Alphabeta MathPropositionStatement: Literature-sourcedProof: AI-adaptedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07
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.
The cone object of a map is unique up to nonunique isomorphism
Statement
Two distinguished completions of the same map have isomorphic third objects. The isomorphism need not be unique or canonical.
Facts & Assumptions
Given: Two distinguished triangles beginning with the same map .
Proof
1.1given
TR3 extends the identity square on to a morphism between the two triangles.
2.1step 1.1given∎
Its first two components are identities, so the two-isomorphisms proposition makes its third component an isomorphism; TR3 supplies no uniqueness for that component.