{"data":{"id":"kill-txgraffiti-saturation-harmonic-2026","statement_oneline":"For every nontrivial connected graph, the minimum maximal matching number is at most the harmonic index (TxGraffiti conjecture, 2023).","renown":{"score":1,"rationale":"Machine-generated 2023 conjecture known within automated conjecturing.","scored_by":"founder"},"attackability":{"score":5,"rationale":"Nine-vertex counterexample existed the whole time; the archetype of a ripe target.","subscores":{"finite_witness":5,"oracle_cost":5,"freshness":3,"seedability":4},"scored_by":"founder"},"ranking_score":5,"verification_tier":null,"ai_systems":[],"posed_by":null,"years_open":null,"notability":null,"source_trackers":[],"status":"confirmed","added":"2026-06-20","resolution_type":"counterexample","resolver":"Bıyıkoğlu; smallest cases identified by Gupta","resolution_date":"2026-06-20","evidence_url":"https://arxiv.org/abs/2606.15761","evidence_note":"Refuted with unbounded violation ratio; the smallest counterexample is the friendship graph F4 on nine vertices, and the smallest tree counterexample is the subdivided star on eleven vertices.","method_note":null,"effective_status":"confirmed","claims":[],"status_events":[{"id":"seed-kill-txgraffiti-saturation-harmonic-2026","conjecture_id":"kill-txgraffiti-saturation-harmonic-2026","status":"confirmed","date":"2026-06-20T00:00:00.000Z","actor":"human-admin","rationale":"Loaded from unified seed data.","note":"Loaded from unified seed data."}],"public_actions":[],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}