{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":8,"contract":"For positive integer width, partition numeric observations into consecutive buckets including a final short bucket. Emit each bucket first-occurring minimum and first-occurring maximum once, in original observation order, as [global index,value]. Flat buckets emit one point.","contract_signature":"xs, width","evaluation_group":"s3-na-bucket-extrema-downsampling","failed_approach":"Magnitude maximization selects a large negative trough instead of a numerical maximum.","family":"s3-numerical-aggregation-bucket-extrema-downsampling-extrema-last-maximum","id":"FA-14031","implementations":{"attempt":{"sha256":"9f61f54377db9b7442f9b4bd014edabcbe24bad915baaafff279b4f110bb5c86","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, width):\n    out=[]\n    for start in range(0,len(xs),width):\n        bucket=xs[start:start+width]\n        low=min(range(len(bucket)),key=lambda i:(bucket[i],i))\n        high=max(range(len(bucket)),key=lambda i:(abs(bucket[i]),-i))\n        for i in sorted(set([low,high])):\n            out.append([start+i,bucket[i]])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([8, 1, 6, 2, 9, 3, 4], 3)), [[0, 8], [1, 1], [3, 2], [4, 9], [6, 4]])\ncheck('regression 2', solve(*([], 2)), [])\ncheck('regression 3', solve(*([3, 3, 3, 1, 1], 3)), [[0, 3], [3, 1]])\ncheck('regression 4', solve(*([-4, -1, -8, 0], 2)), [[0, -4], [1, -1], [2, -8], [3, 0]])\ncheck('regression 5', solve(*([9, 1, 5], 1)), [[0, 9], [1, 1], [2, 5]])\ncheck('regression 6', solve(*([4, 2, 8, 3], 9)), [[1, 2], [2, 8]])\ncheck('regression 7', solve(*([5, 5, 1, 1, 9, 9], 6)), [[2, 1], [4, 9]])\ncheck(\"variable bucket amplitude\",solve([N,0,2*N],3),[[1,0],[2,2*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":"15e91aeaf4764850992dccd466f3b43601b8f24faa9b0696e520fda19e2a963d","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, width):\n    out=[]\n    for start in range(0,len(xs),width):\n        bucket=xs[start:start+width]\n        low=min(range(len(bucket)),key=lambda i:(bucket[i],i))\n        high=max(range(len(bucket)),key=lambda i:(bucket[i],i))\n        for i in sorted(set([low,high])):\n            out.append([start+i,bucket[i]])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([8, 1, 6, 2, 9, 3, 4], 3)), [[0, 8], [1, 1], [3, 2], [4, 9], [6, 4]])\ncheck('regression 2', solve(*([], 2)), [])\ncheck('regression 3', solve(*([3, 3, 3, 1, 1], 3)), [[0, 3], [3, 1]])\ncheck('regression 4', solve(*([-4, -1, -8, 0], 2)), [[0, -4], [1, -1], [2, -8], [3, 0]])\ncheck('regression 5', solve(*([9, 1, 5], 1)), [[0, 9], [1, 1], [2, 5]])\ncheck('regression 6', solve(*([4, 2, 8, 3], 9)), [[1, 2], [2, 8]])\ncheck('regression 7', solve(*([5, 5, 1, 1, 9, 9], 6)), [[2, 1], [4, 9]])\ncheck(\"variable bucket amplitude\",solve([N,0,2*N],3),[[1,0],[2,2*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-bucket-extrema-downsampling-extrema-last-maximum","generated_at":"2026-09-29T14:39:13.142290+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.","root_cause":"Equal maxima select the last occurrence.","sha256":"d85a5a9bb5d6814c01c9cc6ef0914a29eff559c8f85b8815d202196b9b0b9dba","title":"Bucket extrema downsampling: Equal maxima select the last occurrence. · 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":44.525,"exit_code":1,"observations":[{"actual":[[0,8],[1,1],[3,2],[4,9],[6,4]],"check":"regression 1","expected":[[0,8],[1,1],[3,2],[4,9],[6,4]],"passed":true},{"actual":[],"check":"regression 2","expected":[],"passed":true},{"actual":[[0,3],[3,1]],"check":"regression 3","expected":[[0,3],[3,1]],"passed":true},{"actual":[[0,-4],[2,-8]],"check":"regression 4","expected":[[0,-4],[1,-1],[2,-8],[3,0]],"passed":false},{"actual":[[0,9],[1,1],[2,5]],"check":"regression 5","expected":[[0,9],[1,1],[2,5]],"passed":true},{"actual":[[1,2],[2,8]],"check":"regression 6","expected":[[1,2],[2,8]],"passed":true},{"actual":[[2,1],[4,9]],"check":"regression 7","expected":[[2,1],[4,9]],"passed":true},{"actual":[[1,0],[2,2]],"check":"variable bucket amplitude","expected":[[1,0],[2,2]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [[0, 8], [1, 1], [3, 2], [4, 9], [6, 4]], \"expected\": [[0, 8], [1, 1], [3, 2], [4, 9], [6, 4]], \"passed\": true}, {\"check\": \"regression 2\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"regression 3\", \"actual\": [[0, 3], [3, 1]], \"expected\": [[0, 3], [3, 1]], \"passed\": true}, {\"check\": \"regression 4\", \"actual\": [[0, -4], [2, -8]], \"expected\": [[0, -4], [1, -1], [2, -8], [3, 0]], \"passed\": false}, {\"check\": \"regression 5\", \"actual\": [[0, 9], [1, 1], [2, 5]], \"expected\": [[0, 9], [1, 1], [2, 5]], \"passed\": true}, {\"check\": \"regression 6\", \"actual\": [[1, 2], [2, 8]], \"expected\": [[1, 2], [2, 8]], \"passed\": true}, {\"check\": \"regression 7\", \"actual\": [[2, 1], [4, 9]], \"expected\": [[2, 1], [4, 9]], \"passed\": true}, {\"check\": \"variable bucket amplitude\", \"actual\": [[1, 0], [2, 2]], \"expected\": [[1, 0], [2, 2]], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.096,"exit_code":1,"observations":[{"actual":[[0,8],[1,1],[3,2],[4,9],[6,4]],"check":"regression 1","expected":[[0,8],[1,1],[3,2],[4,9],[6,4]],"passed":true},{"actual":[],"check":"regression 2","expected":[],"passed":true},{"actual":[[0,3],[2,3],[3,1],[4,1]],"check":"regression 3","expected":[[0,3],[3,1]],"passed":false},{"actual":[[0,-4],[1,-1],[2,-8],[3,0]],"check":"regression 4","expected":[[0,-4],[1,-1],[2,-8],[3,0]],"passed":true},{"actual":[[0,9],[1,1],[2,5]],"check":"regression 5","expected":[[0,9],[1,1],[2,5]],"passed":true},{"actual":[[1,2],[2,8]],"check":"regression 6","expected":[[1,2],[2,8]],"passed":true},{"actual":[[2,1],[5,9]],"check":"regression 7","expected":[[2,1],[4,9]],"passed":false},{"actual":[[1,0],[2,2]],"check":"variable bucket amplitude","expected":[[1,0],[2,2]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [[0, 8], [1, 1], [3, 2], [4, 9], [6, 4]], \"expected\": [[0, 8], [1, 1], [3, 2], [4, 9], [6, 4]], \"passed\": true}, {\"check\": \"regression 2\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"regression 3\", \"actual\": [[0, 3], [2, 3], [3, 1], [4, 1]], \"expected\": [[0, 3], [3, 1]], \"passed\": false}, {\"check\": \"regression 4\", \"actual\": [[0, -4], [1, -1], [2, -8], [3, 0]], \"expected\": [[0, -4], [1, -1], [2, -8], [3, 0]], \"passed\": true}, {\"check\": \"regression 5\", \"actual\": [[0, 9], [1, 1], [2, 5]], \"expected\": [[0, 9], [1, 1], [2, 5]], \"passed\": true}, {\"check\": \"regression 6\", \"actual\": [[1, 2], [2, 8]], \"expected\": [[1, 2], [2, 8]], \"passed\": true}, {\"check\": \"regression 7\", \"actual\": [[2, 1], [5, 9]], \"expected\": [[2, 1], [4, 9]], \"passed\": false}, {\"check\": \"variable bucket amplitude\", \"actual\": [[1, 0], [2, 2]], \"expected\": [[1, 0], [2, 2]], \"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."}}