{"anchors": [], "axis_coords": {"axis": "combinatorics", "dimensions": ["conservation_balance", "reasoning"]}, "content_hash": "b7807a96bdad28ab5ec46b81440bc5ce34b7f534ac40a1b639088ba64de05751", "gate_results": [{"details": {"broken_at": null, "confirmed_steps": 2, "gap_at": null, "steps": 2, "verdict": "HOLDS"}, "gate": "RED", "reasons": ["derivation verdict: HOLDS"], "status": "PASS"}], "overall": "PASS", "schema_version": "2.0", "verifier_results": [{"data": {"claim": "P(5,2) = 5!/3! = 20", "domain": "combinatorics", "link_ok": true, "uses": []}, "detail": "combinatorics.permutations: P(5,2) = 20 (matches claim)", "name": "pm1", "status": "CONFIRMED"}, {"data": {"claim": "C(5,2) = 10", "domain": "combinatorics", "link_ok": true, "uses": ["pm1"]}, "detail": "combinatorics.combinations: C(5,2) = 10 (matches claim)", "name": "cm1", "status": "CONFIRMED"}]}