{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":11,"contract":"Process add/remove integer factors; each removal removes one currently present equal factor. Return the exact product of active factors with empty product one. Preserve zero multiplicity and signed parity while zero factors temporarily hide the nonzero product.","evaluation_group":"s3-na-retractable-zero-aware-product","failed_approach":"Clearing all negative factors loses remaining sign contributions.","family":"s3-numerical-aggregation-retractable-zero-aware-product-product-negative-removal","id":"FA-13881","implementations":{"attempt":{"sha256":"99670db5b26a62ef56cd65df6402b90b2406159cc6466d4979fd93865a4780fd","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(events):\n    magnitude=1\n    negative=zero=0\n    for op,x in events:\n        if op==\"add\":\n            if x==0: zero+=1\n            else:\n                magnitude*=abs(x)\n                negative+=int(x<0)\n        else:\n            if x==0: zero-=1\n            else:\n                magnitude//=abs(x)\n                negative=0\n    return 0 if zero else (-magnitude if negative%2 else magnitude)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([('add', 0), ('add', 0)],)), 0)\ncheck('regression 2', solve(*([('add', 0), ('add', -3)],)), 0)\ncheck('regression 3', solve(*([('add', -1), ('add', -2), ('add', -3)],)), -6)\ncheck('regression 4', solve(*([('add', 2), ('add', 0), ('add', -3), ('remove', 0)],)), -6)\ncheck('regression 5', solve(*([('add', 0), ('add', 0), ('remove', 0)],)), 0)\ncheck('regression 6', solve(*([],)), 1)\ncheck('regression 7', solve(*([('add', -2), ('add', -3), ('remove', -2)],)), -3)\ncheck('regression 8', solve(*([('add', 3), ('add', 3), ('remove', 3)],)), 3)\ncheck('regression 9', solve(*([('add', -1), ('remove', -1)],)), 1)\ncheck('regression 10', solve(*([('add', -2), ('add', 5), ('add', -3)],)), 30)\ncheck(\"variable zero removal\",solve([(\"add\",N),(\"add\",0),(\"add\",-2),(\"remove\",0)]),-2*N)\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":"4566316e62487864797b6e90c42094401518cfae862b189f786ecf7e5339b8e9","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(events):\n    magnitude=1\n    negative=zero=0\n    for op,x in events:\n        if op==\"add\":\n            if x==0: zero+=1\n            else:\n                magnitude*=abs(x)\n                negative+=int(x<0)\n        else:\n            if x==0: zero-=1\n            else:\n                magnitude//=abs(x)\n                negative-=0\n    return 0 if zero else (-magnitude if negative%2 else magnitude)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([('add', 0), ('add', 0)],)), 0)\ncheck('regression 2', solve(*([('add', 0), ('add', -3)],)), 0)\ncheck('regression 3', solve(*([('add', -1), ('add', -2), ('add', -3)],)), -6)\ncheck('regression 4', solve(*([('add', 2), ('add', 0), ('add', -3), ('remove', 0)],)), -6)\ncheck('regression 5', solve(*([('add', 0), ('add', 0), ('remove', 0)],)), 0)\ncheck('regression 6', solve(*([],)), 1)\ncheck('regression 7', solve(*([('add', -2), ('add', -3), ('remove', -2)],)), -3)\ncheck('regression 8', solve(*([('add', 3), ('add', 3), ('remove', 3)],)), 3)\ncheck('regression 9', solve(*([('add', -1), ('remove', -1)],)), 1)\ncheck('regression 10', solve(*([('add', -2), ('add', 5), ('add', -3)],)), 30)\ncheck(\"variable zero removal\",solve([(\"add\",N),(\"add\",0),(\"add\",-2),(\"remove\",0)]),-2*N)\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":"1bb442ee98d0bbc1471b2730c04a6948b7095d4fc21edc79a63fefdbe5e00033","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(events):\n    magnitude=1\n    negative=zero=0\n    for op,x in events:\n        if op==\"add\":\n            if x==0: zero+=1\n            else:\n                magnitude*=abs(x)\n                negative+=int(x<0)\n        else:\n            if x==0: zero-=1\n            else:\n                magnitude//=abs(x)\n                negative-=int(x<0)\n    return 0 if zero else (-magnitude if negative%2 else magnitude)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([('add', 0), ('add', 0)],)), 0)\ncheck('regression 2', solve(*([('add', 0), ('add', -3)],)), 0)\ncheck('regression 3', solve(*([('add', -1), ('add', -2), ('add', -3)],)), -6)\ncheck('regression 4', solve(*([('add', 2), ('add', 0), ('add', -3), ('remove', 0)],)), -6)\ncheck('regression 5', solve(*([('add', 0), ('add', 0), ('remove', 0)],)), 0)\ncheck('regression 6', solve(*([],)), 1)\ncheck('regression 7', solve(*([('add', -2), ('add', -3), ('remove', -2)],)), -3)\ncheck('regression 8', solve(*([('add', 3), ('add', 3), ('remove', 3)],)), 3)\ncheck('regression 9', solve(*([('add', -1), ('remove', -1)],)), 1)\ncheck('regression 10', solve(*([('add', -2), ('add', 5), ('add', -3)],)), 30)\ncheck(\"variable zero removal\",solve([(\"add\",N),(\"add\",0),(\"add\",-2),(\"remove\",0)]),-2*N)\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-retractable-zero-aware-product-product-negative-removal","generated_at":"2026-09-29T14:39:11.424479+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 retractable zero aware product contract at the identified reduction decision.","root_cause":"Removing a negative factor leaves negative parity unchanged.","sha256":"718f589b4a37401f4b7822affdc2cc35babf5a67c106f0721dc44f1928351dc5","title":"Retractable zero aware product: Removing a negative factor leaves negative parity unchanged. · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":45.835,"exit_code":1,"observations":[{"actual":0,"check":"regression 1","expected":0,"passed":true},{"actual":0,"check":"regression 2","expected":0,"passed":true},{"actual":-6,"check":"regression 3","expected":-6,"passed":true},{"actual":-6,"check":"regression 4","expected":-6,"passed":true},{"actual":0,"check":"regression 5","expected":0,"passed":true},{"actual":1,"check":"regression 6","expected":1,"passed":true},{"actual":3,"check":"regression 7","expected":-3,"passed":false},{"actual":3,"check":"regression 8","expected":3,"passed":true},{"actual":1,"check":"regression 9","expected":1,"passed":true},{"actual":30,"check":"regression 10","expected":30,"passed":true},{"actual":-2,"check":"variable zero removal","expected":-2,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 2\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 3\", \"actual\": -6, \"expected\": -6, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": -6, \"expected\": -6, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"regression 7\", \"actual\": 3, \"expected\": -3, \"passed\": false}, {\"check\": \"regression 8\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"regression 9\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"regression 10\", \"actual\": 30, \"expected\": 30, \"passed\": true}, {\"check\": \"variable zero removal\", \"actual\": -2, \"expected\": -2, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.885,"exit_code":1,"observations":[{"actual":0,"check":"regression 1","expected":0,"passed":true},{"actual":0,"check":"regression 2","expected":0,"passed":true},{"actual":-6,"check":"regression 3","expected":-6,"passed":true},{"actual":-6,"check":"regression 4","expected":-6,"passed":true},{"actual":0,"check":"regression 5","expected":0,"passed":true},{"actual":1,"check":"regression 6","expected":1,"passed":true},{"actual":3,"check":"regression 7","expected":-3,"passed":false},{"actual":3,"check":"regression 8","expected":3,"passed":true},{"actual":-1,"check":"regression 9","expected":1,"passed":false},{"actual":30,"check":"regression 10","expected":30,"passed":true},{"actual":-2,"check":"variable zero removal","expected":-2,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 2\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 3\", \"actual\": -6, \"expected\": -6, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": -6, \"expected\": -6, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"regression 7\", \"actual\": 3, \"expected\": -3, \"passed\": false}, {\"check\": \"regression 8\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"regression 9\", \"actual\": -1, \"expected\": 1, \"passed\": false}, {\"check\": \"regression 10\", \"actual\": 30, \"expected\": 30, \"passed\": true}, {\"check\": \"variable zero removal\", \"actual\": -2, \"expected\": -2, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.797,"exit_code":0,"observations":[{"actual":0,"check":"regression 1","expected":0,"passed":true},{"actual":0,"check":"regression 2","expected":0,"passed":true},{"actual":-6,"check":"regression 3","expected":-6,"passed":true},{"actual":-6,"check":"regression 4","expected":-6,"passed":true},{"actual":0,"check":"regression 5","expected":0,"passed":true},{"actual":1,"check":"regression 6","expected":1,"passed":true},{"actual":-3,"check":"regression 7","expected":-3,"passed":true},{"actual":3,"check":"regression 8","expected":3,"passed":true},{"actual":1,"check":"regression 9","expected":1,"passed":true},{"actual":30,"check":"regression 10","expected":30,"passed":true},{"actual":-2,"check":"variable zero removal","expected":-2,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 2\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 3\", \"actual\": -6, \"expected\": -6, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": -6, \"expected\": -6, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"regression 7\", \"actual\": -3, \"expected\": -3, \"passed\": true}, {\"check\": \"regression 8\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"regression 9\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"regression 10\", \"actual\": 30, \"expected\": 30, \"passed\": true}, {\"check\": \"variable zero removal\", \"actual\": -2, \"expected\": -2, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}