{"data":{"id":"lf-multiset-partition-dimension-of-prism-graphs","statement_oneline":"For every prism P_m with m≥8, mpd(P_m)=6.","statement_full_latex":"For every prism P_m with m≥8, mpd(P_m)=6. Open residue: Upper bound 6 is known for all m≥8.","source":{"title":"Multiset Partition Dimension of Graphs","arxiv":"2607.07407v1","url":"https://arxiv.org/abs/2607.07407","year":2026,"area":"Graph metric dimension"},"renown":{"score":1,"rationale":"Recent research-paper conjecture; renown scored at catalog level per Rubric v1.","scored_by":"rubric-v1"},"attackability":{"score":5,"rationale":"The source already constructs a size-6 partition; only a finite lower-bound obstruction to size 5 is needed for each m.","scored_by":"rubric-v1","subscores":{"finite_witness":4,"oracle_cost":4,"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":"SAT/ILP encode resolving partitions of size 5; return a partition or unsat certificate, then seek periodic reduction in m. — 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":"4479","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-multiset-partition-dimension-of-prism-graphs","conjecture_id":"lf-multiset-partition-dimension-of-prism-graphs","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-multiset-partition-dimension-of-prism-graphs/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-multiset-partition-dimension-of-prism-graphs/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}