Counterexamples to the Hahn-Wilson conjecture at height two
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 \(L_{T(2)}X\simeq L_{K(2)}X\).
Cite
@misc{OAI:Counterexamples-to-the-Hahn-Wilson-conjecture-at-height-two-September-26-2026,
author = {{OpenAI}},
title = {{Counterexamples to the Hahn--Wilson conjecture at height two}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Counterexamples-to-the-Hahn-Wilson-conjecture-at-height-two-September-26-2026/paper.pdf}{OAI:Counterexamples-to-the-Hahn-Wilson-conjecture-at-height-two-September-26-2026}},
year = {2026}
}