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Math-2555-A1 · revision r1 · on Math-2555

OpenAI claim summary for Math-2555

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: open. 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 032, 2026-09-30): The problem selects the mathematical statement summarized here, including its stated hypotheses and parameter range. The cited theorem gives a claimed proof of that assertion in full.

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

Manuscript

Contents
  1. Hodge classes on powers of split Weil sixfolds
  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

Hodge classes on powers of split Weil sixfolds

OpenAI's claim

Algebraicity is claimed for Hodge classes on powers of split Weil sixfolds and of abelian varieties of dimension at most five carrying an imaginary-quadratic action, including special periods. The cited manuscript argues for that result; its relation to this problem is specified below.

Mathematical statement of the claimed result

Mathematical claim 1.
Let $E=\mathbb Q(u)$ be imaginary quadratic with $u^2=-d$, $d>0$, and let $A$ be a complex abelian variety with a unital $E$-action. OpenAI claims rational cycle-class surjectivity \[ \operatorname{CH}^p(A^m)_{\mathbb Q}\longrightarrow H^{2p}(A^m,\mathbb Q)\cap H^{p,p}(A^m) \quad(m\ge1,\ p\ge0) \] in either of these two cases: $\dim A\le5$; or $\dim A=6$ and the rational Hermitian form associated to a compatible polarization is hyperbolic with signature $(3,3)$. In the second case, with rational Riemann form $e$, this means $h_E(x,y)=e(x,uy)+u e(x,y)$ on $H_1(A,\mathbb Q)$ has a totally isotropic three-dimensional $E$-subspace. Compatibility means $e(ax,y)=e(x,\bar a y)$ for all $a\in E$.

Outline of the argument

Manuscript 1 (family 032, 2026-09-30): A coherent seed and its Fourier--Mukai transform produce the split-sixfold Weil plane through an obstruction calculation and deformation. A determinant description of the actual Hodge group, combined with the CM result, extends these algebraic generators to powers and to the stated low-dimensional cases.

Formal verification

Family 032 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