{"data":{"id":"lf-dean-s-remaining-k-5-cycle-divisibility-case","statement_oneline":"Every graph of minimum degree at least 5 contains a cycle whose length is divisible by 5.","statement_full_latex":"Every graph of minimum degree at least 5 contains a cycle whose length is divisible by 5. Open residue: Only k=5 remains.","source":{"title":"Existence of cycles of length divisible by 3 or 4","arxiv":"2605.02731v1","url":"https://arxiv.org/abs/2605.02731","year":2026,"area":"Graph cycle theory"},"renown":{"score":1,"rationale":"Recent research-paper conjecture; renown scored at catalog level per Rubric v1.","scored_by":"rubric-v1"},"attackability":{"score":4,"rationale":"The original all-k conjecture is now settled for every k except 5, leaving one crisp graph-search target.","scored_by":"rubric-v1","subscores":{"finite_witness":4,"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":4,"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":"Enumerate or SAT-generate minimum-degree-5 graphs and test cycle lengths; a counterexample is an explicit graph. — Current arXiv revision checked; source-stated open/partial. Independent literature and author confirmation still required. Editorially screened candidate; not independently certified open. Author confirmation pending.","openconjecture_id":"2455","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-dean-s-remaining-k-5-cycle-divisibility-case","conjecture_id":"lf-dean-s-remaining-k-5-cycle-divisibility-case","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-dean-s-remaining-k-5-cycle-divisibility-case/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-dean-s-remaining-k-5-cycle-divisibility-case/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}