DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)verified 2026-10-22 (gpt-6.1-sol)

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.

Lobachevsky function

For real $θ$ , define the Lobachevsky function

Λ (θ) = - \int_{0}^{θ} \log ∣ 2 \sin u ∣ d u,

where the integral is interpreted improperly at zeros of $\sin u$ .

Used by

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