{"data":{"id":"lf-c4-free-extremal-number-of-q8","statement_oneline":"The maximum number of edges in a C4-free subgraph of the 8-cube is ex(Q8,C4)=680.","statement_full_latex":"The maximum number of edges in a C4-free subgraph of the 8-cube is ex(Q8,C4)=680. Open residue: Fixed graph Q8; known lower bound 680.","source":{"title":"New Lower Bounds for C4-Free Subgraphs of the Hypercubes Q6, Q7, and Q8: Constructions, Structure, and Computational Method","arxiv":"2603.29127v4","url":"https://arxiv.org/abs/2603.29127","year":2026,"area":"Extremal graph theory"},"renown":{"score":1,"rationale":"Recent research-paper conjecture; renown scored at catalog level per Rubric v1.","scored_by":"rubric-v1"},"attackability":{"score":5,"rationale":"A 680-edge construction is known and the falsifying witness is simply a 681-edge C4-free subgraph.","scored_by":"rubric-v1","subscores":{"finite_witness":5,"oracle_cost":3,"freshness":5,"seedability":5}},"verification_tier":null,"ai_systems":[],"posed_by":null,"years_open":0,"notability":null,"source_trackers":[],"status":"open","ranking_score":5,"last_verified_open":"2026-07-27","added":"2026-07-27","resolution_type":null,"resolver":null,"resolution_date":null,"evidence_url":null,"evidence_note":null,"method_note":null,"submitted_by":"Luke Francis","verification_note":"Symmetry-reduced SAT/ILP with a checkable model or unsatisfiability certificate. — Current arXiv revision checked; source-stated open/partial. Independent literature and author confirmation still required. The source explicitly asks to determine ex(Q8,C4) exactly; equality 680 is a search-backed editorial formulation rather than a named conjecture in the abstract. Editorially screened candidate; not independently certified open. Author confirmation pending.","openconjecture_id":"1386","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-c4-free-extremal-number-of-q8","conjecture_id":"lf-c4-free-extremal-number-of-q8","status":"open","date":"2026-07-27T00:00:00.000Z","actor":"human-admin","rationale":"Imported Tier 1 contributor candidate from Luke Francis.","note":"Editorially screened candidate; author confirmation pending."}],"public_actions":[{"name":"claim","method":"POST","href":"/c/lf-c4-free-extremal-number-of-q8/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-c4-free-extremal-number-of-q8/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}