ExampleConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedprecheck passverified 2026-09-24 (gpt-6-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.

Multiplier of a cyclic group

Example

Assume the Axiom of Choice and supplied projective-resolution data for group homology. Then $M (C) = 0$ for every cyclic group $C$ .

Facts & Assumptions

Given: The stated choice and resolution hypotheses and a cyclic group $C$ .

Verification

technique · direct

1.1given

Multiplier of a cyclic group applies to every finite or infinite cyclic group and gives $M (C) = 0$ .

2.1step 1.1∎

This is exactly the claimed cyclic-group calculation.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

8 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Clara Löh, Group Cohomology (standard reference, not scraped)