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 third outcome of property (*) gives a pure four-blockade
Example
Assume the trigger hypothesis of property holds for a comb of length and width . If the third outcome of property occurs, the resulting blockade is pure with width .
Facts & Assumptions
Given: A special-vertex comb with and width .
The third branch in Property (*) for a finite graph family gives a pure -blockade.
Verification
Applying [L1] with yields a pure blockade whose width is
Since [L1] names the blockade pure rather than complete or anticomplete, this branch keeps exactly the distinction used later on the A page: every pair of blocks is pure, but no stronger global uniformity is asserted.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
12 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, Section 1.4 (standard reference, not scraped)