{"data":{"id":"lf-exact-count-of-cyclically-covering-ternary-subspaces","statement_oneline":"For prime n>3 with odd ord_n(3), |N(n,3)|=Σ_{j=0}^{r/2} C(r,j), where r=(n−1)/ord_n(3).","statement_full_latex":"For prime n>3 with odd ord_n(3), |N(n,3)|=Σ_{j=0}^{r/2} C(r,j), where r=(n−1)/ord_n(3). Open residue: Eligible primes with odd multiplicative order.","source":{"title":"Cyclic Codes and Cyclically Covering Subspaces over Finite Fields","arxiv":"2607.02239v1","url":"https://arxiv.org/abs/2607.02239","year":2026,"area":"Coding theory / finite fields"},"renown":{"score":1,"rationale":"Recent research-paper conjecture; renown scored at catalog level per Rubric v1.","scored_by":"rubric-v1"},"attackability":{"score":4,"rationale":"The formula is explicit and each eligible prime gives a finite orbit/subspace enumeration with exact integer output.","scored_by":"rubric-v1","subscores":{"finite_witness":4,"oracle_cost":4,"freshness":5,"seedability":4}},"verification_tier":null,"ai_systems":[],"posed_by":null,"years_open":0,"notability":null,"source_trackers":[],"status":"open","ranking_score":4,"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":"Enumerate the relevant cyclic subspaces or use factorization of x^n−1 over F3, then compare counts. — 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":"4689","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-exact-count-of-cyclically-covering-ternary-subspaces","conjecture_id":"lf-exact-count-of-cyclically-covering-ternary-subspaces","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-exact-count-of-cyclically-covering-ternary-subspaces/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-exact-count-of-cyclically-covering-ternary-subspaces/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}