{"abstract":"The cell width is omitted.","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. mid_values lists midpoint observations for equal cells of rational width h>=0. Exact operational definition: str(Fraction(h)*sum(mid_values))","contract_signature":"mid_values, h","evaluation_group":"model-cccc08cb888c411c","failed_approach":"Averaging cell values loses the number of intervals.","family":"xn-composite-midpoint-cell-integral","id":"FA-6461","implementations":{"attempt":{"sha256":"672557e6d90b78c5d6f9074151c71a8dd58716e9494fbc8ebbc82def2c88a923","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(mid_values, h):\n    return str(Fraction(h)*sum(mid_values)/len(mid_values)) if mid_values else \"0\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 3, 5], 2)', solve(*([1, 3, 5], 2)), '18')\ncheck('fixture 2: ([4, 4], 3)', solve(*([4, 4], 3)), '24')\ncheck('fixture 3: ([], 2)', solve(*([], 2)), '0')\ncheck('fixture 4: ([5], 0)', solve(*([5], 0)), '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":"0f32610d21e16a5b36aa50d71fac0ece86c34c0bc7e17b1a202ca3f554ac2803","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(mid_values, h):\n    return str(sum(mid_values))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 3, 5], 2)', solve(*([1, 3, 5], 2)), '18')\ncheck('fixture 2: ([4, 4], 3)', solve(*([4, 4], 3)), '24')\ncheck('fixture 3: ([], 2)', solve(*([], 2)), '0')\ncheck('fixture 4: ([5], 0)', solve(*([5], 0)), '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-composite-midpoint-cell-integral","generated_at":"2026-09-29T14:38:02.244723+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.","root_cause":"The cell width is omitted.","sha256":"eacf5d5d4fd02ea10e31a49657ea5cbe828abfacee130c25944185db8e08aeb0","title":"Composite midpoint cell integral · 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":44.848,"exit_code":1,"observations":[{"actual":"6","check":"fixture 1: ([1, 3, 5], 2)","expected":"18","passed":false},{"actual":"12","check":"fixture 2: ([4, 4], 3)","expected":"24","passed":false},{"actual":"0","check":"fixture 3: ([], 2)","expected":"0","passed":true},{"actual":"0","check":"fixture 4: ([5], 0)","expected":"0","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 3, 5], 2)\", \"actual\": \"6\", \"expected\": \"18\", \"passed\": false}, {\"check\": \"fixture 2: ([4, 4], 3)\", \"actual\": \"12\", \"expected\": \"24\", \"passed\": false}, {\"check\": \"fixture 3: ([], 2)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"fixture 4: ([5], 0)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.793,"exit_code":1,"observations":[{"actual":"9","check":"fixture 1: ([1, 3, 5], 2)","expected":"18","passed":false},{"actual":"8","check":"fixture 2: ([4, 4], 3)","expected":"24","passed":false},{"actual":"0","check":"fixture 3: ([], 2)","expected":"0","passed":true},{"actual":"5","check":"fixture 4: ([5], 0)","expected":"0","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 3, 5], 2)\", \"actual\": \"9\", \"expected\": \"18\", \"passed\": false}, {\"check\": \"fixture 2: ([4, 4], 3)\", \"actual\": \"8\", \"expected\": \"24\", \"passed\": false}, {\"check\": \"fixture 3: ([], 2)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"fixture 4: ([5], 0)\", \"actual\": \"5\", \"expected\": \"0\", \"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."}}