ExampleConstruction: Literature-sourcedVerification: AI-generatedPipeline-generatedprecheck passaudited 2026-09-06

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 Mathieu groups among the sporadics

Example

$M_{11}$ , $M_{12}$ , $M_{22}$ , $M_{23}$ , and $M_{24}$ are Mathieu entries in the sporadic list.

Facts & Assumptions

Given: Use the sporadic list recorded in The twenty-six sporadic simple groups.

Verification

technique · direct

1.1

The cited list names $M_{11}, M_{12}, M_{22}, M_{23}, M_{24}$ as the five Mathieu sporadic simple groups.

given

2.1

These are therefore exactly the claimed Mathieu entries.

step 1.1∎

Depends on

The twenty-six sporadic simple groups

Used by

Nothing in the library uses this result yet.

Dependency tree · one level

1 result within one dependency step 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

Stephen D. Smith, CFSG—A User’s Manual (standard reference, not scraped)