{"data":{"id":"lf-global-max-cut-threshold-hierarchy-with-geometric-weights","statement_oneline":"For n≥7 and r between consecutive thresholds r_k(n) and r_(k−1)(n), the k-isolated cut C_k is globally maximum.","statement_full_latex":"For n≥7 and r between consecutive thresholds r_k(n) and r_(k−1)(n), the k-isolated cut C_k is globally maximum. Open residue: Exhaustive through n=21; near-isolated checks through n=100.","source":{"title":"Hierarchical threshold structure in Max-Cut with geometric edge weights","arxiv":"2603.08876v1","url":"https://arxiv.org/abs/2603.08876","year":2026,"area":"Combinatorial optimization"},"renown":{"score":1,"rationale":"Recent research-paper conjecture; renown scored at catalog level per Rubric v1.","scored_by":"rubric-v1"},"attackability":{"score":5,"rationale":"All 2^(n−1) cuts were exhausted through n=21 and local verification reaches n=100; the objective is exact and parameterized.","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":"Enumerate cuts or solve parametric MILPs, deriving the exact upper envelope of cut-weight polynomials. — 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":"917","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-global-max-cut-threshold-hierarchy-with-geometric-weights","conjecture_id":"lf-global-max-cut-threshold-hierarchy-with-geometric-weights","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-global-max-cut-threshold-hierarchy-with-geometric-weights/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-global-max-cut-threshold-hierarchy-with-geometric-weights/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}