Alphabeta MathChains, Antichains, Sperner and Dilworth — Examples
About this page
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.
✓ 8 results · all verified · 0 also independently AI-judged
Every result on this page is machine-checked by a proof checker and read in full and owner-audited; the judge is an additional, independent cross-model AI review of the proofs. The 8 not AI-judged were verified by owner audit (typically over a confirmed judge false positive), not failures.
1 · Prerequisites
Abstract Algebra
Combinatorics
Number Theory
Real Analysis
2 · Logical flowchart
3 · Items
Example
The Boolean lattice on four elements: ranks, width, shadows, and a symmetric chain decomposition
Example
A six-element poset of width three and a three-chain cover
Example
The divisors of 60 form a finite distributive lattice and realize Birkhoff's representation concretely
Example
Four explicit petals with a common two-element core form a sunflower
Example
All k-sets through a fixed point form an intersecting family attaining the Erdős-Ko-Rado bound
Counterexample
A maximal antichain of size one in a finite poset of width two
Counterexample
When k<n<2k, the entire kth level is intersecting and exceeds the Erdős-Ko-Rado star bound
Counterexample