ExampleConstruction: Literature-sourcedVerification: AI-generatedprecheck passaudited 2026-08-31

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 star-expansion of $K_{3}$ contains the hatted five-cycle

Example

The star-expansion of $K_{3}$ contains an induced hatted five-cycle.

Facts & Assumptions

Given: The star-expansion of $K_{3}$ .

[L1]

The A-page lemma proves this containment directly (The star-expansion of $K_{3}$ contains the hatted five-cycle).

Verification

technique · direct

1.1

Apply [L1] to the star-expansion of $K_{3}$ .

2.1

The chosen six-vertex induced subgraph is exactly a hatted five-cycle.

step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

9 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, proof of Theorem 8.1 (standard reference, not scraped)

The star-expansion of K3K3​ contains the hatted five-cycle