Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)verified 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.
- 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.
Finite nonsingular linking forms and metabolizers
Definition
A finite nonsingular linking form is a pair , where is a finite abelian group and is symmetric and induces an isomorphism . For , put . A metabolizer is a subgroup with ; equivalently, vanishes on and .
Used by
- A prime-power torsion linking form need not have a metabolizer Counterexample
- Torsion linking form and Casson–Gordon bordism data Definition
- The square knot has a nontrivial character vanishing on a linking metabolizer Example
- A slice disk induces a metabolizer on the branched-cover linking form Lemma
- The boundary kernel of a rational homology ball is a linking metabolizer Lemma
- Casson–Gordon signature-defect obstruction to sliceness Theorem
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)