{"abstract":"The number itself is included among proper divisors.","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. Proper divisor sum. Exact operational definition: sum(d for d in range(1,n) if n%d==0)","evaluation_group":"model-d587a1b2c39f3414","failed_approach":"Removing the unit divisor undercounts every nonunit input.","family":"xn-proper-divisor-sum","id":"FA-5496","implementations":{"attempt":{"sha256":"30bafc181fee112e0e745f5b3e74e47e2f0ecabf6d5c01badbb1a4e12d92ce4d","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 sum(d for d in range(2,n) if n%d==0)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1,)', solve(*(1,)), 0)\ncheck('fixture 2: (6,)', solve(*(6,)), 6)\ncheck('fixture 3: (12,)', solve(*(12,)), 16)\ncheck('fixture 4: (7,)', solve(*(7,)), 1)\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":"058c48f19220dabc470be6174ca53f14623109b451a75dc53a5afa85003207db","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 sum(d for d in range(1,n+1) if n%d==0)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1,)', solve(*(1,)), 0)\ncheck('fixture 2: (6,)', solve(*(6,)), 6)\ncheck('fixture 3: (12,)', solve(*(12,)), 16)\ncheck('fixture 4: (7,)', solve(*(7,)), 1)\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":"fc3c20db99de3b60cb600bcd9b421b3a539e6afa78f9d696e41c75e53d36ba72","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 sum(d for d in range(1,n) if n%d==0)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1,)', solve(*(1,)), 0)\ncheck('fixture 2: (6,)', solve(*(6,)), 6)\ncheck('fixture 3: (12,)', solve(*(12,)), 16)\ncheck('fixture 4: (7,)', solve(*(7,)), 1)\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-proper-divisor-sum","generated_at":"2026-09-29T14:37:50.165373+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.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return sum(d for d in range(1,n) if n%d==0)","root_cause":"The number itself is included among proper divisors.","sha256":"c432bc4e90dcd8965e12c513c15df48bc99e79e220118def54600352d1c78fbc","title":"Proper divisor sum · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.581,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (1,)","expected":0,"passed":true},{"actual":5,"check":"fixture 2: (6,)","expected":6,"passed":false},{"actual":15,"check":"fixture 3: (12,)","expected":16,"passed":false},{"actual":0,"check":"fixture 4: (7,)","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (6,)\", \"actual\": 5, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 3: (12,)\", \"actual\": 15, \"expected\": 16, \"passed\": false}, {\"check\": \"fixture 4: (7,)\", \"actual\": 0, \"expected\": 1, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.484,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: (1,)","expected":0,"passed":false},{"actual":12,"check":"fixture 2: (6,)","expected":6,"passed":false},{"actual":28,"check":"fixture 3: (12,)","expected":16,"passed":false},{"actual":8,"check":"fixture 4: (7,)","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1,)\", \"actual\": 1, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 2: (6,)\", \"actual\": 12, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 3: (12,)\", \"actual\": 28, \"expected\": 16, \"passed\": false}, {\"check\": \"fixture 4: (7,)\", \"actual\": 8, \"expected\": 1, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.391,"exit_code":0,"observations":[{"actual":0,"check":"fixture 1: (1,)","expected":0,"passed":true},{"actual":6,"check":"fixture 2: (6,)","expected":6,"passed":true},{"actual":16,"check":"fixture 3: (12,)","expected":16,"passed":true},{"actual":1,"check":"fixture 4: (7,)","expected":1,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1,)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 2: (6,)\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 3: (12,)\", \"actual\": 16, \"expected\": 16, \"passed\": true}, {\"check\": \"fixture 4: (7,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}