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Math-2594-A1 · revision r1 · on Math-2594

OpenAI claim summary for Math-2594

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, 2026-10-03): 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. A uniform pluricanonical Iitaka degree
  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

A uniform pluricanonical Iitaka degree

OpenAI's claim

A degree depending only on dimension is claimed to define every characteristic-zero smooth projective Iitaka fibration with nonnegative Kodaira dimension and to recover its whole function field. 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 $d\ge1$, OpenAI claims a positive integer $m(d)$ valid for every smooth integral projective $d$-fold $X$ over every algebraically closed characteristic-zero field with $\kappa(X)\ge0$, such that \[ |m(d)K_X|\ne\varnothing,\qquad k(s/t:\ 0\ne s,t\in H^0(X,m(d)K_X))=K(K_X). \] The field on the right is generated by all equal-degree positive pluricanonical section ratios. Thus the one complete system defines the Iitaka fibration, not merely a map of the correct image dimension.

Outline of the argument

Manuscript 1 (family 034, 2026-10-03): Degeneration of individual generic-fiber factors bounds their volume-form characters independently of semistable ramification. Weak positivity and flattening supply compatible small-volume bounds on the base; Frobenius-diagonal estimates and bounded curve chains then complete the dimension induction.

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