{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":6,"contract":"Return sum(abs(x-anchor)); empty input returns zero. Anchor is supplied, not estimated.","evaluation_group":"s3-na-absolute-deviation-about-anchor","failed_approach":"Scaling the anchor still permits cancellation.","family":"s3-numerical-aggregation-absolute-deviation-about-anchor-anchor-once","id":"FA-12871","implementations":{"attempt":{"sha256":"98f46b10be780c16add8d6052bf54f6687f6088d8a5f2c27435c6f2b4c3c52fb","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom collections import Counter, defaultdict\nimport math\nimport itertools\nN = 1\nobservations = []\ndef solve(xs, anchor):\n    return abs(sum(xs)-anchor*len(xs))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([1, 5, 9], 5)), 8)\ncheck('regression 2', solve(*([], 4)), 0)\ncheck('regression 3', solve(*([4, 4], 4)), 0)\ncheck('regression 4', solve(*([-3, -1], 2)), 8)\ncheck('regression 5', solve(*([0, 0, 6], 1)), 7)\ncheck(\"variable anchor\", solve([N-3,N+2,N+2],N),7)\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":"ef62e497021a97545ff8a6607fe57ab70b9ea6a7ae5547b66fd62a4c3e879814","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom collections import Counter, defaultdict\nimport math\nimport itertools\nN = 1\nobservations = []\ndef solve(xs, anchor):\n    return abs(sum(xs)-anchor) if xs else 0\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([1, 5, 9], 5)), 8)\ncheck('regression 2', solve(*([], 4)), 0)\ncheck('regression 3', solve(*([4, 4], 4)), 0)\ncheck('regression 4', solve(*([-3, -1], 2)), 8)\ncheck('regression 5', solve(*([0, 0, 6], 1)), 7)\ncheck(\"variable anchor\", solve([N-3,N+2,N+2],N),7)\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"},"fixed":{"sha256":"fdf32ae20efa0796e6f0e4a7625899e2afdf6315c10f56c9ba996a64f78c8aa0","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom collections import Counter, defaultdict\nimport math\nimport itertools\nN = 1\nobservations = []\ndef solve(xs, anchor):\n    return sum(abs(x-anchor) for x in xs)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([1, 5, 9], 5)), 8)\ncheck('regression 2', solve(*([], 4)), 0)\ncheck('regression 3', solve(*([4, 4], 4)), 0)\ncheck('regression 4', solve(*([-3, -1], 2)), 8)\ncheck('regression 5', solve(*([0, 0, 6], 1)), 7)\ncheck(\"variable anchor\", solve([N-3,N+2,N+2],N),7)\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":"Small offline integer/rational inputs only; no performance, statistical inference, or production-library 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-numerical-aggregation-absolute-deviation-about-anchor-anchor-once","generated_at":"2026-09-29T14:39:00.890246+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Exact bounded examples isolate a reduction defect without floating-point or external-service effects.","repair":"Preserve the absolute deviation about anchor contract at the identified reduction decision.","root_cause":"The anchor is subtracted once from the total instead of once per observation.","sha256":"5f672f043b109832d1862a527763ae9449c433ab877dd2126c6f4b07eb75c96f","title":"Absolute deviation about anchor: The anchor is subtracted once from the total instead of once per observation. · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":51.38,"exit_code":1,"observations":[{"actual":0,"check":"regression 1","expected":8,"passed":false},{"actual":0,"check":"regression 2","expected":0,"passed":true},{"actual":0,"check":"regression 3","expected":0,"passed":true},{"actual":8,"check":"regression 4","expected":8,"passed":true},{"actual":3,"check":"regression 5","expected":7,"passed":false},{"actual":1,"check":"variable anchor","expected":7,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": 0, \"expected\": 8, \"passed\": false}, {\"check\": \"regression 2\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 3\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": 3, \"expected\": 7, \"passed\": false}, {\"check\": \"variable anchor\", \"actual\": 1, \"expected\": 7, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.853,"exit_code":1,"observations":[{"actual":10,"check":"regression 1","expected":8,"passed":false},{"actual":0,"check":"regression 2","expected":0,"passed":true},{"actual":4,"check":"regression 3","expected":0,"passed":false},{"actual":6,"check":"regression 4","expected":8,"passed":false},{"actual":5,"check":"regression 5","expected":7,"passed":false},{"actual":3,"check":"variable anchor","expected":7,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": 10, \"expected\": 8, \"passed\": false}, {\"check\": \"regression 2\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 3\", \"actual\": 4, \"expected\": 0, \"passed\": false}, {\"check\": \"regression 4\", \"actual\": 6, \"expected\": 8, \"passed\": false}, {\"check\": \"regression 5\", \"actual\": 5, \"expected\": 7, \"passed\": false}, {\"check\": \"variable anchor\", \"actual\": 3, \"expected\": 7, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":89.073,"exit_code":0,"observations":[{"actual":8,"check":"regression 1","expected":8,"passed":true},{"actual":0,"check":"regression 2","expected":0,"passed":true},{"actual":0,"check":"regression 3","expected":0,"passed":true},{"actual":8,"check":"regression 4","expected":8,"passed":true},{"actual":7,"check":"regression 5","expected":7,"passed":true},{"actual":7,"check":"variable anchor","expected":7,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"regression 2\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 3\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": 7, \"expected\": 7, \"passed\": true}, {\"check\": \"variable anchor\", \"actual\": 7, \"expected\": 7, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}