{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":7,"contract":"A stipulated nonnegative weighted count-min table has exactly three independent rows of positive width, with bucket functions k%w,(3*k+1)%w,(k//w)%w for nonnegative integer keys. Add all block contributions, then estimate each query by the minimum of its three cells. Return [table,estimates]; no probabilistic error guarantee is claimed.","evaluation_group":"s3-na-three-row-count-sketch","failed_approach":"Copying only one row leaves two hash accumulators aliased.","family":"s3-numerical-aggregation-three-row-count-sketch-sketch-row-alias","id":"FA-14241","implementations":{"attempt":{"sha256":"f7b640b43a2762c69d1cc44f0a37fe130a93dd27ceb702e4dc248baae28486a0","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(blocks, width, queries):\n    shared=[0]*width\n    table=[shared,shared,list(shared)]\n    for block in blocks:\n        for key,weight in block:\n            buckets=[key%width,(3*key+1)%width,(key//width)%width]\n            for row,col in enumerate(buckets):\n                table[row][col]+=weight\n    estimates=[]\n    for key in queries:\n        buckets=[key%width,(3*key+1)%width,(key//width)%width]\n        estimates.append(min(table[row][col] for row,col in enumerate(buckets)))\n    return [table,estimates]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[(0, 2), (1, 3)], [(4, 1)]], 4, [0, 1, 4, 8])), [[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]])\ncheck('regression 2', solve(*([], 3, [0, 1])), [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]])\ncheck('regression 3', solve(*([[(2, 5)], [], [(2, 2)]], 3, [2, 5])), [[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]])\ncheck('regression 4', solve(*([[(0, 1), (0, 1)]], 1, [0, 3])), [[[2], [2], [2]], [2, 2]])\ncheck('regression 5', solve(*([[(7, 0), (2, 4), (5, 1)]], 4, [2, 5, 7])), [[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]])\ncheck('regression 6', solve(*([[(1, 2)], [(8, 5), (3, 4)]], 5, [1, 8, 3, 13])), [[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]])\ncheck(\"variable sketch contribution\",solve([[(0,N)]],2,[0]),[[[N,0],[0,N],[N,0]],[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":"6a593ba06a3097c5047f58bc5e6c2479bffe6305396cb2290436035289a8f20a","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(blocks, width, queries):\n    table=[[0]*width]*3\n    for block in blocks:\n        for key,weight in block:\n            buckets=[key%width,(3*key+1)%width,(key//width)%width]\n            for row,col in enumerate(buckets):\n                table[row][col]+=weight\n    estimates=[]\n    for key in queries:\n        buckets=[key%width,(3*key+1)%width,(key//width)%width]\n        estimates.append(min(table[row][col] for row,col in enumerate(buckets)))\n    return [table,estimates]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[(0, 2), (1, 3)], [(4, 1)]], 4, [0, 1, 4, 8])), [[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]])\ncheck('regression 2', solve(*([], 3, [0, 1])), [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]])\ncheck('regression 3', solve(*([[(2, 5)], [], [(2, 2)]], 3, [2, 5])), [[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]])\ncheck('regression 4', solve(*([[(0, 1), (0, 1)]], 1, [0, 3])), [[[2], [2], [2]], [2, 2]])\ncheck('regression 5', solve(*([[(7, 0), (2, 4), (5, 1)]], 4, [2, 5, 7])), [[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]])\ncheck('regression 6', solve(*([[(1, 2)], [(8, 5), (3, 4)]], 5, [1, 8, 3, 13])), [[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]])\ncheck(\"variable sketch contribution\",solve([[(0,N)]],2,[0]),[[[N,0],[0,N],[N,0]],[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":"c6d9eeecd646bee9d90bdbd7c194e3a43e64dc71d005356f968d60d9e621c585","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(blocks, width, queries):\n    table=[[0]*width for _ in range(3)]\n    for block in blocks:\n        for key,weight in block:\n            buckets=[key%width,(3*key+1)%width,(key//width)%width]\n            for row,col in enumerate(buckets):\n                table[row][col]+=weight\n    estimates=[]\n    for key in queries:\n        buckets=[key%width,(3*key+1)%width,(key//width)%width]\n        estimates.append(min(table[row][col] for row,col in enumerate(buckets)))\n    return [table,estimates]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[(0, 2), (1, 3)], [(4, 1)]], 4, [0, 1, 4, 8])), [[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]])\ncheck('regression 2', solve(*([], 3, [0, 1])), [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]])\ncheck('regression 3', solve(*([[(2, 5)], [], [(2, 2)]], 3, [2, 5])), [[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]])\ncheck('regression 4', solve(*([[(0, 1), (0, 1)]], 1, [0, 3])), [[[2], [2], [2]], [2, 2]])\ncheck('regression 5', solve(*([[(7, 0), (2, 4), (5, 1)]], 4, [2, 5, 7])), [[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]])\ncheck('regression 6', solve(*([[(1, 2)], [(8, 5), (3, 4)]], 5, [1, 8, 3, 13])), [[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]])\ncheck(\"variable sketch contribution\",solve([[(0,N)]],2,[0]),[[[N,0],[0,N],[N,0]],[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-three-row-count-sketch-sketch-row-alias","generated_at":"2026-09-29T14:39:15.028270+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 three row count sketch contract at the identified reduction decision.","root_cause":"All rows share the same mutable storage.","sha256":"66a0f30e258f68408cef5f85d4fff7b8492732f371f46e9d85c8f33c70e48d6b","title":"Three row count sketch: All rows share the same mutable storage. · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.455,"exit_code":1,"observations":[{"actual":[[[6,6,0,0],[6,6,0,0],[5,1,0,0]],[5,5,1,0]],"check":"regression 1","expected":[[[3,3,0,0],[3,3,0,0],[5,1,0,0]],[3,3,1,0]],"passed":false},{"actual":[[[0,0,0],[0,0,0],[0,0,0]],[0,0]],"check":"regression 2","expected":[[[0,0,0],[0,0,0],[0,0,0]],[0,0]],"passed":true},{"actual":[[[0,7,7],[0,7,7],[7,0,0]],[7,0]],"check":"regression 3","expected":[[[0,0,7],[0,7,0],[7,0,0]],[7,0]],"passed":false},{"actual":[[[4],[4],[2]],[2,2]],"check":"regression 4","expected":[[[2],[2],[2]],[2,2]],"passed":false},{"actual":[[[1,1,4,4],[1,1,4,4],[4,1,0,0]],[4,1,1]],"check":"regression 5","expected":[[[0,1,4,0],[1,0,0,4],[4,1,0,0]],[4,1,0]],"passed":false},{"actual":[[[9,2,0,9,2],[9,2,0,9,2],[6,5,0,0,0]],[2,5,6,0]],"check":"regression 6","expected":[[[0,2,0,9,0],[9,0,0,0,2],[6,5,0,0,0]],[2,5,6,0]],"passed":false},{"actual":[[[1,1],[1,1],[1,0]],[1]],"check":"variable sketch contribution","expected":[[[1,0],[0,1],[1,0]],[1]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [[[6, 6, 0, 0], [6, 6, 0, 0], [5, 1, 0, 0]], [5, 5, 1, 0]], \"expected\": [[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]], \"passed\": false}, {\"check\": \"regression 2\", \"actual\": [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]], \"expected\": [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]], \"passed\": true}, {\"check\": \"regression 3\", \"actual\": [[[0, 7, 7], [0, 7, 7], [7, 0, 0]], [7, 0]], \"expected\": [[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]], \"passed\": false}, {\"check\": \"regression 4\", \"actual\": [[[4], [4], [2]], [2, 2]], \"expected\": [[[2], [2], [2]], [2, 2]], \"passed\": false}, {\"check\": \"regression 5\", \"actual\": [[[1, 1, 4, 4], [1, 1, 4, 4], [4, 1, 0, 0]], [4, 1, 1]], \"expected\": [[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]], \"passed\": false}, {\"check\": \"regression 6\", \"actual\": [[[9, 2, 0, 9, 2], [9, 2, 0, 9, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]], \"expected\": [[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]], \"passed\": false}, {\"check\": \"variable sketch contribution\", \"actual\": [[[1, 1], [1, 1], [1, 0]], [1]], \"expected\": [[[1, 0], [0, 1], [1, 0]], [1]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.421,"exit_code":1,"observations":[{"actual":[[[11,7,0,0],[11,7,0,0],[11,7,0,0]],[7,7,7,0]],"check":"regression 1","expected":[[[3,3,0,0],[3,3,0,0],[5,1,0,0]],[3,3,1,0]],"passed":false},{"actual":[[[0,0,0],[0,0,0],[0,0,0]],[0,0]],"check":"regression 2","expected":[[[0,0,0],[0,0,0],[0,0,0]],[0,0]],"passed":true},{"actual":[[[7,7,7],[7,7,7],[7,7,7]],[7,7]],"check":"regression 3","expected":[[[0,0,7],[0,7,0],[7,0,0]],[7,0]],"passed":false},{"actual":[[[6],[6],[6]],[6,6]],"check":"regression 4","expected":[[[2],[2],[2]],[2,2]],"passed":false},{"actual":[[[5,2,4,4],[5,2,4,4],[5,2,4,4]],[4,2,2]],"check":"regression 5","expected":[[[0,1,4,0],[1,0,0,4],[4,1,0,0]],[4,1,0]],"passed":false},{"actual":[[[15,7,0,9,2],[15,7,0,9,2],[15,7,0,9,2]],[2,7,9,0]],"check":"regression 6","expected":[[[0,2,0,9,0],[9,0,0,0,2],[6,5,0,0,0]],[2,5,6,0]],"passed":false},{"actual":[[[2,1],[2,1],[2,1]],[1]],"check":"variable sketch contribution","expected":[[[1,0],[0,1],[1,0]],[1]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [[[11, 7, 0, 0], [11, 7, 0, 0], [11, 7, 0, 0]], [7, 7, 7, 0]], \"expected\": [[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]], \"passed\": false}, {\"check\": \"regression 2\", \"actual\": [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]], \"expected\": [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]], \"passed\": true}, {\"check\": \"regression 3\", \"actual\": [[[7, 7, 7], [7, 7, 7], [7, 7, 7]], [7, 7]], \"expected\": [[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]], \"passed\": false}, {\"check\": \"regression 4\", \"actual\": [[[6], [6], [6]], [6, 6]], \"expected\": [[[2], [2], [2]], [2, 2]], \"passed\": false}, {\"check\": \"regression 5\", \"actual\": [[[5, 2, 4, 4], [5, 2, 4, 4], [5, 2, 4, 4]], [4, 2, 2]], \"expected\": [[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]], \"passed\": false}, {\"check\": \"regression 6\", \"actual\": [[[15, 7, 0, 9, 2], [15, 7, 0, 9, 2], [15, 7, 0, 9, 2]], [2, 7, 9, 0]], \"expected\": [[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]], \"passed\": false}, {\"check\": \"variable sketch contribution\", \"actual\": [[[2, 1], [2, 1], [2, 1]], [1]], \"expected\": [[[1, 0], [0, 1], [1, 0]], [1]], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.823,"exit_code":0,"observations":[{"actual":[[[3,3,0,0],[3,3,0,0],[5,1,0,0]],[3,3,1,0]],"check":"regression 1","expected":[[[3,3,0,0],[3,3,0,0],[5,1,0,0]],[3,3,1,0]],"passed":true},{"actual":[[[0,0,0],[0,0,0],[0,0,0]],[0,0]],"check":"regression 2","expected":[[[0,0,0],[0,0,0],[0,0,0]],[0,0]],"passed":true},{"actual":[[[0,0,7],[0,7,0],[7,0,0]],[7,0]],"check":"regression 3","expected":[[[0,0,7],[0,7,0],[7,0,0]],[7,0]],"passed":true},{"actual":[[[2],[2],[2]],[2,2]],"check":"regression 4","expected":[[[2],[2],[2]],[2,2]],"passed":true},{"actual":[[[0,1,4,0],[1,0,0,4],[4,1,0,0]],[4,1,0]],"check":"regression 5","expected":[[[0,1,4,0],[1,0,0,4],[4,1,0,0]],[4,1,0]],"passed":true},{"actual":[[[0,2,0,9,0],[9,0,0,0,2],[6,5,0,0,0]],[2,5,6,0]],"check":"regression 6","expected":[[[0,2,0,9,0],[9,0,0,0,2],[6,5,0,0,0]],[2,5,6,0]],"passed":true},{"actual":[[[1,0],[0,1],[1,0]],[1]],"check":"variable sketch contribution","expected":[[[1,0],[0,1],[1,0]],[1]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]], \"expected\": [[[3, 3, 0, 0], [3, 3, 0, 0], [5, 1, 0, 0]], [3, 3, 1, 0]], \"passed\": true}, {\"check\": \"regression 2\", \"actual\": [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]], \"expected\": [[[0, 0, 0], [0, 0, 0], [0, 0, 0]], [0, 0]], \"passed\": true}, {\"check\": \"regression 3\", \"actual\": [[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]], \"expected\": [[[0, 0, 7], [0, 7, 0], [7, 0, 0]], [7, 0]], \"passed\": true}, {\"check\": \"regression 4\", \"actual\": [[[2], [2], [2]], [2, 2]], \"expected\": [[[2], [2], [2]], [2, 2]], \"passed\": true}, {\"check\": \"regression 5\", \"actual\": [[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]], \"expected\": [[[0, 1, 4, 0], [1, 0, 0, 4], [4, 1, 0, 0]], [4, 1, 0]], \"passed\": true}, {\"check\": \"regression 6\", \"actual\": [[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]], \"expected\": [[[0, 2, 0, 9, 0], [9, 0, 0, 0, 2], [6, 5, 0, 0, 0]], [2, 5, 6, 0]], \"passed\": true}, {\"check\": \"variable sketch contribution\", \"actual\": [[[1, 0], [0, 1], [1, 0]], [1]], \"expected\": [[[1, 0], [0, 1], [1, 0]], [1]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}