Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-01
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.

A Baumslag-Solitar group gives a noninjective completion map

Example

The Baumslag-Solitar group

BS⁡(2,3)=⟨a,t∣t−1a2t=a3⟩

is a standard example whose canonical map to its profinite completion is not injective.

Facts & Assumptions

Given: The classical theorem of Meskin that BS⁡(m,n) is residually finite exactly when ∣m∣=∣n∣ or ∣m∣=1 or ∣n∣=1.

[L1]

The canonical map is injective exactly when the group is residually finite (The canonical map is injective exactly when the group is residually finite).

Verification

technique · direct
1.1

For (m,n)=(2,3), the Meskin criterion in the Given clause fails. Therefore BS⁡(2,3) is not residually finite.

given
2.1

Apply [L1] to BS⁡(2,3). Since the group is not residually finite, its canonical map into the profinite completion is not injective.

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