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.

The Bird graph and co-Bird by finite adjacency data

Example

The Bird graph is obtained from the bull by attaching one more pendant vertex to a horn, and co-Bird is its complement.

Facts & Assumptions

Given: The labelled vertices x1,x2,x3,y,z,w.

[L1]

The Bird graph consists of the bull on {x1,x2,x3,y,z} together with the extra edge yw, and co-Bird is its complement (The Bird graph and co-Bird, Graph isomorphisms, automorphisms and graph complements).

[L2]

In the bull, the triangle is x1x2x3, the horn vertices are y,z, and y is adjacent only to x1 while z is adjacent only to x2 (The bull graph).

Verification

technique · direct finite check
1.1

By [L1] and [L2], the vertices {x1,x2,x3,y,z} span the bull, and the new vertex w is adjacent only to the horn vertex y. Therefore the labelled graph is exactly the Bird graph.

L1L2
2.1

By [L1], co-Bird is obtained by complementing that six-vertex graph on the same label set.

step 1.1L1∎

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