-math/Counterexamples-to-the-Hahn-Wilson-conjecture-at-height-two","pdf":"https://github.com/openai/math/blob/main/preprints/Counterexamples-to-the-Hahn-Wilson-conjecture-at-height-two-September-26-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Counterexamples-to-the-Hahn-Wilson-conjecture-at-height-two-September-26-2026","tags":["algebraic-topology","chromatic-homotopy","spectra"],"score":0,"title":"Counterexamples to the Hahn-Wilson conjecture at height two","domain":"Topology","family":"319","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GT","summary":"We disprove the Hahn–Wilson conjecture at height two. For every sufficiently large prime p , we construct a connective p -complete spectrum X of exact fp-type two outside the ordinary thick subcategory generated by the specified standard form of $`\\mathrm{BP}\\langle2\\rangle_p^\\wedge`$. The same spectrum satisfies both localization comparisons $`L_2^fX\\simeq L_2X`$ and $`L_{T(2)}X\\simeq L_{K(2)}X`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-26","reactions":{},"formalized":false,"family_title":"Counterexamples to finite generation at chromatic height two"}