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Math-2575-A1 · revision r1 · on Math-2575

OpenAI claim summary for Math-2575

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 041, 2026-09-23): 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. Bases of projective Lagrangian fibrations
  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

Bases of projective Lagrangian fibrations

OpenAI's claim

Every projective Lagrangian fibration of a compact Kähler IHS manifold is claimed to have projective space as its base. 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 $(X,\sigma)$ be a compact Kähler irreducible holomorphic symplectic manifold of dimension $2n$, with $n\ge1$. Assume a projective connected-fiber surjective holomorphic morphism $f:X\to B$ to normal projective $B$ of dimension $n$, with every fiber component of dimension $n$ and $\sigma$ zero on each component's smooth locus. OpenAI claims \[ B\simeq\mathbb P^n_{\mathbb C}. \] The base need not initially be smooth; the hypotheses include projectivity of the morphism and the componentwise Lagrangian condition on every fiber.

Outline of the argument

Manuscript 1 (family 041, 2026-09-23): The first stage excludes nonquotient singularities using fixed-base deformations, Euler obstructions, and Hodge variation. A finite abelian cover and a second varying fibration eliminate the residual quotient stabilizers, establishing smoothness before the known smooth-base theorem is applied.

Formal verification

Family 041 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