{"abstract":"The terminal value is excluded by a half-open iteration.","category":"Integer arithmetic","checks":4,"contract":"Integer arguments; denominators, steps, moduli, and bit widths are positive. Unsigned word inputs fit the specified width except where masking is explicitly the operation. Sequence sizes are nonnegative. a<=b; sum every integer in the closed interval. Exact operational definition: (b-a+1)*(a+b)//2","evaluation_group":"model-3f8e309013ad9395","failed_approach":"The term count lacks the inclusive endpoint.","family":"xn-sum-integer-range-inclusive","id":"FA-5476","implementations":{"attempt":{"sha256":"904f051401a4348ef31332f6b2c03933469c319bdfe93e9404fa147c67d02687","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(a, b):\n    return (b-a)*(a+b)//2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 4)', solve(*(1, 4)), 10)\ncheck('fixture 2: (-2, 2)', solve(*(-2, 2)), 0)\ncheck('fixture 3: (3, 3)', solve(*(3, 3)), 3)\ncheck('fixture 4: (-4, -2)', solve(*(-4, -2)), -9)\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":"cd8b3241368d79180b49df6b078a188dcc06591c80354ef5552a996456aa1307","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(a, b):\n    return sum(range(a,b))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 4)', solve(*(1, 4)), 10)\ncheck('fixture 2: (-2, 2)', solve(*(-2, 2)), 0)\ncheck('fixture 3: (3, 3)', solve(*(3, 3)), 3)\ncheck('fixture 4: (-4, -2)', solve(*(-4, -2)), -9)\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":"f403facbc5400d53d0cb0ee9bed3ef8a287083c24cfd5eb19b09224ccf446dbd","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(a, b):\n    return (b-a+1)*(a+b)//2\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (1, 4)', solve(*(1, 4)), 10)\ncheck('fixture 2: (-2, 2)', solve(*(-2, 2)), 0)\ncheck('fixture 3: (3, 3)', solve(*(3, 3)), 3)\ncheck('fixture 4: (-4, -2)', solve(*(-4, -2)), -9)\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-sum-integer-range-inclusive","generated_at":"2026-09-29T14:37:50.024401+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. Integer mathematics results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return (b-a+1)*(a+b)//2","root_cause":"The terminal value is excluded by a half-open iteration.","sha256":"7c152a0a3e97a9b4e4be19854c271bafb5512777a556eda8d9f15a1e39506d61","title":"Sum integer range inclusive · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":54.492,"exit_code":1,"observations":[{"actual":7,"check":"fixture 1: (1, 4)","expected":10,"passed":false},{"actual":0,"check":"fixture 2: (-2, 2)","expected":0,"passed":true},{"actual":0,"check":"fixture 3: (3, 3)","expected":3,"passed":false},{"actual":-6,"check":"fixture 4: (-4, -2)","expected":-9,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 4)\", \"actual\": 7, \"expected\": 10, \"passed\": false}, {\"check\": \"fixture 2: (-2, 2)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 3: (3, 3)\", \"actual\": 0, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 4: (-4, -2)\", \"actual\": -6, \"expected\": -9, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.968,"exit_code":1,"observations":[{"actual":6,"check":"fixture 1: (1, 4)","expected":10,"passed":false},{"actual":-2,"check":"fixture 2: (-2, 2)","expected":0,"passed":false},{"actual":0,"check":"fixture 3: (3, 3)","expected":3,"passed":false},{"actual":-7,"check":"fixture 4: (-4, -2)","expected":-9,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 4)\", \"actual\": 6, \"expected\": 10, \"passed\": false}, {\"check\": \"fixture 2: (-2, 2)\", \"actual\": -2, \"expected\": 0, \"passed\": false}, {\"check\": \"fixture 3: (3, 3)\", \"actual\": 0, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 4: (-4, -2)\", \"actual\": -7, \"expected\": -9, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":50.567,"exit_code":0,"observations":[{"actual":10,"check":"fixture 1: (1, 4)","expected":10,"passed":true},{"actual":0,"check":"fixture 2: (-2, 2)","expected":0,"passed":true},{"actual":3,"check":"fixture 3: (3, 3)","expected":3,"passed":true},{"actual":-9,"check":"fixture 4: (-4, -2)","expected":-9,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (1, 4)\", \"actual\": 10, \"expected\": 10, \"passed\": true}, {\"check\": \"fixture 2: (-2, 2)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 3: (3, 3)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 4: (-4, -2)\", \"actual\": -9, \"expected\": -9, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}