Alphabeta MathHow 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 singleton family is viral
Example
The singleton family is viral.
Facts & Assumptions
Given: The three-vertex path .
Every graph on at most three vertices has the Erdős–Hajnal property (Every graph on at most three vertices has the Erdős–Hajnal property).
For a single graph, the Erdős–Hajnal property, the polynomial Rödl property, and virality are equivalent (For a single graph, the Erdős–Hajnal property, the polynomial Rödl property, and virality are equivalent).
is the standard three-vertex path (Empty and complete graphs, complete bipartite graphs, and the convention that and have vertices).
Verification
By [L3], the graph has three vertices, so [L1] gives the Erdős–Hajnal property for .
Applying [L2] to the graph of step 1.1 shows that the singleton family is viral.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
17 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.