{"abstract":"Interval widths are assumed to be one.","category":"Discrete calculus","checks":4,"contract":"Integer sample values and compatible sample-array lengths. Rational results are reduced Fraction strings; spacing is positive unless explicitly stated otherwise. x has distinct ordered coordinates and matches y; descending x yields negative integral. Exact operational definition: str(sum((Fraction((b-a)*(v+u),2) for a,b,u,v in zip(x,x[1:],y,y[1:])),Fraction()))","evaluation_group":"model-7d8ac29d1ad1dce8","failed_approach":"Left endpoint values replace linear interpolation across each interval.","family":"xn-trapezoidal-integral-nonuniform-grid","id":"FA-6376","implementations":{"attempt":{"sha256":"b1d2605c9fbf02602a9f0e46754b4526a186d4f49cbb177b54c68f07e0c41c0d","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(x, y):\n    return str(sum((Fraction((b-a)*u) for a,b,u in zip(x,x[1:],y)),Fraction()))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 1, 3], [0, 2, 2])', solve(*([0, 1, 3], [0, 2, 2])), '5')\ncheck('fixture 2: ([0, 2], [1, 3])', solve(*([0, 2], [1, 3])), '4')\ncheck('fixture 3: ([2, 0], [3, 1])', solve(*([2, 0], [3, 1])), '-4')\ncheck('fixture 4: ([1], [4])', solve(*([1], [4])), '0')\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":"0457a57a58a028800e5f26e99301c330de7311aaf0b1c50eceddc20d36b98e03","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(x, y):\n    return str(sum((Fraction(u+v,2) for u,v in zip(y,y[1:])),Fraction()))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 1, 3], [0, 2, 2])', solve(*([0, 1, 3], [0, 2, 2])), '5')\ncheck('fixture 2: ([0, 2], [1, 3])', solve(*([0, 2], [1, 3])), '4')\ncheck('fixture 3: ([2, 0], [3, 1])', solve(*([2, 0], [3, 1])), '-4')\ncheck('fixture 4: ([1], [4])', solve(*([1], [4])), '0')\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":"6bbbfd298d5b515c531a7c6c29fd60cc81030e1e9b85e5dd1c63f825e263cc9e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(x, y):\n    return str(sum((Fraction((b-a)*(v+u),2) for a,b,u,v in zip(x,x[1:],y,y[1:])),Fraction()))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 1, 3], [0, 2, 2])', solve(*([0, 1, 3], [0, 2, 2])), '5')\ncheck('fixture 2: ([0, 2], [1, 3])', solve(*([0, 2], [1, 3])), '4')\ncheck('fixture 3: ([2, 0], [3, 1])', solve(*([2, 0], [3, 1])), '-4')\ncheck('fixture 4: ([1], [4])', solve(*([1], [4])), '0')\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":" 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":"xn-trapezoidal-integral-nonuniform-grid","generated_at":"2026-09-29T14:38:00.993738+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Discrete calculus results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return str(sum((Fraction((b-a)*(v+u),2) for a,b,u,v in zip(x,x[1:],y,y[1:])),Fraction()))","root_cause":"Interval widths are assumed to be one.","sha256":"3732ae6db1e15927cb410a2cbd48e14577ec0ad564281b4684bc726951f9987c","title":"Trapezoidal integral nonuniform grid · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":48.939,"exit_code":1,"observations":[{"actual":"4","check":"fixture 1: ([0, 1, 3], [0, 2, 2])","expected":"5","passed":false},{"actual":"2","check":"fixture 2: ([0, 2], [1, 3])","expected":"4","passed":false},{"actual":"-6","check":"fixture 3: ([2, 0], [3, 1])","expected":"-4","passed":false},{"actual":"0","check":"fixture 4: ([1], [4])","expected":"0","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 1, 3], [0, 2, 2])\", \"actual\": \"4\", \"expected\": \"5\", \"passed\": false}, {\"check\": \"fixture 2: ([0, 2], [1, 3])\", \"actual\": \"2\", \"expected\": \"4\", \"passed\": false}, {\"check\": \"fixture 3: ([2, 0], [3, 1])\", \"actual\": \"-6\", \"expected\": \"-4\", \"passed\": false}, {\"check\": \"fixture 4: ([1], [4])\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.62,"exit_code":1,"observations":[{"actual":"3","check":"fixture 1: ([0, 1, 3], [0, 2, 2])","expected":"5","passed":false},{"actual":"2","check":"fixture 2: ([0, 2], [1, 3])","expected":"4","passed":false},{"actual":"2","check":"fixture 3: ([2, 0], [3, 1])","expected":"-4","passed":false},{"actual":"0","check":"fixture 4: ([1], [4])","expected":"0","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 1, 3], [0, 2, 2])\", \"actual\": \"3\", \"expected\": \"5\", \"passed\": false}, {\"check\": \"fixture 2: ([0, 2], [1, 3])\", \"actual\": \"2\", \"expected\": \"4\", \"passed\": false}, {\"check\": \"fixture 3: ([2, 0], [3, 1])\", \"actual\": \"2\", \"expected\": \"-4\", \"passed\": false}, {\"check\": \"fixture 4: ([1], [4])\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":135.063,"exit_code":0,"observations":[{"actual":"5","check":"fixture 1: ([0, 1, 3], [0, 2, 2])","expected":"5","passed":true},{"actual":"4","check":"fixture 2: ([0, 2], [1, 3])","expected":"4","passed":true},{"actual":"-4","check":"fixture 3: ([2, 0], [3, 1])","expected":"-4","passed":true},{"actual":"0","check":"fixture 4: ([1], [4])","expected":"0","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 1, 3], [0, 2, 2])\", \"actual\": \"5\", \"expected\": \"5\", \"passed\": true}, {\"check\": \"fixture 2: ([0, 2], [1, 3])\", \"actual\": \"4\", \"expected\": \"4\", \"passed\": true}, {\"check\": \"fixture 3: ([2, 0], [3, 1])\", \"actual\": \"-4\", \"expected\": \"-4\", \"passed\": true}, {\"check\": \"fixture 4: ([1], [4])\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}