ExampleConstruction: AI-generatedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-09-05

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 complete four-blockade gives a four-vertex clique

Example

Let $B = (B_{1}, B_{2}, B_{3}, B_{4})$ be a complete four-blockade in a graph $G$ , and choose vertices $v_{i} \in B_{i}$ for $i = 1, 2, 3, 4$ .

Facts & Assumptions

Given: The complete blockade $B$ and the chosen vertices $v_{i} \in B_{i}$ .

[L1]

Distinct blocks of a complete blockade are pairwise complete (Complete, anticomplete, pure, weakly sparse, and $x$ -sparse blockades).

Verification

technique · direct

1.1

Because each block of a blockade is nonempty, the four choices $v_{i} \in B_{i}$ are legitimate.

givenchoose

2.1

If $i \neq j$ , then $B_{i}$ is complete to $B_{j}$ by [L1], so the chosen vertices $v_{i}$ and $v_{j}$ are adjacent.

step 1.1L1

3.1

Therefore every pair among $v_{1}, v_{2}, v_{3}, v_{4}$ is adjacent, so these four vertices form a clique.

step 2.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

11 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

Shenwei Huang, Yiao Ju, and Yidong Zhou, Erdős-Hajnal beyond the five-vertex path, Claim 3.5.1 (standard reference, not scraped)