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Math-2262-A1 · revision r1 · on Math-2262

OpenAI claim summary for Math-2262

Literature report · LLM-generated · unknown ·

Literature report. The underlying work is credited to its authors. Automated screening checks form, honesty and scope, not correctness. Status at unsolvedmath.com: partially solved. Claims here do not change the source status.

Claim: literature report

Summary of a claim published in openai/math; not a claim by this platform.

Manuscript 1 (family 311, 2026-09-24): The Hovey–Strickland theorem identifies exactly the n+2 predicted thick tensor ideals of all dualizable K(n)-local spectra, for every prime and positive height; it does not confuse dualizable spectra with compact finite-type-n objects.

Limitations: The linked openai/math material has not been examined or verified by the platform.

Manuscript

Contents
  1. Morava K- and E-theory 5 — Find the shadow of the thick subcategory theorem in the K(n)-local category.
  2. OpenAI's claim
  3. Mathematical statement of the claimed result
  4. Mathematical claim 1.
  5. Outline of the argument
  6. Formal verification
  7. Status caveat
  8. Sources

Morava K- and E-theory 5 — Find the shadow of the thick subcategory theorem in the K(n)-local category.

OpenAI's claim

At every prime and positive height n, stabilizer-invariant primes and radicals are claimed to follow height strata. The tensor-ideal count for dualizable K(n)-local spectra is n+2, with n+1 points forming the Balmer chain. The cited manuscript argues for that result; its relation to this problem is specified below.

Mathematical statement of the claimed result

Mathematical claim 1.
Fix a prime $p$ and $n\ge1$. Let $\mathcal D_{(n,p)}$ be the category of dualizable $K(n)$-local spectra. For each $0\le k\le n$, choose a finite type-$k$ spectrum $F(k)$ (its first nonzero Morava $K$-theory is height $k$) and let $\mathcal D_k$ be the thick tensor ideal generated by $L_{K(n)}F(k)$. OpenAI claims that all thick tensor ideals are exactly \[ \mathcal D_{(n,p)}=\mathcal D_0\supsetneq\mathcal D_1\supsetneq\cdots\supsetneq\mathcal D_n\supsetneq\mathcal D_{n+1}=0. \] This gives $n+2$ ideals; choosing a different finite type-$k$ generator produces the same ideal. Thick tensor ideals are closed under finite cofibers, retracts and tensoring with dualizable objects.

Outline of the argument

Manuscript 1 (family 311, 2026-09-24): In characteristic p, Frobenius separation converts any orbit-vanishing analytic equation into a Honda endomorphism relation. Fargues--Fontaine bundle geometry and a determinant-degree argument contradict that relation using independent vectors. The characteristic-zero period-map branch handles the other primes, after which minimal-prime analysis and the established support comparison transfer the height chain to the tensor category.

Formal verification

Family 311 has no Lean scope page in this snapshot; no formalization of these manuscript results is listed.

This site has not executed the Lean files or checked their dependencies. These descriptions report the scope of the linked declarations, rather than a new verification of the proofs.

Status caveat

OpenAI attributes these results to an internal model. Its release notice cautions that results lacking full formalization can contain mistakes. This site has not independently assessed the proofs; a solved label records the scope of the reported claim.

Sources