we-solve (beta)

Math-2503-A1 · revision r1 · on Math-2503

OpenAI claim summary for Math-2503

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: 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.

An abelian variety is a semiabelian variety with no torus part. The source therefore addresses the abelian case over algebraic numbers, using the smallest containing torsion coset for the atypicality comparison. The displayed question allows an arbitrary semiabelian ambient variety. The manuscript does not assert the extension to a nontrivial torus part or all more general constant fields.

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

Manuscript

Contents
  1. Torsion-Anomalous Conjecture for Semiabelian Varieties
  2. OpenAI's claim
  3. Mathematical statement of the claimed result
  4. Manuscript 1.
  5. Outline of the argument
  6. Formal verification
  7. Status caveat
  8. Sources

Torsion-Anomalous Conjecture for Semiabelian Varieties

OpenAI's claim

For subvarieties of abelian varieties over algebraic numbers, the selected manuscript claims finiteness of maximal atypical intersections, with dimensions measured inside the smallest containing torsion coset. This supplies the abelian branch of the semiabelian question. The mathematical statement below specifies that ambient variety and its field of definition.

Mathematical statement of the claimed result

Manuscript 1.
For a number field $K$, abelian variety $A/K$, and irreducible $X\subseteq A_{\bar K}$, let $S$ be the smallest special subvariety containing $X$; special subvarieties are torsion translates of abelian subvarieties. An irreducible component $Y$ of $X\cap Z$, $Z\subseteq S$ special, is atypical when \[ \dim Y>\dim X+\dim Z-\dim S. \] The claim is finiteness of maximal atypical subvarieties of $X$, equivalently existence of finitely many proper atypical $Y_j\subsetneq X$ containing every atypical subvariety. No dimension bound on $A$ or $X$ is imposed.

Outline of the argument

For manuscript 1 (family 016; 2026-09-24), a counterexample sequence is decomposed into distinct height scales. Uniform tangent positivity and weighted small sections give a height inequality despite growing homomorphism coefficients and point degrees; passing to suitable quotients rules out the remaining scale configurations.

Formal verification

No Lean formalization is listed at this snapshot for the selected manuscript (family 016; 2026-09-24).

This site has not executed the Lean code. Described statement coverage is not an independent proof check.

Status caveat

The manuscripts were produced by an internal OpenAI model. OpenAI cautions that results without formalization can contain mistakes. This site has not independently checked the proofs; the label records the scope of OpenAI's claim.

Sources