OpenAI reports height-two Hahn–Wilson counterexamples

For every sufficiently large prime p, a connective p-complete spectrum of exact fp-type two lies outside the ordinary thick subcategory generated by the specified standard BP⟨2⟩ p-completion, even though its finite and telescopic localization comparisons hold.

Sources for this record

What was already known

The Hahn–Wilson conjecture predicted that its stated localization and finite-type hypotheses would force ordinary thick generation by standard truncated Brown–Peterson spectra. The height-two case remained open.

AI involvement AI-led

OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.

OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.

Importance Notable

Disproves that universal thick-generation conjecture already at height two for sufficiently large primes.

Limitations

The assertion fixes a standard form of BP⟨2⟩ and ordinary thick closure; it does not address all primes or broader localizing tensor ideals.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.

Correction and publication history

2026-10-18 · publication

Primary manuscript, attribution, and prior-work review for non-notifying local inclusion; technical verification remains Reported.

Read this published revision