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.
FALSE: every comb has pairwise anticomplete blocks
Statement
Every comb has pairwise anticomplete blocks.
Facts & Assumptions
Given: The counterexample item A comb can have an edge between two blocks.
The previous counterexample exhibits a comb whose two blocks are joined by an edge (A comb can have an edge between two blocks).
Refutation
By [L1], there exists a specific comb with two blocks that are not anticomplete.
Therefore the universal statement is false. The anticomplete-block conclusion on the A page needs the extra rooted stable-tooth structure together with -freeness, not merely the definition of a comb.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
3 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, Erdős-Hajnal for graphs with no 5-hole, proof context for Theorem 4.4 (standard reference, not scraped)