{"abstract":"Nearest root differs from a floor root between cubes.","category":"Number theory","checks":4,"contract":"Integer inputs; n is positive unless a zero or negative fixture explicitly extends that operation. A modulus is greater than one; p is prime; exponent k may be signed when an inverse exists. n is any integer in the small bounded fixture domain; return greatest r with r**3<=n. The linear search is an illustrative algorithm, not a large-input performance claim. Exact operational definition: next(k-1 for k in range(abs(n)+2) if k**3>n) if n>=0 else -next(k for k in range(abs(n)+1) if k**3>=-n)","contract_signature":"n","evaluation_group":"model-6580325ddf148f44","failed_approach":"Truncating the magnitude rounds negative noncubes toward zero.","family":"xn-integer-cube-root-floor","id":"FA-5586","implementations":{"attempt":{"sha256":"e0174cbc218664ddc4afdad4047ba265f367a4bfe4dee835b21f2017aced2501","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(n):\n    return int(abs(n)**(1/3))*(1 if n>=0 else -1)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (26,)', solve(*(26,)), 2)\ncheck('fixture 2: (27,)', solve(*(27,)), 3)\ncheck('fixture 3: (-9,)', solve(*(-9,)), -3)\ncheck('fixture 4: (0,)', solve(*(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":"94560392e8e4e1ab8bbb9a611f59130a221e64e2fb0ec5f2dedace9b0197657c","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(n):\n    return round(abs(n)**(1/3))*(1 if n>=0 else -1)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (26,)', solve(*(26,)), 2)\ncheck('fixture 2: (27,)', solve(*(27,)), 3)\ncheck('fixture 3: (-9,)', solve(*(-9,)), -3)\ncheck('fixture 4: (0,)', solve(*(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-integer-cube-root-floor","generated_at":"2026-09-29T14:37:51.024487+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. Number theory results depend on the stated convention.","root_cause":"Nearest root differs from a floor root between cubes.","sha256":"6ccfb67bf3480d461633e0b747ef95a76fb6ecc6ad9cb411843917e6460da458","title":"Integer cube root floor · 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":44.346,"exit_code":1,"observations":[{"actual":2,"check":"fixture 1: (26,)","expected":2,"passed":true},{"actual":3,"check":"fixture 2: (27,)","expected":3,"passed":true},{"actual":-2,"check":"fixture 3: (-9,)","expected":-3,"passed":false},{"actual":0,"check":"fixture 4: (0,)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (26,)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 2: (27,)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 3: (-9,)\", \"actual\": -2, \"expected\": -3, \"passed\": false}, {\"check\": \"fixture 4: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.477,"exit_code":1,"observations":[{"actual":3,"check":"fixture 1: (26,)","expected":2,"passed":false},{"actual":3,"check":"fixture 2: (27,)","expected":3,"passed":true},{"actual":-2,"check":"fixture 3: (-9,)","expected":-3,"passed":false},{"actual":0,"check":"fixture 4: (0,)","expected":0,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (26,)\", \"actual\": 3, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 2: (27,)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 3: (-9,)\", \"actual\": -2, \"expected\": -3, \"passed\": false}, {\"check\": \"fixture 4: (0,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}], \"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."}}