{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":10,"contract":"Process add/remove integer observations; each removal names one active equal-valued observation. Maintain [count, exact mean, unnormalised squared central scatter]. Empty state is [0,\"0\",\"0\"].","evaluation_group":"s3-na-retractable-central-summary","failed_approach":"Using only the new residual instead undercounts insertion scatter.","family":"s3-numerical-aggregation-retractable-central-summary-add-old-center-square","id":"FA-13461","implementations":{"attempt":{"sha256":"0055991d2032421cbde1906d7164e56ea77376b9b069e3f8eb77528760679e98","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    n=0\n    mean=m2=Fraction(0)\n    for op,x in events:\n        if op==\"add\":\n            new_n=n+1\n            delta=x-mean\n            new_mean=mean+delta/new_n\n            m2+=(x-new_mean)**2\n            mean=new_mean\n            n=new_n\n        else:\n            new_n=n-1\n            if new_n==0:\n                n=0\n                mean=m2=Fraction(0)\n                continue\n            new_mean=(n*mean-x)/new_n\n            m2-=(x-mean)*(x-new_mean)\n            mean=new_mean\n            n=new_n\n    return [n,str(mean),str(m2)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([('add', -3), ('add', 8), ('remove', -3)],)), [1, '8', '0'])\ncheck('regression 2', solve(*([('add', 6), ('remove', 6)],)), [0, '0', '0'])\ncheck('regression 3', solve(*([('add', 1), ('add', 4), ('add', 8), ('remove', 4)],)), [2, '9/2', '49/2'])\ncheck('regression 4', solve(*([('add', -5), ('remove', -5), ('add', 9)],)), [1, '9', '0'])\ncheck('regression 5', solve(*([],)), [0, '0', '0'])\ncheck('regression 6', solve(*([('add', 2), ('add', 2), ('remove', 2)],)), [1, '2', '0'])\ncheck('regression 7', solve(*([('add', 0), ('add', 4), ('add', 9), ('add', -1), ('remove', 0), ('remove', 9)],)), [2, '3/2', '25/2'])\ncheck('regression 8', solve(*([('add', 3), ('add', 8)],)), [2, '11/2', '25/2'])\ncheck('regression 9', solve(*([('add', 1), ('add', 6), ('add', 9), ('remove', 1)],)), [2, '15/2', '9/2'])\ncheck(\"variable removal\",solve([(\"add\",0),(\"add\",N),(\"add\",3*N),(\"remove\",N)]),[2,str(Fraction(3*N,2)),str(Fraction(9*N*N,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":"9912630ce38877ebeb866dc66d88d9de23c9ff3b06d5594cd7691b761a467039","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    n=0\n    mean=m2=Fraction(0)\n    for op,x in events:\n        if op==\"add\":\n            new_n=n+1\n            delta=x-mean\n            new_mean=mean+delta/new_n\n            m2+=delta*delta\n            mean=new_mean\n            n=new_n\n        else:\n            new_n=n-1\n            if new_n==0:\n                n=0\n                mean=m2=Fraction(0)\n                continue\n            new_mean=(n*mean-x)/new_n\n            m2-=(x-mean)*(x-new_mean)\n            mean=new_mean\n            n=new_n\n    return [n,str(mean),str(m2)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([('add', -3), ('add', 8), ('remove', -3)],)), [1, '8', '0'])\ncheck('regression 2', solve(*([('add', 6), ('remove', 6)],)), [0, '0', '0'])\ncheck('regression 3', solve(*([('add', 1), ('add', 4), ('add', 8), ('remove', 4)],)), [2, '9/2', '49/2'])\ncheck('regression 4', solve(*([('add', -5), ('remove', -5), ('add', 9)],)), [1, '9', '0'])\ncheck('regression 5', solve(*([],)), [0, '0', '0'])\ncheck('regression 6', solve(*([('add', 2), ('add', 2), ('remove', 2)],)), [1, '2', '0'])\ncheck('regression 7', solve(*([('add', 0), ('add', 4), ('add', 9), ('add', -1), ('remove', 0), ('remove', 9)],)), [2, '3/2', '25/2'])\ncheck('regression 8', solve(*([('add', 3), ('add', 8)],)), [2, '11/2', '25/2'])\ncheck('regression 9', solve(*([('add', 1), ('add', 6), ('add', 9), ('remove', 1)],)), [2, '15/2', '9/2'])\ncheck(\"variable removal\",solve([(\"add\",0),(\"add\",N),(\"add\",3*N),(\"remove\",N)]),[2,str(Fraction(3*N,2)),str(Fraction(9*N*N,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"},"fixed":{"sha256":"934603062c82331399a360a442923d58c38e14789ee6f7fbc7fe7e8ec85b9813","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    n=0\n    mean=m2=Fraction(0)\n    for op,x in events:\n        if op==\"add\":\n            new_n=n+1\n            delta=x-mean\n            new_mean=mean+delta/new_n\n            m2+=delta*(x-new_mean)\n            mean=new_mean\n            n=new_n\n        else:\n            new_n=n-1\n            if new_n==0:\n                n=0\n                mean=m2=Fraction(0)\n                continue\n            new_mean=(n*mean-x)/new_n\n            m2-=(x-mean)*(x-new_mean)\n            mean=new_mean\n            n=new_n\n    return [n,str(mean),str(m2)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([('add', -3), ('add', 8), ('remove', -3)],)), [1, '8', '0'])\ncheck('regression 2', solve(*([('add', 6), ('remove', 6)],)), [0, '0', '0'])\ncheck('regression 3', solve(*([('add', 1), ('add', 4), ('add', 8), ('remove', 4)],)), [2, '9/2', '49/2'])\ncheck('regression 4', solve(*([('add', -5), ('remove', -5), ('add', 9)],)), [1, '9', '0'])\ncheck('regression 5', solve(*([],)), [0, '0', '0'])\ncheck('regression 6', solve(*([('add', 2), ('add', 2), ('remove', 2)],)), [1, '2', '0'])\ncheck('regression 7', solve(*([('add', 0), ('add', 4), ('add', 9), ('add', -1), ('remove', 0), ('remove', 9)],)), [2, '3/2', '25/2'])\ncheck('regression 8', solve(*([('add', 3), ('add', 8)],)), [2, '11/2', '25/2'])\ncheck('regression 9', solve(*([('add', 1), ('add', 6), ('add', 9), ('remove', 1)],)), [2, '15/2', '9/2'])\ncheck(\"variable removal\",solve([(\"add\",0),(\"add\",N),(\"add\",3*N),(\"remove\",N)]),[2,str(Fraction(3*N,2)),str(Fraction(9*N*N,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":"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-central-summary-add-old-center-square","generated_at":"2026-09-29T14:39:07.240542+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 central summary contract at the identified reduction decision.","root_cause":"Insertion squares the old-center residual instead of multiplying old and new residuals.","sha256":"08e4bab9c7b36bff1fc596943ff783c8d2b5e06de625635cae1a5e3208bbffdf","title":"Retractable central summary: Insertion squares the old-center residual instead of multiplying old and new residuals. · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":46.399,"exit_code":1,"observations":[{"actual":[1,"8","-121/4"],"check":"regression 1","expected":[1,"8","0"],"passed":false},{"actual":[0,"0","0"],"check":"regression 2","expected":[0,"0","0"],"passed":true},{"actual":[2,"9/2","559/36"],"check":"regression 3","expected":[2,"9/2","49/2"],"passed":false},{"actual":[1,"9","0"],"check":"regression 4","expected":[1,"9","0"],"passed":true},{"actual":[0,"0","0"],"check":"regression 5","expected":[0,"0","0"],"passed":true},{"actual":[1,"2","0"],"check":"regression 6","expected":[1,"2","0"],"passed":true},{"actual":[2,"3/2","-139/18"],"check":"regression 7","expected":[2,"3/2","25/2"],"passed":false},{"actual":[2,"11/2","25/4"],"check":"regression 8","expected":[2,"11/2","25/2"],"passed":false},{"actual":[2,"15/2","-305/36"],"check":"regression 9","expected":[2,"15/2","9/2"],"passed":false},{"actual":[2,"3/2","103/36"],"check":"variable removal","expected":[2,"3/2","9/2"],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [1, \"8\", \"-121/4\"], \"expected\": [1, \"8\", \"0\"], \"passed\": false}, {\"check\": \"regression 2\", \"actual\": [0, \"0\", \"0\"], \"expected\": [0, \"0\", \"0\"], \"passed\": true}, {\"check\": \"regression 3\", \"actual\": [2, \"9/2\", \"559/36\"], \"expected\": [2, \"9/2\", \"49/2\"], \"passed\": false}, {\"check\": \"regression 4\", \"actual\": [1, \"9\", \"0\"], \"expected\": [1, \"9\", \"0\"], \"passed\": true}, {\"check\": \"regression 5\", \"actual\": [0, \"0\", \"0\"], \"expected\": [0, \"0\", \"0\"], \"passed\": true}, {\"check\": \"regression 6\", \"actual\": [1, \"2\", \"0\"], \"expected\": [1, \"2\", \"0\"], \"passed\": true}, {\"check\": \"regression 7\", \"actual\": [2, \"3/2\", \"-139/18\"], \"expected\": [2, \"3/2\", \"25/2\"], \"passed\": false}, {\"check\": \"regression 8\", \"actual\": [2, \"11/2\", \"25/4\"], \"expected\": [2, \"11/2\", \"25/2\"], \"passed\": false}, {\"check\": \"regression 9\", \"actual\": [2, \"15/2\", \"-305/36\"], \"expected\": [2, \"15/2\", \"9/2\"], \"passed\": false}, {\"check\": \"variable removal\", \"actual\": [2, \"3/2\", \"103/36\"], \"expected\": [2, \"3/2\", \"9/2\"], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.967,"exit_code":1,"observations":[{"actual":[1,"8","139/2"],"check":"regression 1","expected":[1,"8","0"],"passed":false},{"actual":[0,"0","0"],"check":"regression 2","expected":[0,"0","0"],"passed":true},{"actual":[2,"9/2","481/12"],"check":"regression 3","expected":[2,"9/2","49/2"],"passed":false},{"actual":[1,"9","81"],"check":"regression 4","expected":[1,"9","0"],"passed":false},{"actual":[0,"0","0"],"check":"regression 5","expected":[0,"0","0"],"passed":true},{"actual":[1,"2","4"],"check":"regression 6","expected":[1,"2","0"],"passed":false},{"actual":[2,"3/2","791/18"],"check":"regression 7","expected":[2,"3/2","25/2"],"passed":false},{"actual":[2,"11/2","34"],"check":"regression 8","expected":[2,"11/2","25/2"],"passed":false},{"actual":[2,"15/2","337/12"],"check":"regression 9","expected":[2,"15/2","9/2"],"passed":false},{"actual":[2,"3/2","85/12"],"check":"variable removal","expected":[2,"3/2","9/2"],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [1, \"8\", \"139/2\"], \"expected\": [1, \"8\", \"0\"], \"passed\": false}, {\"check\": \"regression 2\", \"actual\": [0, \"0\", \"0\"], \"expected\": [0, \"0\", \"0\"], \"passed\": true}, {\"check\": \"regression 3\", \"actual\": [2, \"9/2\", \"481/12\"], \"expected\": [2, \"9/2\", \"49/2\"], \"passed\": false}, {\"check\": \"regression 4\", \"actual\": [1, \"9\", \"81\"], \"expected\": [1, \"9\", \"0\"], \"passed\": false}, {\"check\": \"regression 5\", \"actual\": [0, \"0\", \"0\"], \"expected\": [0, \"0\", \"0\"], \"passed\": true}, {\"check\": \"regression 6\", \"actual\": [1, \"2\", \"4\"], \"expected\": [1, \"2\", \"0\"], \"passed\": false}, {\"check\": \"regression 7\", \"actual\": [2, \"3/2\", \"791/18\"], \"expected\": [2, \"3/2\", \"25/2\"], \"passed\": false}, {\"check\": \"regression 8\", \"actual\": [2, \"11/2\", \"34\"], \"expected\": [2, \"11/2\", \"25/2\"], \"passed\": false}, {\"check\": \"regression 9\", \"actual\": [2, \"15/2\", \"337/12\"], \"expected\": [2, \"15/2\", \"9/2\"], \"passed\": false}, {\"check\": \"variable removal\", \"actual\": [2, \"3/2\", \"85/12\"], \"expected\": [2, \"3/2\", \"9/2\"], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":45.027,"exit_code":0,"observations":[{"actual":[1,"8","0"],"check":"regression 1","expected":[1,"8","0"],"passed":true},{"actual":[0,"0","0"],"check":"regression 2","expected":[0,"0","0"],"passed":true},{"actual":[2,"9/2","49/2"],"check":"regression 3","expected":[2,"9/2","49/2"],"passed":true},{"actual":[1,"9","0"],"check":"regression 4","expected":[1,"9","0"],"passed":true},{"actual":[0,"0","0"],"check":"regression 5","expected":[0,"0","0"],"passed":true},{"actual":[1,"2","0"],"check":"regression 6","expected":[1,"2","0"],"passed":true},{"actual":[2,"3/2","25/2"],"check":"regression 7","expected":[2,"3/2","25/2"],"passed":true},{"actual":[2,"11/2","25/2"],"check":"regression 8","expected":[2,"11/2","25/2"],"passed":true},{"actual":[2,"15/2","9/2"],"check":"regression 9","expected":[2,"15/2","9/2"],"passed":true},{"actual":[2,"3/2","9/2"],"check":"variable removal","expected":[2,"3/2","9/2"],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [1, \"8\", \"0\"], \"expected\": [1, \"8\", \"0\"], \"passed\": true}, {\"check\": \"regression 2\", \"actual\": [0, \"0\", \"0\"], \"expected\": [0, \"0\", \"0\"], \"passed\": true}, {\"check\": \"regression 3\", \"actual\": [2, \"9/2\", \"49/2\"], \"expected\": [2, \"9/2\", \"49/2\"], \"passed\": true}, {\"check\": \"regression 4\", \"actual\": [1, \"9\", \"0\"], \"expected\": [1, \"9\", \"0\"], \"passed\": true}, {\"check\": \"regression 5\", \"actual\": [0, \"0\", \"0\"], \"expected\": [0, \"0\", \"0\"], \"passed\": true}, {\"check\": \"regression 6\", \"actual\": [1, \"2\", \"0\"], \"expected\": [1, \"2\", \"0\"], \"passed\": true}, {\"check\": \"regression 7\", \"actual\": [2, \"3/2\", \"25/2\"], \"expected\": [2, \"3/2\", \"25/2\"], \"passed\": true}, {\"check\": \"regression 8\", \"actual\": [2, \"11/2\", \"25/2\"], \"expected\": [2, \"11/2\", \"25/2\"], \"passed\": true}, {\"check\": \"regression 9\", \"actual\": [2, \"15/2\", \"9/2\"], \"expected\": [2, \"15/2\", \"9/2\"], \"passed\": true}, {\"check\": \"variable removal\", \"actual\": [2, \"3/2\", \"9/2\"], \"expected\": [2, \"3/2\", \"9/2\"], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}