{"abstract":"Subtracting same-height cones omits the mixed-radius term.","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. Conical frustum volume divided by pi. Exact operational definition: h*(r*r+r*R+R*R)/3","evaluation_group":"model-454c453c8aeb948b","failed_approach":"Averaging endpoint disk areas is not exact for a conical frustum.","family":"xn-conical-frustum-volume-divided-by-pi","id":"FA-5931","implementations":{"attempt":{"sha256":"59dc6d7664258844c5d7e691b479aebba83effe7525e629d2a8ae73c20a5d1d9","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, R, h):\n    return h*(r*r+R*R)/2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 2, 3)', solve(*(1, 2, 3)), 7)\ncheck('fixture 2: (2, 2, 3)', solve(*(2, 2, 3)), 12)\ncheck('fixture 3: (0, 3, 4)', solve(*(0, 3, 4)), 12)\ncheck('fixture 4: (1, 3, 0)', solve(*(1, 3, 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":"eebcf8167f4e2bfd77dfe8753aeba2e799952279fff0e938e0c7e4f61be48173","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, R, h):\n    return h*(R*R-r*r)/3\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 2, 3)', solve(*(1, 2, 3)), 7)\ncheck('fixture 2: (2, 2, 3)', solve(*(2, 2, 3)), 12)\ncheck('fixture 3: (0, 3, 4)', solve(*(0, 3, 4)), 12)\ncheck('fixture 4: (1, 3, 0)', solve(*(1, 3, 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"},"fixed":{"sha256":"9fd91c3886011ca23fb4e9b05b85378399bbb220e32f1cf21af3d5eb5afb6500","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, R, h):\n    return h*(r*r+r*R+R*R)/3\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 2, 3)', solve(*(1, 2, 3)), 7)\ncheck('fixture 2: (2, 2, 3)', solve(*(2, 2, 3)), 12)\ncheck('fixture 3: (0, 3, 4)', solve(*(0, 3, 4)), 12)\ncheck('fixture 4: (1, 3, 0)', solve(*(1, 3, 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-conical-frustum-volume-divided-by-pi","generated_at":"2026-09-29T14:37:55.405214+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 h*(r*r+r*R+R*R)/3","root_cause":"Subtracting same-height cones omits the mixed-radius term.","sha256":"c2c88b54fcb553ef5628d2f8f951bf36da6ab492124b338846fb0e86f8313605","title":"Conical frustum volume divided by pi · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":49.427,"exit_code":1,"observations":[{"actual":7.5,"check":"fixture 1: (1, 2, 3)","expected":7,"passed":false},{"actual":12.0,"check":"fixture 2: (2, 2, 3)","expected":12,"passed":true},{"actual":18.0,"check":"fixture 3: (0, 3, 4)","expected":12,"passed":false},{"actual":0.0,"check":"fixture 4: (1, 3, 0)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 2, 3)\", \"actual\": 7.5, \"expected\": 7, \"passed\": false}, {\"check\": \"fixture 2: (2, 2, 3)\", \"actual\": 12.0, \"expected\": 12, \"passed\": true}, {\"check\": \"fixture 3: (0, 3, 4)\", \"actual\": 18.0, \"expected\": 12, \"passed\": false}, {\"check\": \"fixture 4: (1, 3, 0)\", \"actual\": 0.0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.89,"exit_code":1,"observations":[{"actual":3.0,"check":"fixture 1: (1, 2, 3)","expected":7,"passed":false},{"actual":0.0,"check":"fixture 2: (2, 2, 3)","expected":12,"passed":false},{"actual":12.0,"check":"fixture 3: (0, 3, 4)","expected":12,"passed":true},{"actual":0.0,"check":"fixture 4: (1, 3, 0)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 2, 3)\", \"actual\": 3.0, \"expected\": 7, \"passed\": false}, {\"check\": \"fixture 2: (2, 2, 3)\", \"actual\": 0.0, \"expected\": 12, \"passed\": false}, {\"check\": \"fixture 3: (0, 3, 4)\", \"actual\": 12.0, \"expected\": 12, \"passed\": true}, {\"check\": \"fixture 4: (1, 3, 0)\", \"actual\": 0.0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":49.527,"exit_code":0,"observations":[{"actual":7.0,"check":"fixture 1: (1, 2, 3)","expected":7,"passed":true},{"actual":12.0,"check":"fixture 2: (2, 2, 3)","expected":12,"passed":true},{"actual":12.0,"check":"fixture 3: (0, 3, 4)","expected":12,"passed":true},{"actual":0.0,"check":"fixture 4: (1, 3, 0)","expected":0,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 2, 3)\", \"actual\": 7.0, \"expected\": 7, \"passed\": true}, {\"check\": \"fixture 2: (2, 2, 3)\", \"actual\": 12.0, \"expected\": 12, \"passed\": true}, {\"check\": \"fixture 3: (0, 3, 4)\", \"actual\": 12.0, \"expected\": 12, \"passed\": true}, {\"check\": \"fixture 4: (1, 3, 0)\", \"actual\": 0.0, \"expected\": 0, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}