ExampleConstruction: AI-adaptedVerification: AI-generatedSession-authored (Fable 5 assisted)precheck passjudge pass (gpt-5.6-terra)audited 2026-08-28

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 four-block blockade-rainbow copy of P_4

Example

The path $P_{4}$ has a blockade-rainbow copy with four singleton blocks.

Facts & Assumptions

Given: The path $P_{4}$ on vertices $0, 1, 2, 3$ , with blocks $B_{1} : = {0}$ , $B_{2} : = {1}$ , $B_{3} : = {2}$ , and $B_{4} : = {3}$ .

[L1]

An induced subgraph is $B$ -rainbow when it lies in the support of the blockade and meets each block in at most one vertex (A blockade-rainbow induced copy).

[L2]

The graph $P_{4}$ has edges exactly $01, 12, 23$ (Empty and complete graphs, complete bipartite graphs, and the convention that $P_{n}$ and $C_{n}$ have $n$ vertices).

[L3]

The support of the blockade $(B_{1}, B_{2}, B_{3}, B_{4})$ is the union of those four singleton blocks (Blockades, their length, their width, and their support).

Verification

technique · direct construction

1.1

The support of the blockade is ${0, 1, 2, 3}$ by [L3], so the whole graph $P_{4}$ already lies inside that support.

L3given

2.1

Each block $B_{i}$ contains exactly one vertex of $P_{4}$ , so the induced copy of $P_{4}$ given by the whole graph meets each block in at most one vertex. By [L1], it is therefore blockade-rainbow.

step 1.1L1L2

3.1

Hence the path $P_{4}$ has a four-block blockade-rainbow copy.

step 2.1∎

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, Erdos-Hajnal for graphs with no 5-hole, Section 6 (standard reference, not scraped)