{"data":{"id":"kill-brouwer-2026","statement_oneline":"Brouwer's conjecture: the sum of the t largest Laplacian eigenvalues of any graph is at most e(G) + t(t+1)/2.","renown":{"score":4,"rationale":"A well-known Laplacian eigenvalue conjecture, open ~15 years with wide partial results.","scored_by":"founder"},"attackability":{"score":3,"rationale":"Finite witness with cheap oracle, but extensive prior verification left little search room; fell to proof, not search.","subscores":{"finite_witness":5,"oracle_cost":4,"freshness":1,"seedability":3},"scored_by":"founder"},"ranking_score":12,"verification_tier":null,"ai_systems":[],"posed_by":null,"years_open":null,"notability":null,"source_trackers":[],"status":"confirmed","added":"2026-06-10","resolution_type":"proof","resolver":"Kothari and Tudose","resolution_date":"2026-06-10","evidence_url":"https://arxiv.org/abs/2606.12197","evidence_note":"Full proof via an equivalence with the Grone-Merris-Bai theorem; cited as confirmed by subsequent July 2026 literature.","method_note":"A reminder that conjectures leave the open list in both directions: this one was proved, not refuted.","effective_status":"confirmed","claims":[],"status_events":[{"id":"seed-kill-brouwer-2026","conjecture_id":"kill-brouwer-2026","status":"confirmed","date":"2026-06-10T00:00:00.000Z","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."}