{"data":{"id":"lf-negative-coefficient-in-33-remaining-dice-polynomial-pairs","statement_oneline":"In each of the 33 unresolved paired polynomials A_abcd and B_(2-a,2-b,2-c,2-d), at least one polynomial has a negative coefficient.","statement_full_latex":"In each of the 33 unresolved paired polynomials A_abcd and B_(2-a,2-b,2-c,2-d), at least one polynomial has a negative coefficient. Open residue: Exactly 33 finite cases remain.","source":{"title":"Dice Relabeling Using Square-Sided Dice","arxiv":"2606.20311v1","url":"https://arxiv.org/abs/2606.20311","year":2026,"area":"Enumerative combinatorics / dice"},"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 reduces the question to a fixed list of 33 symbolic cases; each case has an immediate coefficient-sign certificate.","scored_by":"rubric-v1","subscores":{"finite_witness":5,"oracle_cost":5,"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":"Expand the two polynomials exactly in a CAS and exhibit a negative coefficient, or isolate a pair with both coefficientwise nonnegative. — 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":"3558","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-negative-coefficient-in-33-remaining-dice-polynomial-pairs","conjecture_id":"lf-negative-coefficient-in-33-remaining-dice-polynomial-pairs","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-negative-coefficient-in-33-remaining-dice-polynomial-pairs/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-negative-coefficient-in-33-remaining-dice-polynomial-pairs/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}