{"abstract":"The torus volume formula replaces surface area.","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. major>=minor>=0; return ring-torus surface area divided by pi squared. Exact operational definition: 4*major*minor","evaluation_group":"model-6465cf5139b06d81","failed_approach":"Adding radii does not multiply the two circumference factors.","family":"xn-torus-area-divided-by-pi-squared","id":"FA-5981","implementations":{"attempt":{"sha256":"324e1afa0b519eb17ebf0a07dd4486ac8bfc999fb57cd4c3abc61ec42ce60722","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(major, minor):\n    return 2*(major+minor)\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)), 12)\ncheck('fixture 2: (4, 2)', solve(*(4, 2)), 32)\ncheck('fixture 3: (5, 0)', solve(*(5, 0)), 0)\ncheck('fixture 4: (6, 3)', solve(*(6, 3)), 72)\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":"dfa285498f3f550dd863b38b1285045fe88fab3ee4b9d19dd789ea683234e630","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(major, minor):\n    return 2*major*minor*minor\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)), 12)\ncheck('fixture 2: (4, 2)', solve(*(4, 2)), 32)\ncheck('fixture 3: (5, 0)', solve(*(5, 0)), 0)\ncheck('fixture 4: (6, 3)', solve(*(6, 3)), 72)\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":"9069aa049ed7b3d08ded53840fbde7cd08dbc06ce08c0826be5dcea5a2d3d3e6","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(major, minor):\n    return 4*major*minor\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)), 12)\ncheck('fixture 2: (4, 2)', solve(*(4, 2)), 32)\ncheck('fixture 3: (5, 0)', solve(*(5, 0)), 0)\ncheck('fixture 4: (6, 3)', solve(*(6, 3)), 72)\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-torus-area-divided-by-pi-squared","generated_at":"2026-09-29T14:37:56.159255+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 4*major*minor","root_cause":"The torus volume formula replaces surface area.","sha256":"e8b035693c368914b01e8d5b096e0a6b1a4f557cbf77da3675928598acb5376b","title":"Torus area divided by pi squared · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":43.584,"exit_code":1,"observations":[{"actual":8,"check":"fixture 1: (3, 1)","expected":12,"passed":false},{"actual":12,"check":"fixture 2: (4, 2)","expected":32,"passed":false},{"actual":10,"check":"fixture 3: (5, 0)","expected":0,"passed":false},{"actual":18,"check":"fixture 4: (6, 3)","expected":72,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 1)\", \"actual\": 8, \"expected\": 12, \"passed\": false}, {\"check\": \"fixture 2: (4, 2)\", \"actual\": 12, \"expected\": 32, \"passed\": false}, {\"check\": \"fixture 3: (5, 0)\", \"actual\": 10, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 4: (6, 3)\", \"actual\": 18, \"expected\": 72, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.28,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: (3, 1)","expected":12,"passed":false},{"actual":32,"check":"fixture 2: (4, 2)","expected":32,"passed":true},{"actual":0,"check":"fixture 3: (5, 0)","expected":0,"passed":true},{"actual":108,"check":"fixture 4: (6, 3)","expected":72,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 1)\", \"actual\": 6, \"expected\": 12, \"passed\": false}, {\"check\": \"fixture 2: (4, 2)\", \"actual\": 32, \"expected\": 32, \"passed\": true}, {\"check\": \"fixture 3: (5, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (6, 3)\", \"actual\": 108, \"expected\": 72, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":45.655,"exit_code":0,"observations":[{"actual":12,"check":"fixture 1: (3, 1)","expected":12,"passed":true},{"actual":32,"check":"fixture 2: (4, 2)","expected":32,"passed":true},{"actual":0,"check":"fixture 3: (5, 0)","expected":0,"passed":true},{"actual":72,"check":"fixture 4: (6, 3)","expected":72,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (3, 1)\", \"actual\": 12, \"expected\": 12, \"passed\": true}, {\"check\": \"fixture 2: (4, 2)\", \"actual\": 32, \"expected\": 32, \"passed\": true}, {\"check\": \"fixture 3: (5, 0)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: (6, 3)\", \"actual\": 72, \"expected\": 72, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}