Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-31
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.

Two large anticonnected components give a complete two-blockade

Example

If G has two distinct anticonnected components A and B, each of size at least w, then (A,B) is a complete (2,w)-blockade.

Facts & Assumptions

Given: Two distinct anticonnected components A,B of a graph G with ∣A∣,∣B∣≥w>0.

[L1]

Distinct anticonnected components are complete to one another (Distinct connected components are anticomplete, and distinct anticonnected components are complete).

Verification

technique · direct
1.1

The sets A and B are disjoint and nonempty because they are distinct components, and each has size at least w by hypothesis.

given
2.1

By [L1], the pair (A,B) is complete. Therefore (A,B) is a complete (2,w)-blockade.

step 1.1L1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

10 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