{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":9,"contract":"Merge ordered disjoint integer blocks, preserving concatenation order. Return [total, maximum prefix sum, maximum suffix sum, maximum contiguous subarray sum]; empty subarrays are allowed and have sum zero.","contract_signature":"blocks","evaluation_group":"s3-na-maximum-subarray-block-summary","failed_approach":"The incoming best subarray may stop before the global right edge.","family":"s3-numerical-aggregation-maximum-subarray-block-summary-suffix-carry","id":"FA-13186","implementations":{"attempt":{"sha256":"48d8cc58bbd020b44d03b554669c2e50bb57378ad9e6d90d7b141541d7feb6e1","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):\n    total=prefix=suffix=best=0\n    for block in blocks:\n        t=sum(block)\n        p=max([0]+[sum(block[:i]) for i in range(1,len(block)+1)])\n        s=max([0]+[sum(block[i:]) for i in range(len(block))])\n        b=max([0]+[sum(block[i:j]) for i in range(len(block)) for j in range(i+1,len(block)+1)])\n        new_best=max(best,b,suffix+p)\n        new_prefix=max(prefix,total+p)\n        new_suffix=max(s,suffix+b)\n        total=total+t\n        prefix,suffix,best=new_prefix,new_suffix,new_best\n    return [total,prefix,suffix,best]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[-100, 5]],)), [-95, 0, 5, 5])\ncheck('regression 2', solve(*([[2, -7, 4], [3, -1]],)), [1, 2, 6, 7])\ncheck('regression 3', solve(*([[-8, -2], [-3]],)), [-13, 0, 0, 0])\ncheck('regression 4', solve(*([],)), [0, 0, 0, 0])\ncheck('regression 5', solve(*([[4, -2], [], [3, -9, 6]],)), [2, 5, 6, 6])\ncheck('regression 6', solve(*([[-2, 7], [-3, 5, -9], [2]],)), [0, 7, 2, 9])\ncheck('regression 7', solve(*([[8, -9], [1, -4, 9]],)), [5, 8, 9, 9])\ncheck('regression 8', solve(*([[1, 2], [3, 4]],)), [10, 10, 10, 10])\ncheck(\"variable cross block peak\",solve([[-N,2*N],[N,-4*N]]),[-2*N,2*N,0,3*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":"ab533d053bcbf4e6aa91ffd2f11b09021b78b89a75aad1e321594a454334a075","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):\n    total=prefix=suffix=best=0\n    for block in blocks:\n        t=sum(block)\n        p=max([0]+[sum(block[:i]) for i in range(1,len(block)+1)])\n        s=max([0]+[sum(block[i:]) for i in range(len(block))])\n        b=max([0]+[sum(block[i:j]) for i in range(len(block)) for j in range(i+1,len(block)+1)])\n        new_best=max(best,b,suffix+p)\n        new_prefix=max(prefix,total+p)\n        new_suffix=max(s,suffix+p)\n        total=total+t\n        prefix,suffix,best=new_prefix,new_suffix,new_best\n    return [total,prefix,suffix,best]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[-100, 5]],)), [-95, 0, 5, 5])\ncheck('regression 2', solve(*([[2, -7, 4], [3, -1]],)), [1, 2, 6, 7])\ncheck('regression 3', solve(*([[-8, -2], [-3]],)), [-13, 0, 0, 0])\ncheck('regression 4', solve(*([],)), [0, 0, 0, 0])\ncheck('regression 5', solve(*([[4, -2], [], [3, -9, 6]],)), [2, 5, 6, 6])\ncheck('regression 6', solve(*([[-2, 7], [-3, 5, -9], [2]],)), [0, 7, 2, 9])\ncheck('regression 7', solve(*([[8, -9], [1, -4, 9]],)), [5, 8, 9, 9])\ncheck('regression 8', solve(*([[1, 2], [3, 4]],)), [10, 10, 10, 10])\ncheck(\"variable cross block peak\",solve([[-N,2*N],[N,-4*N]]),[-2*N,2*N,0,3*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-maximum-subarray-block-summary-suffix-carry","generated_at":"2026-09-29T14:39:04.617375+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":"Extending a suffix adds incoming prefix instead of its entire total.","sha256":"704f2ec881737362bfcb28dead5afbb6037523117bba7985b6452720cbdf5993","title":"Maximum subarray block summary: Extending a suffix adds incoming prefix instead of its entire total. · 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":45.839,"exit_code":1,"observations":[{"actual":[-95,0,5,5],"check":"regression 1","expected":[-95,0,5,5],"passed":true},{"actual":[1,2,7,7],"check":"regression 2","expected":[1,2,6,7],"passed":false},{"actual":[-13,0,0,0],"check":"regression 3","expected":[-13,0,0,0],"passed":true},{"actual":[0,0,0,0],"check":"regression 4","expected":[0,0,0,0],"passed":true},{"actual":[2,5,10,7],"check":"regression 5","expected":[2,5,6,6],"passed":false},{"actual":[0,7,14,14],"check":"regression 6","expected":[0,7,2,9],"passed":false},{"actual":[5,8,17,14],"check":"regression 7","expected":[5,8,9,9],"passed":false},{"actual":[10,10,10,10],"check":"regression 8","expected":[10,10,10,10],"passed":true},{"actual":[-2,2,3,3],"check":"variable cross block peak","expected":[-2,2,0,3],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [-95, 0, 5, 5], \"expected\": [-95, 0, 5, 5], \"passed\": true}, {\"check\": \"regression 2\", \"actual\": [1, 2, 7, 7], \"expected\": [1, 2, 6, 7], \"passed\": false}, {\"check\": \"regression 3\", \"actual\": [-13, 0, 0, 0], \"expected\": [-13, 0, 0, 0], \"passed\": true}, {\"check\": \"regression 4\", \"actual\": [0, 0, 0, 0], \"expected\": [0, 0, 0, 0], \"passed\": true}, {\"check\": \"regression 5\", \"actual\": [2, 5, 10, 7], \"expected\": [2, 5, 6, 6], \"passed\": false}, {\"check\": \"regression 6\", \"actual\": [0, 7, 14, 14], \"expected\": [0, 7, 2, 9], \"passed\": false}, {\"check\": \"regression 7\", \"actual\": [5, 8, 17, 14], \"expected\": [5, 8, 9, 9], \"passed\": false}, {\"check\": \"regression 8\", \"actual\": [10, 10, 10, 10], \"expected\": [10, 10, 10, 10], \"passed\": true}, {\"check\": \"variable cross block peak\", \"actual\": [-2, 2, 3, 3], \"expected\": [-2, 2, 0, 3], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.314,"exit_code":1,"observations":[{"actual":[-95,0,5,5],"check":"regression 1","expected":[-95,0,5,5],"passed":true},{"actual":[1,2,7,7],"check":"regression 2","expected":[1,2,6,7],"passed":false},{"actual":[-13,0,0,0],"check":"regression 3","expected":[-13,0,0,0],"passed":true},{"actual":[0,0,0,0],"check":"regression 4","expected":[0,0,0,0],"passed":true},{"actual":[2,5,7,7],"check":"regression 5","expected":[2,5,6,6],"passed":false},{"actual":[0,7,11,11],"check":"regression 6","expected":[0,7,2,9],"passed":false},{"actual":[5,8,14,14],"check":"regression 7","expected":[5,8,9,9],"passed":false},{"actual":[10,10,10,10],"check":"regression 8","expected":[10,10,10,10],"passed":true},{"actual":[-2,2,3,3],"check":"variable cross block peak","expected":[-2,2,0,3],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [-95, 0, 5, 5], \"expected\": [-95, 0, 5, 5], \"passed\": true}, {\"check\": \"regression 2\", \"actual\": [1, 2, 7, 7], \"expected\": [1, 2, 6, 7], \"passed\": false}, {\"check\": \"regression 3\", \"actual\": [-13, 0, 0, 0], \"expected\": [-13, 0, 0, 0], \"passed\": true}, {\"check\": \"regression 4\", \"actual\": [0, 0, 0, 0], \"expected\": [0, 0, 0, 0], \"passed\": true}, {\"check\": \"regression 5\", \"actual\": [2, 5, 7, 7], \"expected\": [2, 5, 6, 6], \"passed\": false}, {\"check\": \"regression 6\", \"actual\": [0, 7, 11, 11], \"expected\": [0, 7, 2, 9], \"passed\": false}, {\"check\": \"regression 7\", \"actual\": [5, 8, 14, 14], \"expected\": [5, 8, 9, 9], \"passed\": false}, {\"check\": \"regression 8\", \"actual\": [10, 10, 10, 10], \"expected\": [10, 10, 10, 10], \"passed\": true}, {\"check\": \"variable cross block peak\", \"actual\": [-2, 2, 3, 3], \"expected\": [-2, 2, 0, 3], \"passed\": false}], \"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."}}