Source labels openChecked July 26, 2026

Sidorenko's conjecture (1993)

Sidorenko's conjecture (1993).*

Mathematical statement

Sidorenko's conjecture (1993).*

For every finite bipartite simple graph $H$ and every finite simple graph $G$ : $t(H, G) \ge t(K_2, G)^{e(H)}$ , where $K_2$ denotes the single-edge graph on 2 vertices (i.e. completeGraph (Fin 2)).

Statement source: Wikipedia statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

sidorenko_conjecture

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem sidorenko_conjecture : answer(sorry) ↔    ∀ {V W : Type} [Fintype V] [Fintype W] [DecidableEq V] [DecidableEq W] [Nonempty W]      (H : SimpleGraph V) (G : SimpleGraph W)      [DecidableRel H.Adj] [DecidableRel G.Adj],      H.IsBipartite →      homDensity (completeGraph (Fin 2)) G ^ H.edgeFinset.card ≤ homDensity H G := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization Wikipediabackground