{"abstract":"Trapezoidal weights replace the quadratic-exact Simpson weights.","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. y0,y1,y2 are equally spaced samples separated by h>0; integrate over a span of 2*h. Exact operational definition: str(Fraction(h*(y0+4*y1+y2),3))","evaluation_group":"model-ac0ff3afdae412ad","failed_approach":"The center weight and two-interval span are lost.","family":"xn-simpson-three-point-integral","id":"FA-6381","implementations":{"attempt":{"sha256":"9a6e652a8d1a89304d558ff4a0dc3107a50e3d96c3991729fd4d86158a8ac576","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(y0, y1, y2, h):\n    return str(Fraction(h*(y0+y1+y2),3))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0, 1, 4, 1)', solve(*(0, 1, 4, 1)), '8/3')\ncheck('fixture 2: (3, 3, 3, 1)', solve(*(3, 3, 3, 1)), '6')\ncheck('fixture 3: (1, 0, 1, 2)', solve(*(1, 0, 1, 2)), '4/3')\ncheck('fixture 4: (0, 0, 0, 1)', solve(*(0, 0, 0, 1)), '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":"5b958920e0f71fc77305018938c18efe57e9fe8150610dc9b48e4b8a3473c8f5","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(y0, y1, y2, h):\n    return str(Fraction(h*(y0+2*y1+y2),2))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0, 1, 4, 1)', solve(*(0, 1, 4, 1)), '8/3')\ncheck('fixture 2: (3, 3, 3, 1)', solve(*(3, 3, 3, 1)), '6')\ncheck('fixture 3: (1, 0, 1, 2)', solve(*(1, 0, 1, 2)), '4/3')\ncheck('fixture 4: (0, 0, 0, 1)', solve(*(0, 0, 0, 1)), '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":"cf3dd67673d4fb316893ecd6f14cd326772504e992ec3986a9fb083c8b9cf3df","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(y0, y1, y2, h):\n    return str(Fraction(h*(y0+4*y1+y2),3))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0, 1, 4, 1)', solve(*(0, 1, 4, 1)), '8/3')\ncheck('fixture 2: (3, 3, 3, 1)', solve(*(3, 3, 3, 1)), '6')\ncheck('fixture 3: (1, 0, 1, 2)', solve(*(1, 0, 1, 2)), '4/3')\ncheck('fixture 4: (0, 0, 0, 1)', solve(*(0, 0, 0, 1)), '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-simpson-three-point-integral","generated_at":"2026-09-29T14:38:01.210990+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(Fraction(h*(y0+4*y1+y2),3))","root_cause":"Trapezoidal weights replace the quadratic-exact Simpson weights.","sha256":"798b3bac5c4f7ed6824fb261191698b8a0b9e5edc59f019b7186f43bad688a3c","title":"Simpson three point integral · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":96.655,"exit_code":1,"observations":[{"actual":"5/3","check":"fixture 1: (0, 1, 4, 1)","expected":"8/3","passed":false},{"actual":"3","check":"fixture 2: (3, 3, 3, 1)","expected":"6","passed":false},{"actual":"4/3","check":"fixture 3: (1, 0, 1, 2)","expected":"4/3","passed":true},{"actual":"0","check":"fixture 4: (0, 0, 0, 1)","expected":"0","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0, 1, 4, 1)\", \"actual\": \"5/3\", \"expected\": \"8/3\", \"passed\": false}, {\"check\": \"fixture 2: (3, 3, 3, 1)\", \"actual\": \"3\", \"expected\": \"6\", \"passed\": false}, {\"check\": \"fixture 3: (1, 0, 1, 2)\", \"actual\": \"4/3\", \"expected\": \"4/3\", \"passed\": true}, {\"check\": \"fixture 4: (0, 0, 0, 1)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.651,"exit_code":1,"observations":[{"actual":"3","check":"fixture 1: (0, 1, 4, 1)","expected":"8/3","passed":false},{"actual":"6","check":"fixture 2: (3, 3, 3, 1)","expected":"6","passed":true},{"actual":"2","check":"fixture 3: (1, 0, 1, 2)","expected":"4/3","passed":false},{"actual":"0","check":"fixture 4: (0, 0, 0, 1)","expected":"0","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0, 1, 4, 1)\", \"actual\": \"3\", \"expected\": \"8/3\", \"passed\": false}, {\"check\": \"fixture 2: (3, 3, 3, 1)\", \"actual\": \"6\", \"expected\": \"6\", \"passed\": true}, {\"check\": \"fixture 3: (1, 0, 1, 2)\", \"actual\": \"2\", \"expected\": \"4/3\", \"passed\": false}, {\"check\": \"fixture 4: (0, 0, 0, 1)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":71.997,"exit_code":0,"observations":[{"actual":"8/3","check":"fixture 1: (0, 1, 4, 1)","expected":"8/3","passed":true},{"actual":"6","check":"fixture 2: (3, 3, 3, 1)","expected":"6","passed":true},{"actual":"4/3","check":"fixture 3: (1, 0, 1, 2)","expected":"4/3","passed":true},{"actual":"0","check":"fixture 4: (0, 0, 0, 1)","expected":"0","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0, 1, 4, 1)\", \"actual\": \"8/3\", \"expected\": \"8/3\", \"passed\": true}, {\"check\": \"fixture 2: (3, 3, 3, 1)\", \"actual\": \"6\", \"expected\": \"6\", \"passed\": true}, {\"check\": \"fixture 3: (1, 0, 1, 2)\", \"actual\": \"4/3\", \"expected\": \"4/3\", \"passed\": true}, {\"check\": \"fixture 4: (0, 0, 0, 1)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}