Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-28
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 finite group fixing the centre of a tree

Example

Let P5 be the path with vertices −2,−1,0,1,2 and edges joining consecutive integers. Reflection r(n)=−n defines an action of C2 on P5, and the centre vertex 0 is fixed.

Facts & Assumptions

Given: The path P5 and the reflection action of C2.

[L1]

A finite group acting on a tree fixes a vertex after subdivision. (Finite groups acting on trees have a global fixed vertex after subdivision)

Verification

technique · direct
1.1

The reflection preserves adjacency and the unique diameter path of P5, so it is an automorphism of the tree.

L1given
2.1

Its midpoint is already the vertex 0, so the fixed vertex promised by [L1] occurs without needing any further subdivision in this example.

L1step 1.1algebra∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 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