{"data":{"id":"lf-recursive-4-2-3-codes-at-q-14-and-18","statement_oneline":"For every alphabet size q not in {2,6}, a complete recursive [4,2,3]_q code exists.","statement_full_latex":"For every alphabet size q not in {2,6}, a complete recursive [4,2,3]_q code exists. Open residue: Only q=14 and q=18 remain after the source resolves q=26.","source":{"title":"On the Construction of Recursively Differentiable Quasigroups and an Example of a Recursive $[4,2,3]_{26}$-Code","arxiv":"2604.01105v2","url":"https://arxiv.org/abs/2604.01105","year":2026,"area":"Coding theory / quasigroups"},"renown":{"score":1,"rationale":"Recent research-paper conjecture; renown scored at catalog level per Rubric v1.","scored_by":"rubric-v1"},"attackability":{"score":5,"rationale":"All orders are known except q=14 and q=18, turning the general conjecture into two finite construction problems.","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":"Produce a code/quasigroup table and verify the MDS and recursive-differentiability conditions exactly. — 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":"1280","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-recursive-4-2-3-codes-at-q-14-and-18","conjecture_id":"lf-recursive-4-2-3-codes-at-q-14-and-18","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-recursive-4-2-3-codes-at-q-14-and-18/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-recursive-4-2-3-codes-at-q-14-and-18/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}