{"abstract":"Unreversed kernel computes correlation instead of 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, or [] if the signal is shorter. Exact operational definition: [sum(signal[i+j]*kernel[-1-j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel)+1)]","evaluation_group":"model-93a96d4767b042e1","failed_approach":"Adding kernel and sample values replaces multiplication.","family":"xn-finite-impulse-valid-convolution","id":"FA-6416","implementations":{"attempt":{"sha256":"d9d2d60179690f39d3573bedb8dd1aee79f6b2195e5bfe593b8ce2d3d960ac8b","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])), [4, 7])\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":"fa49bf66d825d189dd4209efdd0a910e4c98a6551881ec2d878ea7b346bfe923","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])), [4, 7])\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":"55be508465c39bb8c483856765bc2e5aae9dbb7086d9e3c02393cc786b6854cb","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])), [4, 7])\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-finite-impulse-valid-convolution","generated_at":"2026-09-29T14:38:01.583087+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[-1-j] for j in range(len(kernel))) for i in range(len(signal)-len(kernel)+1)]","root_cause":"Unreversed kernel computes correlation instead of convolution.","sha256":"a2dd50392e8913828100813cd821c12f6360a8c373b1dab6b8a8d17868a5703a","title":"Finite impulse valid convolution · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":55.075,"exit_code":1,"observations":[{"actual":[6,8],"check":"fixture 1: ([1, 2, 3], [1, 2])","expected":[4,7],"passed":false},{"actual":[1,1],"check":"fixture 2: ([1, 0, 1], [1, -1])","expected":[-1,1],"passed":false},{"actual":[5],"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\": [6, 8], \"expected\": [4, 7], \"passed\": false}, {\"check\": \"fixture 2: ([1, 0, 1], [1, -1])\", \"actual\": [1, 1], \"expected\": [-1, 1], \"passed\": false}, {\"check\": \"fixture 3: ([2], [3])\", \"actual\": [5], \"expected\": [6], \"passed\": false}, {\"check\": \"fixture 4: ([1], [1, 2])\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":60.677,"exit_code":1,"observations":[{"actual":[5,8],"check":"fixture 1: ([1, 2, 3], [1, 2])","expected":[4,7],"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\": [5, 8], \"expected\": [4, 7], \"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":48.58,"exit_code":0,"observations":[{"actual":[4,7],"check":"fixture 1: ([1, 2, 3], [1, 2])","expected":[4,7],"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\": [4, 7], \"expected\": [4, 7], \"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"}