{"abstract":"The cap is mistaken for a flat disk based on cap height.","category":"Solid geometry","checks":4,"contract":"Nonnegative integer dimensions; exact products and ordinary Python real division. Quantities named divided by pi or pi-squared deliberately omit that factor from the returned result. R>=0 and 0<=h<=2*R; return curved cap surface area divided by pi, excluding the flat base. Exact operational definition: 2*R*h","evaluation_group":"model-50a0e39de183e473","failed_approach":"A hemisphere area is returned regardless of cap height.","family":"xn-spherical-cap-area-divided-by-pi","id":"FA-5971","implementations":{"attempt":{"sha256":"7b57084a2a8b03fbc77f98749b85a3914943b08e31e829ff7d2d2ecb72b6f7d2","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(R, h):\n    return 2*R*R\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 1)', solve(*(3, 1)), 6)\ncheck('fixture 2: (3, 3)', solve(*(3, 3)), 18)\ncheck('fixture 3: (4, 0)', solve(*(4, 0)), 0)\ncheck('fixture 4: (2, 4)', solve(*(2, 4)), 16)\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":"9e3dfed40c9e37b4d1bda96732a0e1108312e905e64b039423224864d83d5d3a","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(R, h):\n    return h*h\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 1)', solve(*(3, 1)), 6)\ncheck('fixture 2: (3, 3)', solve(*(3, 3)), 18)\ncheck('fixture 3: (4, 0)', solve(*(4, 0)), 0)\ncheck('fixture 4: (2, 4)', solve(*(2, 4)), 16)\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":"4b3731290ec49116317bcfd6a8651ad831a233accef60f209c57406f11393be2","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(R, h):\n    return 2*R*h\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 1)', solve(*(3, 1)), 6)\ncheck('fixture 2: (3, 3)', solve(*(3, 3)), 18)\ncheck('fixture 3: (4, 0)', solve(*(4, 0)), 0)\ncheck('fixture 4: (2, 4)', solve(*(2, 4)), 16)\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-spherical-cap-area-divided-by-pi","generated_at":"2026-09-29T14:37:56.112693+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. Solid geometry results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return 2*R*h","root_cause":"The cap is mistaken for a flat disk based on cap height.","sha256":"381798a2fd74e596b2631fd007a83bf325048148ff77d207d6410f39fe9689b1","title":"Spherical cap area divided by pi · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.58,"exit_code":1,"observations":[{"actual":18,"check":"fixture 1: (3, 1)","expected":6,"passed":false},{"actual":18,"check":"fixture 2: (3, 3)","expected":18,"passed":true},{"actual":32,"check":"fixture 3: (4, 0)","expected":0,"passed":false},{"actual":8,"check":"fixture 4: (2, 4)","expected":16,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 1)\", \"actual\": 18, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 2: (3, 3)\", \"actual\": 18, \"expected\": 18, \"passed\": true}, {\"check\": \"fixture 3: (4, 0)\", \"actual\": 32, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 4: (2, 4)\", \"actual\": 8, \"expected\": 16, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":136.543,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: (3, 1)","expected":6,"passed":false},{"actual":9,"check":"fixture 2: (3, 3)","expected":18,"passed":false},{"actual":0,"check":"fixture 3: (4, 0)","expected":0,"passed":true},{"actual":16,"check":"fixture 4: (2, 4)","expected":16,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 1)\", \"actual\": 1, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 2: (3, 3)\", \"actual\": 9, \"expected\": 18, \"passed\": false}, {\"check\": \"fixture 3: (4, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (2, 4)\", \"actual\": 16, \"expected\": 16, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":49.008,"exit_code":0,"observations":[{"actual":6,"check":"fixture 1: (3, 1)","expected":6,"passed":true},{"actual":18,"check":"fixture 2: (3, 3)","expected":18,"passed":true},{"actual":0,"check":"fixture 3: (4, 0)","expected":0,"passed":true},{"actual":16,"check":"fixture 4: (2, 4)","expected":16,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 1)\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 2: (3, 3)\", \"actual\": 18, \"expected\": 18, \"passed\": true}, {\"check\": \"fixture 3: (4, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (2, 4)\", \"actual\": 16, \"expected\": 16, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}