Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedprecheck 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.

The word problem in a finite cyclic presentation

Example

In the cyclic presentation ⟨x∣x6=e⟩, the word x14 is equal to x2 and therefore is not trivial.

Facts & Assumptions

Given: The word problem is solvable in finitely generated abelian groups.

[L1]

Every finitely generated abelian group has solvable word problem. (The word problem for finitely generated abelian groups is solvable)

Verification

technique · direct
1.1given

In the cyclic group of order 6, exponents are taken modulo 6, so x14=x2.

2.1L1step 1.1∎

Because 2≢0(mod6), the element x2 is not the identity. This is the abelian coordinate check promised by [L1].

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 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