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 pure blockade that is neither complete nor anticomplete

Example

Take three singleton blocks $B_{1} = {1}$ , $B_{2} = {2}$ , $B_{3} = {3}$ , and let the graph have edges $12$ and $23$ but not $13$ . Then

$(B_{1}, B_{2})$ is complete,
$(B_{2}, B_{3})$ is complete, and
$(B_{1}, B_{3})$ is anticomplete.

So $(B_{1}, B_{2}, B_{3})$ is pure, but it is neither complete nor anticomplete.

Depends on

Complete, anticomplete, pure, weakly sparse, and $x$-sparse blockades

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

Maria Chudnovsky, Alex Scott, Paul Seymour, and Sophie Spirkl, Erdős-Hajnal for graphs with no 5-hole, §5 (standard reference, not scraped)