Alphabeta Math
ExampleConstruction: AI-adaptedVerification: 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.

The bull graph is self-complementary

Example

The bull graph is isomorphic to its complement.

Facts & Assumptions

Given: The bull graph on vertices {x1,x2,x3,y,z}.

[F1]

The bull has edges x1x2, x2x3, x1x3, x1y, and x2z (The bull graph).

[F2]

In the complement graph, two distinct vertices are adjacent exactly when they are nonadjacent in the original graph (Graph isomorphisms, automorphisms and graph complements).

Verification

technique · direct
1.1

Define φ by φ(x1)=y, φ(x2)=z, φ(x3)=x3, φ(y)=x2, and φ(z)=x1. Using [F1] and [F2], one checks that the five complement-edges are exactly the images under φ of the five bull edges.

F1F2constructalgebra
2.1

Thus φ is an isomorphism from the bull to its complement, so the bull is self-complementary.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

4 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