Alphabeta Math
ExampleConstruction: AI-generatedVerification: AI-generatedprecheck 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.

The path-antipath theorem specialized to P5 and P5‾

Example

Graphs with no induced P5 and no induced P5‾ have the Erdős–Hajnal property.

Facts & Assumptions

Given: The standard five-vertex path P5.

[L1]

For every integer k≥2, the class forbidding Pk and Pk‾ has the Erdős–Hajnal property (For every k, the class forbidding Pk and Pk‾ has the Erdős–Hajnal property).

[L2]

The graph P5 is the standard path on five vertices (Empty and complete graphs, complete bipartite graphs, and the convention that Pn and Cn have n vertices).

Verification

technique · direct
1.1L1L2

By [L2], the parameter choice k=5 in [L1] is exactly the class forbidding P5 and P5‾.

2.1step 1.1∎

Therefore graphs with no induced P5 and no induced P5‾ have the Erdős–Hajnal property.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

8 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.