DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedverified 2026-11-05 (gpt-6.1-sol)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Strict Calabi–Yau manifold convention

Definition

A strict Calabi–Yau $n$ -fold in this library is a smooth connected compact Kähler complex manifold $X$ of complex dimension $n$ , with a specified holomorphic trivialization $K_{X} ≅ O_{X}$ , and with $H^{0} (X, Ω_{X}^{p}) = 0$ for every integer $p$ satisfying $0 < p < n$ . The broad Calabi–Yau and canonical-bundle notation are as defined by the preceding page suppliers. Projectivity is an additional hypothesis whenever a theorem requires an algebraic variety. This convention does not assert exact $S U (n)$ holonomy.

Strict Calabi–Yau manifold convention

Definition

Definition references

Depends on

Dependency tree · 2 levels

Sources