Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-28
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.
Object of finite length
Definition
An object of an abelian category has finite length when it admits a composition series in the sense of Composition series and composition factors of an object.
Its length is the number of successive simple factors in any composition series. The Jordan-Hölder theorem Jordan-Holder theorem in an abelian category makes this number independent of the chosen series.