{"abstract":"Recursive UNION ALL deduplicates repeated recursive join rules.","category":"Data systems","checks":7,"contract":"Evaluate a bounded recursive UNION ALL query. Anchors are integer values; each frontier value joins all rules [source,target], preserving duplicate anchors and duplicate rules. Emit [depth,value] for depth zero through max-depth, expanding only the newest frontier. Preserve anchor and rule encounter order.","contract_signature":"d","evaluation_group":"s3-data-systems-recursive-bag-frontier","failed_approach":"Distinct recursive rules remove valid repeated derivations.","family":"s3-data-systems-recursive-bag-frontier-rule-dedup","id":"FA-45791","implementations":{"attempt":{"sha256":"751e393fbfc8afaa9c6f59a71836583a333e08cbc801d74c24160b867d98c5de","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    try:\n        anchors,rules,depth_limit=d\n        frontier=list(anchors); result=[[0,v] for v in frontier]\n        for depth in range(1,depth_limit+1):\n            next_rows=[]\n            for value in frontier:\n                for source,target in sorted(set(tuple(r) for r in rules)):\n                    if source==value: next_rows.append(target)\n            result.extend([[depth,v] for v in next_rows])\n            frontier=next_rows\n        return result\n    except (IndexError, KeyError, ValueError, StopIteration) as exc:\n        return {\"representation_error\": type(exc).__name__}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nif N == 1:\n    check('chain frontier', solve([[1], [[1, 2], [2, 3]], 2]), [[0, 1], [1, 2], [2, 3]])\n    check('duplicate anchors', solve([[1, 1], [[1, 2]], 1]), [[0, 1], [0, 1], [1, 2], [1, 2]])\n    check('duplicate rules', solve([[1], [[1, 2], [1, 2]], 1]), [[0, 1], [1, 2], [1, 2]])\n    check('zero depth', solve([[1], [[1, 2]], 0]), [[0, 1]])\n    check('reverse nonedge', solve([[2], [[1, 2]], 1]), [[0, 2]])\n    check('bounded cycle', solve([[1], [[1, 1]], 2]), [[0, 1], [1, 1], [2, 1]])\n    check('empty anchor', solve([[], [[1, 2]], 2]), [])\nelif N == 2:\n    check('chain frontier', solve([[2], [[2, 3], [3, 4]], 2]), [[0, 2], [1, 3], [2, 4]])\n    check('duplicate anchors', solve([[2, 2], [[2, 3]], 1]), [[0, 2], [0, 2], [1, 3], [1, 3]])\n    check('duplicate rules', solve([[2], [[2, 3], [2, 3]], 1]), [[0, 2], [1, 3], [1, 3]])\n    check('zero depth', solve([[2], [[2, 3]], 0]), [[0, 2]])\n    check('reverse nonedge', solve([[3], [[2, 3]], 1]), [[0, 3]])\n    check('bounded cycle', solve([[2], [[2, 2]], 2]), [[0, 2], [1, 2], [2, 2]])\n    check('empty anchor', solve([[], [[2, 3]], 2]), [])\nelif N == 3:\n    check('chain frontier', solve([[3], [[3, 4], [4, 5]], 2]), [[0, 3], [1, 4], [2, 5]])\n    check('duplicate anchors', solve([[3, 3], [[3, 4]], 1]), [[0, 3], [0, 3], [1, 4], [1, 4]])\n    check('duplicate rules', solve([[3], [[3, 4], [3, 4]], 1]), [[0, 3], [1, 4], [1, 4]])\n    check('zero depth', solve([[3], [[3, 4]], 0]), [[0, 3]])\n    check('reverse nonedge', solve([[4], [[3, 4]], 1]), [[0, 4]])\n    check('bounded cycle', solve([[3], [[3, 3]], 2]), [[0, 3], [1, 3], [2, 3]])\n    check('empty anchor', solve([[], [[3, 4]], 2]), [])\nelif N == 4:\n    check('chain frontier', solve([[4], [[4, 5], [5, 6]], 2]), [[0, 4], [1, 5], [2, 6]])\n    check('duplicate anchors', solve([[4, 4], [[4, 5]], 1]), [[0, 4], [0, 4], [1, 5], [1, 5]])\n    check('duplicate rules', solve([[4], [[4, 5], [4, 5]], 1]), [[0, 4], [1, 5], [1, 5]])\n    check('zero depth', solve([[4], [[4, 5]], 0]), [[0, 4]])\n    check('reverse nonedge', solve([[5], [[4, 5]], 1]), [[0, 5]])\n    check('bounded cycle', solve([[4], [[4, 4]], 2]), [[0, 4], [1, 4], [2, 4]])\n    check('empty anchor', solve([[], [[4, 5]], 2]), [])\nelif N == 5:\n    check('chain frontier', solve([[5], [[5, 6], [6, 7]], 2]), [[0, 5], [1, 6], [2, 7]])\n    check('duplicate anchors', solve([[5, 5], [[5, 6]], 1]), [[0, 5], [0, 5], [1, 6], [1, 6]])\n    check('duplicate rules', solve([[5], [[5, 6], [5, 6]], 1]), [[0, 5], [1, 6], [1, 6]])\n    check('zero depth', solve([[5], [[5, 6]], 0]), [[0, 5]])\n    check('reverse nonedge', solve([[6], [[5, 6]], 1]), [[0, 6]])\n    check('bounded cycle', solve([[5], [[5, 5]], 2]), [[0, 5], [1, 5], [2, 5]])\n    check('empty anchor', solve([[], [[5, 6]], 2]), [])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"f283f920f461b80e096891597380bba11b30ada52d0a445ef024dbea27409a4d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(d):\n    try:\n        anchors,rules,depth_limit=d\n        frontier=list(anchors); result=[[0,v] for v in frontier]\n        for depth in range(1,depth_limit+1):\n            next_rows=[]\n            for value in frontier:\n                for source,target in dict.fromkeys(tuple(r) for r in rules):\n                    if source==value: next_rows.append(target)\n            result.extend([[depth,v] for v in next_rows])\n            frontier=next_rows\n        return result\n    except (IndexError, KeyError, ValueError, StopIteration) as exc:\n        return {\"representation_error\": type(exc).__name__}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nif N == 1:\n    check('chain frontier', solve([[1], [[1, 2], [2, 3]], 2]), [[0, 1], [1, 2], [2, 3]])\n    check('duplicate anchors', solve([[1, 1], [[1, 2]], 1]), [[0, 1], [0, 1], [1, 2], [1, 2]])\n    check('duplicate rules', solve([[1], [[1, 2], [1, 2]], 1]), [[0, 1], [1, 2], [1, 2]])\n    check('zero depth', solve([[1], [[1, 2]], 0]), [[0, 1]])\n    check('reverse nonedge', solve([[2], [[1, 2]], 1]), [[0, 2]])\n    check('bounded cycle', solve([[1], [[1, 1]], 2]), [[0, 1], [1, 1], [2, 1]])\n    check('empty anchor', solve([[], [[1, 2]], 2]), [])\nelif N == 2:\n    check('chain frontier', solve([[2], [[2, 3], [3, 4]], 2]), [[0, 2], [1, 3], [2, 4]])\n    check('duplicate anchors', solve([[2, 2], [[2, 3]], 1]), [[0, 2], [0, 2], [1, 3], [1, 3]])\n    check('duplicate rules', solve([[2], [[2, 3], [2, 3]], 1]), [[0, 2], [1, 3], [1, 3]])\n    check('zero depth', solve([[2], [[2, 3]], 0]), [[0, 2]])\n    check('reverse nonedge', solve([[3], [[2, 3]], 1]), [[0, 3]])\n    check('bounded cycle', solve([[2], [[2, 2]], 2]), [[0, 2], [1, 2], [2, 2]])\n    check('empty anchor', solve([[], [[2, 3]], 2]), [])\nelif N == 3:\n    check('chain frontier', solve([[3], [[3, 4], [4, 5]], 2]), [[0, 3], [1, 4], [2, 5]])\n    check('duplicate anchors', solve([[3, 3], [[3, 4]], 1]), [[0, 3], [0, 3], [1, 4], [1, 4]])\n    check('duplicate rules', solve([[3], [[3, 4], [3, 4]], 1]), [[0, 3], [1, 4], [1, 4]])\n    check('zero depth', solve([[3], [[3, 4]], 0]), [[0, 3]])\n    check('reverse nonedge', solve([[4], [[3, 4]], 1]), [[0, 4]])\n    check('bounded cycle', solve([[3], [[3, 3]], 2]), [[0, 3], [1, 3], [2, 3]])\n    check('empty anchor', solve([[], [[3, 4]], 2]), [])\nelif N == 4:\n    check('chain frontier', solve([[4], [[4, 5], [5, 6]], 2]), [[0, 4], [1, 5], [2, 6]])\n    check('duplicate anchors', solve([[4, 4], [[4, 5]], 1]), [[0, 4], [0, 4], [1, 5], [1, 5]])\n    check('duplicate rules', solve([[4], [[4, 5], [4, 5]], 1]), [[0, 4], [1, 5], [1, 5]])\n    check('zero depth', solve([[4], [[4, 5]], 0]), [[0, 4]])\n    check('reverse nonedge', solve([[5], [[4, 5]], 1]), [[0, 5]])\n    check('bounded cycle', solve([[4], [[4, 4]], 2]), [[0, 4], [1, 4], [2, 4]])\n    check('empty anchor', solve([[], [[4, 5]], 2]), [])\nelif N == 5:\n    check('chain frontier', solve([[5], [[5, 6], [6, 7]], 2]), [[0, 5], [1, 6], [2, 7]])\n    check('duplicate anchors', solve([[5, 5], [[5, 6]], 1]), [[0, 5], [0, 5], [1, 6], [1, 6]])\n    check('duplicate rules', solve([[5], [[5, 6], [5, 6]], 1]), [[0, 5], [1, 6], [1, 6]])\n    check('zero depth', solve([[5], [[5, 6]], 0]), [[0, 5]])\n    check('reverse nonedge', solve([[6], [[5, 6]], 1]), [[0, 6]])\n    check('bounded cycle', solve([[5], [[5, 5]], 2]), [[0, 5], [1, 5], [2, 5]])\n    check('empty anchor', solve([[], [[5, 6]], 2]), [])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Offline stipulated semantics over valid small inputs; no performance, concurrency, or production-engine conformance claim. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"s3-data-systems-recursive-bag-frontier-rule-dedup","generated_at":"2026-09-29T14:44:25.858506+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"A bounded deterministic data engine model makes representation and changelog faults reproducible.","root_cause":"recursive-bag-frontier: Recursive UNION ALL deduplicates repeated recursive join rules.","sha256":"4175ed42b9bc5a3c4907b88ad9e1e680a1cff8f4e294c4f0ca937a973409f4f3","title":"Recursive UNION ALL deduplicates repeated recursive join rules · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":45.787,"exit_code":1,"observations":[{"actual":[[0,1],[1,2],[2,3]],"check":"chain frontier","expected":[[0,1],[1,2],[2,3]],"passed":true},{"actual":[[0,1],[0,1],[1,2],[1,2]],"check":"duplicate anchors","expected":[[0,1],[0,1],[1,2],[1,2]],"passed":true},{"actual":[[0,1],[1,2]],"check":"duplicate rules","expected":[[0,1],[1,2],[1,2]],"passed":false},{"actual":[[0,1]],"check":"zero depth","expected":[[0,1]],"passed":true},{"actual":[[0,2]],"check":"reverse nonedge","expected":[[0,2]],"passed":true},{"actual":[[0,1],[1,1],[2,1]],"check":"bounded cycle","expected":[[0,1],[1,1],[2,1]],"passed":true},{"actual":[],"check":"empty anchor","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"chain frontier\", \"actual\": [[0, 1], [1, 2], [2, 3]], \"expected\": [[0, 1], [1, 2], [2, 3]], \"passed\": true}, {\"check\": \"duplicate anchors\", \"actual\": [[0, 1], [0, 1], [1, 2], [1, 2]], \"expected\": [[0, 1], [0, 1], [1, 2], [1, 2]], \"passed\": true}, {\"check\": \"duplicate rules\", \"actual\": [[0, 1], [1, 2]], \"expected\": [[0, 1], [1, 2], [1, 2]], \"passed\": false}, {\"check\": \"zero depth\", \"actual\": [[0, 1]], \"expected\": [[0, 1]], \"passed\": true}, {\"check\": \"reverse nonedge\", \"actual\": [[0, 2]], \"expected\": [[0, 2]], \"passed\": true}, {\"check\": \"bounded cycle\", \"actual\": [[0, 1], [1, 1], [2, 1]], \"expected\": [[0, 1], [1, 1], [2, 1]], \"passed\": true}, {\"check\": \"empty anchor\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.737,"exit_code":1,"observations":[{"actual":[[0,1],[1,2],[2,3]],"check":"chain frontier","expected":[[0,1],[1,2],[2,3]],"passed":true},{"actual":[[0,1],[0,1],[1,2],[1,2]],"check":"duplicate anchors","expected":[[0,1],[0,1],[1,2],[1,2]],"passed":true},{"actual":[[0,1],[1,2]],"check":"duplicate rules","expected":[[0,1],[1,2],[1,2]],"passed":false},{"actual":[[0,1]],"check":"zero depth","expected":[[0,1]],"passed":true},{"actual":[[0,2]],"check":"reverse nonedge","expected":[[0,2]],"passed":true},{"actual":[[0,1],[1,1],[2,1]],"check":"bounded cycle","expected":[[0,1],[1,1],[2,1]],"passed":true},{"actual":[],"check":"empty anchor","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"chain frontier\", \"actual\": [[0, 1], [1, 2], [2, 3]], \"expected\": [[0, 1], [1, 2], [2, 3]], \"passed\": true}, {\"check\": \"duplicate anchors\", \"actual\": [[0, 1], [0, 1], [1, 2], [1, 2]], \"expected\": [[0, 1], [0, 1], [1, 2], [1, 2]], \"passed\": true}, {\"check\": \"duplicate rules\", \"actual\": [[0, 1], [1, 2]], \"expected\": [[0, 1], [1, 2], [1, 2]], \"passed\": false}, {\"check\": \"zero depth\", \"actual\": [[0, 1]], \"expected\": [[0, 1]], \"passed\": true}, {\"check\": \"reverse nonedge\", \"actual\": [[0, 2]], \"expected\": [[0, 2]], \"passed\": true}, {\"check\": \"bounded cycle\", \"actual\": [[0, 1], [1, 1], [2, 1]], \"expected\": [[0, 1], [1, 1], [2, 1]], \"passed\": true}, {\"check\": \"empty anchor\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}