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Sidorenko's conjecture

Theorem 1.1: for the explicit bipartite incidence graph $H$ of 22 triples on 13 points ( $35$ vertices, $66$ edges, connected, degrees 4 to 6 on one side and 3 on the other) there is a finite simple graph $G$ with an edge and $t(H,G)<p(G)^{66}$ . Corollaries: tensor powers make $t(H,F)/p(F)^{66}$ arbitrarily small, and blow-ups give a fixed deficit for injective copies at a positive limiting density. Not given: an explicit host graph, the smallest counterexample, or which other bipartite graphs fail.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Sidorenko's conjecture

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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Attribution

VibeMathed
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Unreleased internal OpenAI model
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Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Sidorenko's conjecture

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the abstract and Theorem 1.1 of 'A counterexample to Sidorenko's conjecture', read against the conjecture in its homomorphism-density form. The proof (symmetric-matrix kernels over F_q, a sign model, Lagrangian intersection estimates) was not refereed. Lean: lean/ComparatorChallenges/SidorenkoCounterexample.json exists with solution_module OAI.Combinatorics.Sidorenko.RandomHost, present at the pinned commit; the challenge is not in the formalization catalogue. Its statement was read: H is defined explicitly as the incidence graph of the 22 listed triples on Fin 13 (bipartite by construction, 66 edges), and the theorem asserts a finite simple graph on Fin n with an edge and homDensity H G < edgeDensity G ^ 66, homomorphisms counted with repetitions. That is the headline. Permitted axioms propext, Quot.sound, Classical.choice. Not rebuilt here. The host is existential, so no finite certificate can be re-run.

Source ↗

The forcing conjecture for bipartite graphs

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Lean: Sidorenko counterexample (challenge not in formalization.yaml)

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

Source ↗

Sidorenko 1993, A correlation inequality for bipartite graphs

specialist registry · pending

problem-record link supplied by the VibeMathed registry.