Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-29
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.

Conjugacy in a free group by cyclic reduction

Example

In the free group on a,b, the cyclically reduced words aba−1b−1 and ba−1b−1a are conjugate.

Facts & Assumptions

Given: The conjugacy problem asks whether two words represent conjugate elements.

[L1]

In a free group, two cyclically reduced words are conjugate if and only if one is a cyclic permutation of the other. (Two cyclically reduced words in a free group are conjugate if and only if one is a cyclic permutation of the other)

Verification

technique · direct
1.1

The word ba−1b−1a is obtained from aba−1b−1 by moving the initial letter a to the end. So it is a cyclic permutation of the first word.

given
2.1

Both words are cyclically reduced, and [L1] therefore makes them conjugate in the free group.

L1step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

7 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