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Math-2590-A1 · revision r1 · on Math-2590

OpenAI claim summary for Math-2590

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 035, 2026-09-24): 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. Terminal numerical-dimension-one abundance in positive characteristic
  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

Terminal numerical-dimension-one abundance in positive characteristic

OpenAI's claim

For terminal factorial projective threefolds in characteristic $p>3$, a nef canonical divisor of numerical dimension one is claimed to have Kodaira dimension one and be semiample. The cited manuscript argues for that result; its relation to this problem is specified below.

Mathematical statement of the claimed result

Mathematical claim 1.
Over an algebraically closed field of characteristic $p>3$, let $X$ be a normal projective rational-factorial terminal threefold with nef $K_X$. If an ample Cartier $H$ satisfies $K_XH^2>0$ and $K_X^2H=0$, OpenAI claims \[ \exists m>0:\ mK_X\text{ Cartier},\ h^0(X,mK_X)\ge2,\qquad\kappa(X,K_X)=1, \] and $K_X$ semiample. This is the boundary-zero terminal numerical-dimension-one theorem in the stated prime range.

Outline of the argument

Manuscript 1 (family 035, 2026-09-24): The proof starts from known positive-characteristic nonvanishing and seeks a second independent canonical section. A primitive-cycle obstruction combines tangent-sheaf foliations, strongly semistable inequalities, surface abundance, and Cartier descent; the resulting positive Kodaira dimension invokes the existing semiampleness theorem.

Formal verification

Family 035 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