{"data":{"id":"sidorenko-smallest-open-1993","statement_oneline":"Sidorenko's conjecture in its smallest unresolved instance: the bipartite graph K(5,5) minus a 10-cycle satisfies the Sidorenko density inequality.","statement_full_latex":"For the bipartite graph $H = K_{5,5} \\setminus C_{10}$ and every graph $G$, the homomorphism densities satisfy $t(H, G) \\ge t(K_2, G)^{e(H)}$. (Sidorenko's conjecture asserts this for every bipartite $H$; $K_{5,5} \\setminus C_{10}$ is the smallest case not covered by known results.)","source":{"title":"Sidorenko's conjecture (smallest open case)","arxiv":null,"url":"https://en.wikipedia.org/wiki/Sidorenko%27s_conjecture","year":1993,"area":"math.CO"},"renown":{"score":4,"rationale":"A major conjecture in extremal graph theory; a refutation of even this single instance would be front-page news in the field."},"attackability":{"score":2,"rationale":"A counterexample is a single weighted graph violating a density inequality, and homomorphism counting is differentiable, so gradient methods apply rather than only annealing. Widely believed true, and the continuous search space is unforgiving.","subscores":{"finite_witness":4,"oracle_cost":2,"freshness":1,"seedability":2}},"status":"open","last_verified_open":"2026-01-15","added":"2026-07-24","effective_status":"open","claims":[],"status_events":[{"id":"seed-sidorenko-smallest-open-1993","conjecture_id":"sidorenko-smallest-open-1993","status":"open","date":"2026-07-24T00:00:00.000Z","note":"Loaded from seed data."}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}