{"data":{"id":"lf-odd-cycles-are-p-positions-in-the-geodetic-removing-game","statement_oneline":"For every odd n, the game TER(C_n) has nim-value 0.","statement_full_latex":"For every odd n, the game TER(C_n) has nim-value 0. Open residue: First unchecked odd n is above 21.","source":{"title":"Impartial geodetic removing games on graphs","arxiv":"2606.05483v1","url":"https://arxiv.org/abs/2606.05483","year":2026,"area":"Combinatorial game theory"},"renown":{"score":1,"rationale":"Recent research-paper conjecture; renown scored at catalog level per Rubric v1.","scored_by":"rubric-v1"},"attackability":{"score":4,"rationale":"Exact dynamic programming has verified odd cycles through n=21; the state space is finite for each n and counterexamples are directly checkable.","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":"Compute the game graph and Sprague–Grundy values, retaining a full move table as the 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":"4079","effective_status":"open","claims":[],"status_events":[{"id":"seed-lf-odd-cycles-are-p-positions-in-the-geodetic-removing-game","conjecture_id":"lf-odd-cycles-are-p-positions-in-the-geodetic-removing-game","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-odd-cycles-are-p-positions-in-the-geodetic-removing-game/claim","verification":"email magic link"},{"name":"report_resolution","method":"POST","href":"/c/lf-odd-cycles-are-p-positions-in-the-geodetic-removing-game/resolve","verification":"admin review"}],"resolutions":[]},"notice":"Status is community- and machine-tracked and may lag. Verify independently before investing effort."}