{"abstract":"The cap cubic correction is omitted.","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; the output is spherical-cap volume divided by pi. Exact operational definition: h*h*(R-h/3)","contract_signature":"R, h","evaluation_group":"model-621acecdf998484d","failed_approach":"The radius term is divided by three along with the height term.","family":"xn-spherical-cap-volume-divided-by-pi","id":"FA-5966","implementations":{"attempt":{"sha256":"8cb42e5697bfc3dfc9c1a1216c13170ff94b5f6576ce74218e2e5834d3ef9928","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*(R-h)/3\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 3)', solve(*(3, 3)), 18)\ncheck('fixture 2: (3, 6)', solve(*(3, 6)), 36)\ncheck('fixture 3: (4, 0)', solve(*(4, 0)), 0)\ncheck('fixture 4: (2, 1)', solve(*(2, 1)), 1.6666666666666667)\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":"53fed256a74bb6999eb7b5e0102c78a4541d169537a6c71cab4611f1709ead9a","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 R*h*h\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (3, 3)', solve(*(3, 3)), 18)\ncheck('fixture 2: (3, 6)', solve(*(3, 6)), 36)\ncheck('fixture 3: (4, 0)', solve(*(4, 0)), 0)\ncheck('fixture 4: (2, 1)', solve(*(2, 1)), 1.6666666666666667)\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-volume-divided-by-pi","generated_at":"2026-09-29T14:37:56.056838+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.","root_cause":"The cap cubic correction is omitted.","sha256":"045e891cd2439232f9d3efbc1be53dcad1b73d45d7b08d39ab4269c339951ef6","title":"Spherical cap volume divided by pi · 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":150.414,"exit_code":1,"observations":[{"actual":0.0,"check":"fixture 1: (3, 3)","expected":18,"passed":false},{"actual":-36.0,"check":"fixture 2: (3, 6)","expected":36,"passed":false},{"actual":0.0,"check":"fixture 3: (4, 0)","expected":0,"passed":true},{"actual":0.3333333333333333,"check":"fixture 4: (2, 1)","expected":1.6666666666666667,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 3)\", \"actual\": 0.0, \"expected\": 18, \"passed\": false}, {\"check\": \"fixture 2: (3, 6)\", \"actual\": -36.0, \"expected\": 36, \"passed\": false}, {\"check\": \"fixture 3: (4, 0)\", \"actual\": 0.0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (2, 1)\", \"actual\": 0.3333333333333333, \"expected\": 1.6666666666666667, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":51.572,"exit_code":1,"observations":[{"actual":27,"check":"fixture 1: (3, 3)","expected":18,"passed":false},{"actual":108,"check":"fixture 2: (3, 6)","expected":36,"passed":false},{"actual":0,"check":"fixture 3: (4, 0)","expected":0,"passed":true},{"actual":2,"check":"fixture 4: (2, 1)","expected":1.6666666666666667,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 3)\", \"actual\": 27, \"expected\": 18, \"passed\": false}, {\"check\": \"fixture 2: (3, 6)\", \"actual\": 108, \"expected\": 36, \"passed\": false}, {\"check\": \"fixture 3: (4, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (2, 1)\", \"actual\": 2, \"expected\": 1.6666666666666667, \"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."}}