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Math-2568-A1 · revision r1 · on Math-2568

OpenAI claim summary for Math-2568

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 034, 2026-09-27): 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. Zero Lelong numbers for minimal metrics on nef adjoints
  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

Zero Lelong numbers for minimal metrics on nef adjoints

OpenAI's claim

Minimal semipositive metrics of nef klt adjoints are claimed to have no positive Lelong numbers, and zero-Lelong endpoint metrics are claimed to give the stated interior-boundary $H^1$ injection. The cited manuscript argues for that result; its relation to this problem is specified below.

Mathematical statement of the claimed result

Mathematical claim 1.
For every normal connected projective complex klt pair $(H,\Theta)$ with effective rational $\Theta$ and nef rational Cartier $D_H=K_H+\Theta$, and every projective log resolution $\pi:V\to H$, OpenAI claims that $N=\pi^*D_H$ admits a semipositive singular Hermitian metric of minimal singularities and \[ \nu(h,x)=0\quad\text{for every }x\in V \] for every such metric $h$. Here $\nu$ is the Lelong number; minimal singularities means its weights are no more singular, up to bounded additive error, than the weights of any other semipositive metric on $N$. The components $K_H$ and $\Theta$ need not be separately rational Cartier.

Outline of the argument

Manuscript 1 (family 034, 2026-09-27): An extremal normalized-section argument contradicts a positive Lelong number by improving the minimal weight locally. For injectivity, harmonic forms and local primitives are compared with both endpoint weights; weak convergence in a fixed Hilbert space retains the ordinary coherent-cohomology class.

Formal verification

Family 034 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