DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-01

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 left six-vertex prime $H$ -graph

The left six-vertex prime $H$ -graph is the graph $L$ on vertices

${t_{1}, t_{2}, t_{3}, ℓ_{1}, ℓ_{2}, ℓ_{3}}$

with edge set

${t_{1} t_{2}, t_{2} t_{3}, t_{1} t_{3}, ℓ_{1} t_{1}, ℓ_{2} t_{2}, ℓ_{3} t_{3}} .$

Thus $t_{1}, t_{2}, t_{3}$ span a triangle, and each $ℓ_{i}$ is a leaf attached only to the corresponding triangle vertex $t_{i}$ .

Used by

Nothing. This result depends on no other item in the library.