Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-adaptedprecheck 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
1.1L1given

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

2.1L1step 1.1algebra∎

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

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