DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-07

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-nonisomorphism interactive protocol

Definition

For two graphs $G_{0}, G_{1}$ on the same labelled vertex set, the verifier chooses $b$ uniformly from ${0, 1}$ and, independently, chooses $π$ uniformly from all permutations of the vertex set. It sends $H = π (G_{b})$ , receives a bit $b^{'}$ from the prover, and accepts iff $b^{'} = b$ . This is a one-round instance of the interaction convention in Interactive-proof transcripts, rounds, and prover strategies.

Depends on

Interactive-proof transcripts, rounds, and prover strategies

Used by

Graph nonisomorphism is in IP Theorem

Dependency tree · one level

1 result within one dependency step 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

Arora and Barak, §8.3 (standard reference, not scraped)