{"abstract":"Subtraction order reverses the discrete derivative.","category":"Discrete calculus","checks":4,"contract":"Integer sample values and compatible sample-array lengths. Rational results are reduced Fraction strings; spacing is positive unless explicitly stated otherwise. Forward first difference. Exact operational definition: [b-a for a,b in zip(values,values[1:])]","evaluation_group":"model-a93ba5b792a23017","failed_approach":"Adding neighbors replaces their change.","family":"xn-forward-first-difference","id":"FA-6351","implementations":{"attempt":{"sha256":"ad8d7321a35ac110e982b63b41c5d0405838af0b1e1bd26494d7d96ca8d5df4d","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(values):\n    return [b+a for a,b in zip(values,values[1:])]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 4, 9, 16],)', solve(*([1, 4, 9, 16],)), [3, 5, 7])\ncheck('fixture 2: ([3, 3],)', solve(*([3, 3],)), [0])\ncheck('fixture 3: ([7],)', solve(*([7],)), [])\ncheck('fixture 4: ([],)', solve(*([],)), [])\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":"04b50af72b87793d2889e950996679e25cddeac85f14f3a11cfd2757070a6fee","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(values):\n    return [a-b for a,b in zip(values,values[1:])]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 4, 9, 16],)', solve(*([1, 4, 9, 16],)), [3, 5, 7])\ncheck('fixture 2: ([3, 3],)', solve(*([3, 3],)), [0])\ncheck('fixture 3: ([7],)', solve(*([7],)), [])\ncheck('fixture 4: ([],)', solve(*([],)), [])\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":"4304bf57694df2b762c1346b63cecb1403206c5fe43726fadc3cfd4ee923d796","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(values):\n    return [b-a for a,b in zip(values,values[1:])]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 4, 9, 16],)', solve(*([1, 4, 9, 16],)), [3, 5, 7])\ncheck('fixture 2: ([3, 3],)', solve(*([3, 3],)), [0])\ncheck('fixture 3: ([7],)', solve(*([7],)), [])\ncheck('fixture 4: ([],)', solve(*([],)), [])\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-forward-first-difference","generated_at":"2026-09-29T14:38:00.615884+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. Discrete calculus results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return [b-a for a,b in zip(values,values[1:])]","root_cause":"Subtraction order reverses the discrete derivative.","sha256":"9e8226a828df940037abc71624d8bfccb031d54996eca5cb646821a41941c73f","title":"Forward first difference · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":51.954,"exit_code":1,"observations":[{"actual":[5,13,25],"check":"fixture 1: ([1, 4, 9, 16],)","expected":[3,5,7],"passed":false},{"actual":[6],"check":"fixture 2: ([3, 3],)","expected":[0],"passed":false},{"actual":[],"check":"fixture 3: ([7],)","expected":[],"passed":true},{"actual":[],"check":"fixture 4: ([],)","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 4, 9, 16],)\", \"actual\": [5, 13, 25], \"expected\": [3, 5, 7], \"passed\": false}, {\"check\": \"fixture 2: ([3, 3],)\", \"actual\": [6], \"expected\": [0], \"passed\": false}, {\"check\": \"fixture 3: ([7],)\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":64.829,"exit_code":1,"observations":[{"actual":[-3,-5,-7],"check":"fixture 1: ([1, 4, 9, 16],)","expected":[3,5,7],"passed":false},{"actual":[0],"check":"fixture 2: ([3, 3],)","expected":[0],"passed":true},{"actual":[],"check":"fixture 3: ([7],)","expected":[],"passed":true},{"actual":[],"check":"fixture 4: ([],)","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 4, 9, 16],)\", \"actual\": [-3, -5, -7], \"expected\": [3, 5, 7], \"passed\": false}, {\"check\": \"fixture 2: ([3, 3],)\", \"actual\": [0], \"expected\": [0], \"passed\": true}, {\"check\": \"fixture 3: ([7],)\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":51.305,"exit_code":0,"observations":[{"actual":[3,5,7],"check":"fixture 1: ([1, 4, 9, 16],)","expected":[3,5,7],"passed":true},{"actual":[0],"check":"fixture 2: ([3, 3],)","expected":[0],"passed":true},{"actual":[],"check":"fixture 3: ([7],)","expected":[],"passed":true},{"actual":[],"check":"fixture 4: ([],)","expected":[],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 4, 9, 16],)\", \"actual\": [3, 5, 7], \"expected\": [3, 5, 7], \"passed\": true}, {\"check\": \"fixture 2: ([3, 3],)\", \"actual\": [0], \"expected\": [0], \"passed\": true}, {\"check\": \"fixture 3: ([7],)\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"fixture 4: ([],)\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}