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Math-2596-A1 · revision r1 · on Math-2596

OpenAI claim summary for Math-2596

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 065, 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. Virasoro propagation through projective bundles
  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

Virasoro propagation through projective bundles

OpenAI's claim

Full descendant Virasoro constraints are claimed to pass from any smooth projective base to projectivizations of arbitrary nonsplit algebraic bundles, including all genera, integral curve classes, and odd insertions. 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 a smooth connected projective complex variety $B$, an algebraic vector bundle $E$ of rank $r\ge2$, and $X=\mathbb P_B(E)$ parametrizing lines in the fibers, OpenAI claims \[ \left[L_k^B Z_B=0\text{ for all }k\ge-1\right]\ \Longrightarrow\ \left[L_k^X Z_X=0\text{ for all }k\ge-1\right]. \] For each target $Y$, $Z_Y$ is its ordinary descendant partition function $\exp(\sum_g\hbar^{g-1}F_g^Y)$ with all cohomology classes, stable-map cotangent classes and actual effective integral curve labels. The normally ordered $L_k^Y$ use $\mu_Y|_{H^{p,q}}=p-\dim(Y)/2$, $R_Y=c_1(TY)\cup$, and zero-mode scalar $\chi(Y)/16-\operatorname{str}(\mu_Y^2)/4$; other modes have no scalar correction. The conclusion is coefficientwise in every genus, curve class and descendant list.

Outline of the argument

Manuscript 1 (family 065, 2026-10-05): Localization on the completion by a trivial summand separates the base and projective-bundle blocks. The logarithm of an equivariant shift cancels coefficient differentiation in the grading, giving quantizable modes; ancestor bounds continue their identities coefficientwise, and quantum Riemann--Roch identifies the ordinary constraints on both components.

Formal verification

Family 065 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