{"abstract":"Kernel reversal changes correlation into convolution.","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. kernel is nonempty; return only full-overlap windows, retaining kernel order. Exact operational definition: [sum(signal[i+j]*kernel[j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel)+1)]","evaluation_group":"model-de1bcb6f534218b3","failed_approach":"The last fully overlapping window is omitted.","family":"xn-valid-cross-correlation","id":"FA-6421","implementations":{"attempt":{"sha256":"c777d649e1a6be102b64fe7d972189c75999f584157700b7b0100c7abfa2e537","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(signal, kernel):\n    return [sum(signal[i+j]*kernel[j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel))]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2, 3], [1, 2])', solve(*([1, 2, 3], [1, 2])), [5, 8])\ncheck('fixture 2: ([1, 0, 1], [1, -1])', solve(*([1, 0, 1], [1, -1])), [1, -1])\ncheck('fixture 3: ([2], [3])', solve(*([2], [3])), [6])\ncheck('fixture 4: ([1], [1, 2])', solve(*([1], [1, 2])), [])\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":"63749c90d062f4afa18d752b5d916107737c68658418044dfd7f000dc1d5df71","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(signal, kernel):\n    return [sum(signal[i+j]*kernel[-1-j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel)+1)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2, 3], [1, 2])', solve(*([1, 2, 3], [1, 2])), [5, 8])\ncheck('fixture 2: ([1, 0, 1], [1, -1])', solve(*([1, 0, 1], [1, -1])), [1, -1])\ncheck('fixture 3: ([2], [3])', solve(*([2], [3])), [6])\ncheck('fixture 4: ([1], [1, 2])', solve(*([1], [1, 2])), [])\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":"26dfc8b336ee61faf367c507554543793deb4d1d744f05dd61457cc88f512bf9","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(signal, kernel):\n    return [sum(signal[i+j]*kernel[j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel)+1)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2, 3], [1, 2])', solve(*([1, 2, 3], [1, 2])), [5, 8])\ncheck('fixture 2: ([1, 0, 1], [1, -1])', solve(*([1, 0, 1], [1, -1])), [1, -1])\ncheck('fixture 3: ([2], [3])', solve(*([2], [3])), [6])\ncheck('fixture 4: ([1], [1, 2])', solve(*([1], [1, 2])), [])\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-valid-cross-correlation","generated_at":"2026-09-29T14:38:01.610450+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 [sum(signal[i+j]*kernel[j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel)+1)]","root_cause":"Kernel reversal changes correlation into convolution.","sha256":"14758fdb6863b9b8af5b17e1442da57e69fcda6ea468476e9fc360891d8d586b","title":"Valid cross correlation · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":59.917,"exit_code":1,"observations":[{"actual":[5],"check":"fixture 1: ([1, 2, 3], [1, 2])","expected":[5,8],"passed":false},{"actual":[1],"check":"fixture 2: ([1, 0, 1], [1, -1])","expected":[1,-1],"passed":false},{"actual":[],"check":"fixture 3: ([2], [3])","expected":[6],"passed":false},{"actual":[],"check":"fixture 4: ([1], [1, 2])","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3], [1, 2])\", \"actual\": [5], \"expected\": [5, 8], \"passed\": false}, {\"check\": \"fixture 2: ([1, 0, 1], [1, -1])\", \"actual\": [1], \"expected\": [1, -1], \"passed\": false}, {\"check\": \"fixture 3: ([2], [3])\", \"actual\": [], \"expected\": [6], \"passed\": false}, {\"check\": \"fixture 4: ([1], [1, 2])\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":54.932,"exit_code":1,"observations":[{"actual":[4,7],"check":"fixture 1: ([1, 2, 3], [1, 2])","expected":[5,8],"passed":false},{"actual":[-1,1],"check":"fixture 2: ([1, 0, 1], [1, -1])","expected":[1,-1],"passed":false},{"actual":[6],"check":"fixture 3: ([2], [3])","expected":[6],"passed":true},{"actual":[],"check":"fixture 4: ([1], [1, 2])","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3], [1, 2])\", \"actual\": [4, 7], \"expected\": [5, 8], \"passed\": false}, {\"check\": \"fixture 2: ([1, 0, 1], [1, -1])\", \"actual\": [-1, 1], \"expected\": [1, -1], \"passed\": false}, {\"check\": \"fixture 3: ([2], [3])\", \"actual\": [6], \"expected\": [6], \"passed\": true}, {\"check\": \"fixture 4: ([1], [1, 2])\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":45.988,"exit_code":0,"observations":[{"actual":[5,8],"check":"fixture 1: ([1, 2, 3], [1, 2])","expected":[5,8],"passed":true},{"actual":[1,-1],"check":"fixture 2: ([1, 0, 1], [1, -1])","expected":[1,-1],"passed":true},{"actual":[6],"check":"fixture 3: ([2], [3])","expected":[6],"passed":true},{"actual":[],"check":"fixture 4: ([1], [1, 2])","expected":[],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3], [1, 2])\", \"actual\": [5, 8], \"expected\": [5, 8], \"passed\": true}, {\"check\": \"fixture 2: ([1, 0, 1], [1, -1])\", \"actual\": [1, -1], \"expected\": [1, -1], \"passed\": true}, {\"check\": \"fixture 3: ([2], [3])\", \"actual\": [6], \"expected\": [6], \"passed\": true}, {\"check\": \"fixture 4: ([1], [1, 2])\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}