{"abstract":"Squaring the thickness ignores the annulus mean radius.","category":"Planar geometry","checks":4,"contract":"Integer coordinates and lengths, with exact arithmetic except for indicated division results. Lengths are nonnegative. Rectangles are (xmin,ymin,xmax,ymax) with ordered bounds; coordinate vectors have matching dimensions. Annulus area divided by pi. Exact operational definition: outer**2-inner**2","contract_signature":"outer, inner","evaluation_group":"model-58bb2682f3d0994e","failed_approach":"The hole area is added rather than removed.","family":"xn-annulus-area-divided-by-pi","id":"FA-5801","implementations":{"attempt":{"sha256":"66f26b33f2eee5d41f80881c1f4f37972ff102b4c6a77633bd09de891c2bc7cf","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(outer, inner):\n    return outer**2+inner**2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (5, 3)', solve(*(5, 3)), 16)\ncheck('fixture 2: (3, 3)', solve(*(3, 3)), 0)\ncheck('fixture 3: (4, 0)', solve(*(4, 0)), 16)\ncheck('fixture 4: (2, 1)', solve(*(2, 1)), 3)\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":"c8aedfd7fa91067b306f7243a09511f6ad8782c8a973b6a511807b80aca276ca","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(outer, inner):\n    return (outer-inner)**2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (5, 3)', solve(*(5, 3)), 16)\ncheck('fixture 2: (3, 3)', solve(*(3, 3)), 0)\ncheck('fixture 3: (4, 0)', solve(*(4, 0)), 16)\ncheck('fixture 4: (2, 1)', solve(*(2, 1)), 3)\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-annulus-area-divided-by-pi","generated_at":"2026-09-29T14:37:53.689165+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. Planar geometry results depend on the stated convention.","root_cause":"Squaring the thickness ignores the annulus mean radius.","sha256":"4cc64ad1e3eba71be6c3dc71efe5898eb1aab73d1ad66b7ab0af984e50c4db09","title":"Annulus area 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":48.849,"exit_code":1,"observations":[{"actual":34,"check":"fixture 1: (5, 3)","expected":16,"passed":false},{"actual":18,"check":"fixture 2: (3, 3)","expected":0,"passed":false},{"actual":16,"check":"fixture 3: (4, 0)","expected":16,"passed":true},{"actual":5,"check":"fixture 4: (2, 1)","expected":3,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 3)\", \"actual\": 34, \"expected\": 16, \"passed\": false}, {\"check\": \"fixture 2: (3, 3)\", \"actual\": 18, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: (4, 0)\", \"actual\": 16, \"expected\": 16, \"passed\": true}, {\"check\": \"fixture 4: (2, 1)\", \"actual\": 5, \"expected\": 3, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":113.789,"exit_code":1,"observations":[{"actual":4,"check":"fixture 1: (5, 3)","expected":16,"passed":false},{"actual":0,"check":"fixture 2: (3, 3)","expected":0,"passed":true},{"actual":16,"check":"fixture 3: (4, 0)","expected":16,"passed":true},{"actual":1,"check":"fixture 4: (2, 1)","expected":3,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (5, 3)\", \"actual\": 4, \"expected\": 16, \"passed\": false}, {\"check\": \"fixture 2: (3, 3)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 3: (4, 0)\", \"actual\": 16, \"expected\": 16, \"passed\": true}, {\"check\": \"fixture 4: (2, 1)\", \"actual\": 1, \"expected\": 3, \"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."}}