ExampleConstruction: AI-generatedVerification: Not suppliedSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-27

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 three-block blockade and its width

Example

Let $G$ be any finite graph containing nine distinct vertices $a, b, c, d, e, f, g, h, i$ . If

$B = ({a, b, c}, {d, e}, {f, g, h, i}),$

then $B$ is a blockade of length $3$ and width $2$ , and

$V (B) = {a, b, c, d, e, f, g, h, i} .$

Depends on

Blockades, their length, their width, and their support

Used by

Nothing in the library uses this result yet.

Dependency tree · one level

1 result within one dependency step 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

T. H. Nguyen, Notes on Recent Work on the Erdős–Hajnal Conjecture (standard reference, not scraped)