{"data":{"id":"lf-sign-cutoff-for-ramanujan-s-mock-theta-q","statement_oneline":"For every n≥21, r(n)>0 when n≡0 mod 3 and r(n)<0 when n≡1 or 2 mod 3.","statement_full_latex":"For every n≥21, r(n)>0 when n≡0 mod 3 and r(n)<0 when n≡1 or 2 mod 3. Open residue: Exact cutoff 21; source develops the asymptotic sign mechanism.","source":{"title":"Sign law for Ramanujan's third order mock theta function $ρ(q)$","arxiv":"2606.27902v1","url":"https://arxiv.org/abs/2606.27902","year":2026,"area":"q-series / number 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":"The coefficients are exact integers and the proposed cutoff is explicit; computation can stress-test huge ranges while analytic bounds target the tail.","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 coefficients with exact recurrences; a single sign failure is a certificate. — 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":"4213","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-sign-cutoff-for-ramanujan-s-mock-theta-q","conjecture_id":"lf-sign-cutoff-for-ramanujan-s-mock-theta-q","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-sign-cutoff-for-ramanujan-s-mock-theta-q/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-sign-cutoff-for-ramanujan-s-mock-theta-q/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}