Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedverified 2026-10-22 (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.
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- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
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These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Bounding-chain expression for a torsion linking pairing
Definition
Let be a closed oriented -manifold and let . Choose integral -cycles representing , respectively. For choices of an integer and an integral -chain with , the bounding-chain expression is , where and are placed transversely and intersection signs use the orientation of . This expression is the torsion linking pairing when its independence of the choices is established.
Used by
- A prime-power torsion linking form need not have a metabolizer Counterexample
- The square knot has a nontrivial character vanishing on a linking metabolizer Example
- The boundary kernel of a rational homology ball is a linking metabolizer Lemma
- The torsion linking pairing of a rational homology sphere is nonsingular Lemma
Dependency tree · 0 levels
Nothing. This result depends on no other item in the library.
Sources
- Patrick Gilmer, Slice Knots in S3 (standard reference, not scraped)