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Math-2547-A1 · revision r1 · on Math-2547

OpenAI claim summary for Math-2547

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 056, 2026-10-05): 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. Generalized lc flip termination on Kähler fourfolds
  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

Generalized lc flip termination on Kähler fourfolds

OpenAI's claim

Every existing generalized log-canonical flip sequence in the specified globally factorial compact Kähler fourfold category is claimed to terminate, without scaling or pseudo-effectivity assumptions. 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 $X_0$ be normal irreducible globally Weil rational-factorial compact Kähler of dimension four, with effective rational finite-support $B_0$ of coefficients in $[0,1]$ and a fixed analytically nef rational b-divisor represented on a projective bimeromorphic compact Kähler model. Suppose $D_0=K_{X_0}+B_0+M_0$ rational Cartier and all generalized log discrepancies nonnegative. With strict transforms, the same b-divisor and compatible canonical representatives, OpenAI claims finiteness of every sequence \[ X_i\xrightarrow{f_i}Z_i\xleftarrow{f_i^+}X_{i+1},\qquad -D_i\text{ }f_i\text{-ample},\quad D_{i+1}\text{ }f_i^+\text{-ample}, \] with every $Z_i$ normal compact Kähler, whose maps are projective small nonisomorphic bimeromorphic maps with connected fibers and whose models remain normal irreducible globally Weil rational-factorial compact Kähler fourfolds with rational Cartier adjoints. The coefficients and discrepancy bound permit generalized log canonical, not only generalized canonical, pairs.

Outline of the argument

Manuscript 1 (family 056, 2026-10-05): Relative programs and special termination reduce the sequence to controlled terminal pieces while preserving the nef datum and actual adjoints. Analytic cycle ranks remove divisorial losses, and strict mixed-Hodge weight comparisons bound the residual surface changes, leaving only finitely many possible steps.

Formal verification

Family 056 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