Alphabeta Math
ExampleConstruction: AI-adaptedVerification: AI-adaptedSession-authored (Fable 5 assisted)precheck 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 two-subset model reproduces the Petersen spectrum

Example

The Petersen graph, realised on the two-element subsets of a five-element set, has adjacency spectrum {3,15,(−2)4}.

Facts & Assumptions

Given: The Petersen graph on [Ω]2 for a five-element set Ω.

[F1]

This graph is the Petersen graph exactly when adjacency means disjointness of the two-element subsets (The Petersen graph on the two-element subsets of a five-element set, adjacent when disjoint).

[L1]

The Petersen graph has adjacency spectrum {3,15,(−2)4} (The Petersen graph has adjacency spectrum {3,15,(−2)4}).

Verification

technique · direct
1.1

By [F1], the displayed two-subset construction is precisely the Petersen graph, not merely an isomorphic copy under a different naming convention.

F1
2.1

Therefore [L1] applies directly and yields the spectrum {3,15,(−2)4}.

step 1.1L1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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