Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-adaptedprecheck passjudge pass (gpt-5.6-terra)audited 2026-08-28
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.

The graph K3,3 has adjacency spectrum {3,0,0,0,0,−3}

Example

The complete bipartite graph K3,3 has adjacency spectrum {3,0,0,0,0,−3}.

Facts & Assumptions

Given: The graph K3,3.

[L1]

The graph Km,n has adjacency spectrum {mn,0m+n−2,−mn} (The complete bipartite graph Km,n has adjacency spectrum {mn,0m+n−2,−mn}).

Verification

technique · direct
1.1L1algebra

Applying [L1] with m=n=3 gives the eigenvalues 9=3, 03+3−2=04, and −9=−3.

2.1step 1.1∎

So the ordered spectrum is {3,0,0,0,0,−3}.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

4 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