Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-27
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.

FALSE: every abelian group is hyperbolic

Statement

False claim: every abelian group is hyperbolic.

Facts & Assumptions

Given: The abelian group Z2.

[L1]

Free abelian groups of rank at least two are not hyperbolic (Free abelian groups of rank at least two are not hyperbolic).

Refutation

technique · direct
1.1

The group Z2 is abelian.

given
2.1

The group Z2 has rank 2, so [L1] shows that it is not hyperbolic. Therefore the claim is false.

L1step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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