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Math-2572-A1 · revision r1 · on Math-2572

OpenAI claim summary for Math-2572

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, 2026-09-24): 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. Virasoro constraints for projective complete intersections
  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 constraints for projective complete intersections

OpenAI's claim

Ordinary descendant Virasoro constraints are claimed for smooth projective complete intersections in every genus and curve class, retaining primitive and odd cohomology without semisimplicity. 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 $X\subset\mathbb P^N_{\mathbb C}$ be any smooth complete intersection. Let $F_g^X$ be its connected ordinary, unreduced genus-$g$ descendant potential, with cotangent classes at stable-map markings, arbitrary cohomology insertions and separate Novikov symbols for actual integral curve classes. Set $Z_X=\exp(\sum_{g\ge0}\hbar^{g-1}F_g^X)$. OpenAI claims the formal coefficientwise identities \[ L_k^X Z_X=0\qquad(k\ge-1). \] Here $L_k^X$ are the manuscript's normally ordered Virasoro operators built from the Poincaré pairing, first Hodge grading $\mu|_{H^{p,q}}=p-\dim(X)/2$ and $R=c_1(TX)\cup$, with its stated scalar normalization. The quantifiers include all genera, individual curve classes and primitive or odd insertions; these are descendant rather than ancestor constraints.

Outline of the argument

Manuscript 1 (family 065, 2026-09-24): Relative caps create and detect bounded seam-contact states with coefficientwise finite inversions. Pairing each primitive error tensor with its conjugate realizes a squared norm through these tests; Hodge--Riemann positivity then kills the full tensor without limiting the number of primitive insertions.

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