{"data":{"id":"lf-overpartition-congruence-modulo-7","statement_oneline":"For every m≥0 and k in {11,43,51}, the overpartition number p̄(16(56m+k)) is divisible by 7.","statement_full_latex":"For every m≥0 and k in {11,43,51}, the overpartition number p̄(16(56m+k)) is divisible by 7. Open residue: Three explicit arithmetic progressions.","source":{"title":"New Ramanujan-type congruences for overpartitions modulo $11$ and $13$","arxiv":"2603.08510v1","url":"https://arxiv.org/abs/2603.08510","year":2026,"area":"Partition theory"},"renown":{"score":1,"rationale":"Recent research-paper conjecture; renown scored at catalog level per Rubric v1.","scored_by":"rubric-v1"},"attackability":{"score":5,"rationale":"This is a direct modular sequence claim with rapid exact computation and a compact counterexample witness.","scored_by":"rubric-v1","subscores":{"finite_witness":4,"oracle_cost":5,"freshness":5,"seedability":4}},"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":"Compute p̄(n) modulo 7 via generating-function recurrence; record the first failing index or prove by modular forms. — 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":"933","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-overpartition-congruence-modulo-7","conjecture_id":"lf-overpartition-congruence-modulo-7","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-overpartition-congruence-modulo-7/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-overpartition-congruence-modulo-7/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}