Counterexamples to finite generation at chromatic height two

What OpenAI claims

Refutes the Hahn–Wilson conjecture at chromatic height two. For every sufficiently large prime p, constructs a connective p-complete spectrum of exact fp-type two that cannot be built from completed BP⟨2⟩ by finitely many sums, shifts, cones and retracts. The examples nevertheless satisfy the finite and telescopic localization comparisons.

Paper

1. Counterexamples to the Hahn-Wilson conjecture at height two

   26 September 2026 · Preprint, not peer reviewed · PDF

   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 BP⟨2⟩_p^∧. The same spectrum satisfies both localization comparisons L₂^fX ≃ L₂X and L_T(2)X ≃ L_K(2)X.

Status

Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.