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Math-2583-A1 · revision r1 · on Math-2583

OpenAI claim summary for Math-2583

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 068, 2026-09-26): 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. Invariant anticanonical sections under structure-sheaf acyclicity
  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

Invariant anticanonical sections under structure-sheaf acyclicity

OpenAI's claim

Asymptotically zero curvature-null valuation for a smoothly semipositive anticanonical line is claimed to be attained exactly by an effective rational anticanonical divisor. 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 $X$ be smooth connected projective complex, with a smooth semipositive anticanonical metric and $H^i(X,\mathcal O_X)=0$ for every $i>0$. Given an algebraic torus action by $T$ on $X$, use its differential linearization on $-K_X$, OpenAI claims \[ \exists m>0:\quad H^0(X,\mathcal O_X(-mK_X))^T\ne0. \] The section is invariant under the natural action, not merely an arbitrary character eigensection; smooth semipositivity and the cohomological vanishings are retained.

Outline of the argument

Manuscript 1 (family 068, 2026-09-26): In a finite bigraded ring, sections approaching a boundary ray use off-ray generators in negligible proportion. A boundary generator with suitably small normalized valuation is selected before the exceptional correction is pushed away; centeredness upgrades the resulting upper bound to exact order zero.

Formal verification

Family 068 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