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.

$H_{0}$ is the five-wheel

Example

The graph $H_{0}$ is the five-wheel.

Facts & Assumptions

Given: The graph $H_{0}$ on vertices $w, v_{1}, v_{2}, v_{3}, v_{4}, v_{5}$ .

[L1]

In $H_{0}$ , the vertex $w$ is adjacent to each $v_{i}$ , and $v_{1} v_{2} v_{3} v_{4} v_{5} v_{1}$ is a five-cycle (The graphs $H_{0}, H_{1}, \dots, H_{5}$ , Empty and complete graphs, complete bipartite graphs, and the convention that $P_{n}$ and $C_{n}$ have $n$ vertices).

Verification

technique · direct finite check

1.1

By [L1], the rim vertices $v_{1}, \dots, v_{5}$ induce a $C_{5}$ .

2.1

The same fact [L1] says that the remaining vertex $w$ is adjacent to every rim vertex and that no other edges are present. This is exactly the five-wheel.

step 1.1L1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 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, Figure 7 (standard reference, not scraped)

H0H0​ is the five-wheel