{"abstract":"The exact walsh hadamard transform result violates the stated contract at butterfly span growth.","category":"Numerics","checks":8,"contract":"Input integer list of power-of-two length; return unnormalized Sylvester-ordered Walsh-Hadamard transform. Bounds: length<=1024.","evaluation_group":"s3-numerics-walsh-hadamard-transform","failed_approach":"The partial repair h*4 still violates the butterfly span growth invariant.","family":"s3-numerics-walsh-hadamard-transform-butterfly-span-growth","id":"FA-15761","implementations":{"attempt":{"sha256":"3422b5bbea5a063149e419d0ee99b82d13b1751ea427694d4faa599cceabfb61","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport itertools\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    a=x[:];n=len(a);h=1\n    for _ in range(10):\n     if h>=n:break\n     for i in range(0,n,2*h):\n      for j in range(i,i+h):\n       if j+h>=n:return None\n       u,v=a[j],a[j+h]\n       a[j]=u+v\n       a[j+h]=u-v\n     h=h*4\n    return a\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, -1, -2, 5], [4, -4, -2, 10]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([-4, 3], [-1, -7]), ([2, 3], [5, -1]), ([3, 3], [6, 0]), ([-5, 4], [-1, -9]), ([3, -3], [0, 6])], [([4, 4, 3, 4], [15, -1, 1, 1]), ([1, 2, 1, -4], [0, 4, 6, -6]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([-3, -3], [-6, 0]), ([-4, 0], [-4, -4]), ([-2, 5], [3, -7]), ([3, 1], [4, 2])], [([1, -2, -5, 5], [-1, -7, -1, 13]), ([-3, -4, -3, -1], [-11, -1, -3, 3]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([-5, 3], [-2, -8]), ([-2, 4], [2, -6]), ([3, 2], [5, 1]), ([-1, 5], [4, -6])], [([1, 2, 1, -4], [0, 4, 6, -6]), ([-5, -1, 0, 2], [-4, -6, -8, -2]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([4, 4, 3, 4], [15, -1, 1, 1]), ([1, -2, -5, 5], [-1, -7, -1, 13]), ([2, -2, -2, -1], [-3, 3, 3, 5]), ([0, 3, 2, -3], [2, 2, 4, -8])], [([2, -2, -2, -1], [-3, 3, 3, 5]), ([-2, 2, 5, 2], [7, -1, -7, -7]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([2, -2, -2, 4], [2, -2, -2, 10]), ([5, -2, 5, 4], [12, 8, -6, 6]), ([5, -1, -5, 3], [2, -2, 6, 14]), ([-2, -5, 1, -3], [-9, 7, -5, -1])]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"explicit oracle %d\" % i, solve(args), expected)\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":"5ea6c17ea62eaf96c8a4d48a9fe395dd7913df816b995f4f36b63b313eae9517","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport itertools\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    a=x[:];n=len(a);h=1\n    for _ in range(10):\n     if h>=n:break\n     for i in range(0,n,2*h):\n      for j in range(i,i+h):\n       if j+h>=n:return None\n       u,v=a[j],a[j+h]\n       a[j]=u+v\n       a[j+h]=u-v\n     h=h+1\n    return a\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, -1, -2, 5], [4, -4, -2, 10]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([-4, 3], [-1, -7]), ([2, 3], [5, -1]), ([3, 3], [6, 0]), ([-5, 4], [-1, -9]), ([3, -3], [0, 6])], [([4, 4, 3, 4], [15, -1, 1, 1]), ([1, 2, 1, -4], [0, 4, 6, -6]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([-3, -3], [-6, 0]), ([-4, 0], [-4, -4]), ([-2, 5], [3, -7]), ([3, 1], [4, 2])], [([1, -2, -5, 5], [-1, -7, -1, 13]), ([-3, -4, -3, -1], [-11, -1, -3, 3]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([-5, 3], [-2, -8]), ([-2, 4], [2, -6]), ([3, 2], [5, 1]), ([-1, 5], [4, -6])], [([1, 2, 1, -4], [0, 4, 6, -6]), ([-5, -1, 0, 2], [-4, -6, -8, -2]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([4, 4, 3, 4], [15, -1, 1, 1]), ([1, -2, -5, 5], [-1, -7, -1, 13]), ([2, -2, -2, -1], [-3, 3, 3, 5]), ([0, 3, 2, -3], [2, 2, 4, -8])], [([2, -2, -2, -1], [-3, 3, 3, 5]), ([-2, 2, 5, 2], [7, -1, -7, -7]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([2, -2, -2, 4], [2, -2, -2, 10]), ([5, -2, 5, 4], [12, 8, -6, 6]), ([5, -1, -5, 3], [2, -2, 6, 14]), ([-2, -5, 1, -3], [-9, 7, -5, -1])]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"explicit oracle %d\" % i, solve(args), expected)\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":"fba03ef841a26ef4cb9c31edec78e7f4e0bba9209cca234cb2644979c0b96632","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport itertools\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    a=x[:];n=len(a);h=1\n    for _ in range(10):\n     if h>=n:break\n     for i in range(0,n,2*h):\n      for j in range(i,i+h):\n       if j+h>=n:return None\n       u,v=a[j],a[j+h]\n       a[j]=u+v\n       a[j+h]=u-v\n     h=h*2\n    return a\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, -1, -2, 5], [4, -4, -2, 10]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([-4, 3], [-1, -7]), ([2, 3], [5, -1]), ([3, 3], [6, 0]), ([-5, 4], [-1, -9]), ([3, -3], [0, 6])], [([4, 4, 3, 4], [15, -1, 1, 1]), ([1, 2, 1, -4], [0, 4, 6, -6]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([-3, -3], [-6, 0]), ([-4, 0], [-4, -4]), ([-2, 5], [3, -7]), ([3, 1], [4, 2])], [([1, -2, -5, 5], [-1, -7, -1, 13]), ([-3, -4, -3, -1], [-11, -1, -3, 3]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([-5, 3], [-2, -8]), ([-2, 4], [2, -6]), ([3, 2], [5, 1]), ([-1, 5], [4, -6])], [([1, 2, 1, -4], [0, 4, 6, -6]), ([-5, -1, 0, 2], [-4, -6, -8, -2]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([4, 4, 3, 4], [15, -1, 1, 1]), ([1, -2, -5, 5], [-1, -7, -1, 13]), ([2, -2, -2, -1], [-3, 3, 3, 5]), ([0, 3, 2, -3], [2, 2, 4, -8])], [([2, -2, -2, -1], [-3, 3, 3, 5]), ([-2, 2, 5, 2], [7, -1, -7, -7]), ([-5, -2], [-7, -3]), ([-2, -4, -5, 1, 2, 3, -1, -5, -1, 4, -1, 3, 5, 2, 2, -2], [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13]), ([2, -2, -2, 4], [2, -2, -2, 10]), ([5, -2, 5, 4], [12, 8, -6, 6]), ([5, -1, -5, 3], [2, -2, 6, 14]), ([-2, -5, 1, -3], [-9, 7, -5, -1])]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"explicit oracle %d\" % i, solve(args), expected)\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":"A deterministic bounded teaching model. Inputs are restricted to the explicit contract; this is not a production algebra library. 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":"s3-numerics-walsh-hadamard-transform-butterfly-span-growth","generated_at":"2026-09-29T14:39:30.112069+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Exact discrete arithmetic with observable algorithmic state; no floating point approximation is used.","repair":"Use h*2 at the butterfly span growth step.","root_cause":"The butterfly span growth step uses h+1 instead of h*2.","sha256":"225af955d5bc39097e8c01fcb73d5d2348d59f8f05e5293b3a9e802d57bebcf3","title":"Walsh hadamard transform: butterfly span growth · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.802,"exit_code":1,"observations":[{"actual":[1,3,3,-7],"check":"explicit oracle 0","expected":[4,-4,-2,10],"passed":false},{"actual":[-7,-3],"check":"explicit oracle 1","expected":[-7,-3],"passed":true},{"actual":[-1,1,-10,-2,-11,3,2,-10,10,-2,2,0,-4,-8,2,-8],"check":"explicit oracle 2","expected":[1,-3,17,1,-11,-23,-19,13,-23,1,1,5,-7,9,-7,13],"passed":false},{"actual":[-1,-7],"check":"explicit oracle 3","expected":[-1,-7],"passed":true},{"actual":[5,-1],"check":"explicit oracle 4","expected":[5,-1],"passed":true},{"actual":[6,0],"check":"explicit oracle 5","expected":[6,0],"passed":true},{"actual":[-1,-9],"check":"explicit oracle 6","expected":[-1,-9],"passed":true},{"actual":[0,6],"check":"explicit oracle 7","expected":[0,6],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [1, 3, 3, -7], \"expected\": [4, -4, -2, 10], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [-7, -3], \"expected\": [-7, -3], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [-1, 1, -10, -2, -11, 3, 2, -10, 10, -2, 2, 0, -4, -8, 2, -8], \"expected\": [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [-1, -7], \"expected\": [-1, -7], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [5, -1], \"expected\": [5, -1], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [6, 0], \"expected\": [6, 0], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [-1, -9], \"expected\": [-1, -9], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [0, 6], \"expected\": [0, 6], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.188,"exit_code":1,"observations":[{"actual":null,"check":"explicit oracle 0","expected":[4,-4,-2,10],"passed":false},{"actual":[-7,-3],"check":"explicit oracle 1","expected":[-7,-3],"passed":true},{"actual":null,"check":"explicit oracle 2","expected":[1,-3,17,1,-11,-23,-19,13,-23,1,1,5,-7,9,-7,13],"passed":false},{"actual":[-1,-7],"check":"explicit oracle 3","expected":[-1,-7],"passed":true},{"actual":[5,-1],"check":"explicit oracle 4","expected":[5,-1],"passed":true},{"actual":[6,0],"check":"explicit oracle 5","expected":[6,0],"passed":true},{"actual":[-1,-9],"check":"explicit oracle 6","expected":[-1,-9],"passed":true},{"actual":[0,6],"check":"explicit oracle 7","expected":[0,6],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": null, \"expected\": [4, -4, -2, 10], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [-7, -3], \"expected\": [-7, -3], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": null, \"expected\": [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [-1, -7], \"expected\": [-1, -7], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [5, -1], \"expected\": [5, -1], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [6, 0], \"expected\": [6, 0], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [-1, -9], \"expected\": [-1, -9], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [0, 6], \"expected\": [0, 6], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.257,"exit_code":0,"observations":[{"actual":[4,-4,-2,10],"check":"explicit oracle 0","expected":[4,-4,-2,10],"passed":true},{"actual":[-7,-3],"check":"explicit oracle 1","expected":[-7,-3],"passed":true},{"actual":[1,-3,17,1,-11,-23,-19,13,-23,1,1,5,-7,9,-7,13],"check":"explicit oracle 2","expected":[1,-3,17,1,-11,-23,-19,13,-23,1,1,5,-7,9,-7,13],"passed":true},{"actual":[-1,-7],"check":"explicit oracle 3","expected":[-1,-7],"passed":true},{"actual":[5,-1],"check":"explicit oracle 4","expected":[5,-1],"passed":true},{"actual":[6,0],"check":"explicit oracle 5","expected":[6,0],"passed":true},{"actual":[-1,-9],"check":"explicit oracle 6","expected":[-1,-9],"passed":true},{"actual":[0,6],"check":"explicit oracle 7","expected":[0,6],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [4, -4, -2, 10], \"expected\": [4, -4, -2, 10], \"passed\": true}, {\"check\": \"explicit oracle 1\", \"actual\": [-7, -3], \"expected\": [-7, -3], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13], \"expected\": [1, -3, 17, 1, -11, -23, -19, 13, -23, 1, 1, 5, -7, 9, -7, 13], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [-1, -7], \"expected\": [-1, -7], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [5, -1], \"expected\": [5, -1], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [6, 0], \"expected\": [6, 0], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [-1, -9], \"expected\": [-1, -9], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [0, 6], \"expected\": [0, 6], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}