{"abstract":"The exact polynomial taylor shift result violates the stated contract at target degree triangle.","category":"Numerics","checks":8,"contract":"Input [A,h] ascending integer polynomial, integer h; return coefficients of A(t+h), preserving array length.","evaluation_group":"s3-numerics-polynomial-taylor-shift","failed_approach":"The partial repair range(1,i+1) still violates the target degree triangle invariant.","family":"s3-numerics-polynomial-taylor-shift-target-degree-triangle","id":"FA-14646","implementations":{"attempt":{"sha256":"2e13fbe01a6a7d1e053e634a6fe028b88ce171a3c3a1ac839e99fee4cb70e0ae","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,h=x\n    n=len(A);r=[0]*n\n    for i in range(n):\n     for j in range(1,i+1):\n      r[j]+=(A[i]) * (math.comb(i,j) if j<=i else 0) * (h**(i-j) if j<=i else 0)\n    return r\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, -1, -1], -1], [0, -2, 2, -1]), ([[-1, -1, -1, -1], 0], [-1, -1, -1, -1]), ([[-1, -1, -1, -1], 1], [-4, -6, -4, -1]), ([[-1, -1, -1, -1], 2], [-15, -17, -7, -1]), ([[-1, -1, -1, 0], -2], [-3, 3, -1, 0]), ([[-1, -1, -1, 0], -1], [-1, 1, -1, 0])], [([[-1, -1, -1, -1], -1], [0, -2, 2, -1]), ([[-1, -1, -1, -1], 2], [-15, -17, -7, -1]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, -1, 2], 0], [-1, -1, -1, 2]), ([[-1, -1, -1, 2], 1], [-1, 3, 5, 2]), ([[-1, -1, -1, 2], 2], [9, 19, 11, 2]), ([[-1, -1, 0, -1], -2], [9, -13, 6, -1])], [([[-1, -1, -1, -1], 0], [-1, -1, -1, -1]), ([[-1, -1, -1, 0], 0], [-1, -1, -1, 0]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, 0, 1], 2], [5, 11, 6, 1]), ([[-1, -1, 0, 2], -2], [-15, 23, -12, 2]), ([[-1, -1, 0, 2], -1], [-2, 5, -6, 2]), ([[-1, -1, 0, 2], 0], [-1, -1, 0, 2])], [([[-1, -1, -1, -1], 1], [-4, -6, -4, -1]), ([[-1, -1, -1, 1], -2], [-11, 15, -7, 1]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, 1, 1], -1], [0, 0, -2, 1]), ([[-1, -1, 1, 1], 0], [-1, -1, 1, 1]), ([[-1, -1, 1, 1], 1], [0, 4, 4, 1]), ([[-1, -1, 1, 1], 2], [9, 15, 7, 1])], [([[-1, -1, -1, -1], 2], [-15, -17, -7, -1]), ([[-1, -1, -1, 1], 1], [-2, 0, 2, 1]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, 2, 0], 1], [0, 3, 2, 0]), ([[-1, -1, 2, 0], 2], [5, 7, 2, 0]), ([[-1, -1, 2, 1], -2], [1, 3, -4, 1]), ([[-1, -1, 2, 1], -1], [1, -2, -1, 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":"a24ea28a6aed839925c45fc206faf6d2b05edab17bd9c0cb47efc08dc8ee959c","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,h=x\n    n=len(A);r=[0]*n\n    for i in range(n):\n     for j in range(i):\n      r[j]+=(A[i]) * (math.comb(i,j) if j<=i else 0) * (h**(i-j) if j<=i else 0)\n    return r\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, -1, -1], -1], [0, -2, 2, -1]), ([[-1, -1, -1, -1], 0], [-1, -1, -1, -1]), ([[-1, -1, -1, -1], 1], [-4, -6, -4, -1]), ([[-1, -1, -1, -1], 2], [-15, -17, -7, -1]), ([[-1, -1, -1, 0], -2], [-3, 3, -1, 0]), ([[-1, -1, -1, 0], -1], [-1, 1, -1, 0])], [([[-1, -1, -1, -1], -1], [0, -2, 2, -1]), ([[-1, -1, -1, -1], 2], [-15, -17, -7, -1]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, -1, 2], 0], [-1, -1, -1, 2]), ([[-1, -1, -1, 2], 1], [-1, 3, 5, 2]), ([[-1, -1, -1, 2], 2], [9, 19, 11, 2]), ([[-1, -1, 0, -1], -2], [9, -13, 6, -1])], [([[-1, -1, -1, -1], 0], [-1, -1, -1, -1]), ([[-1, -1, -1, 0], 0], [-1, -1, -1, 0]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, 0, 1], 2], [5, 11, 6, 1]), ([[-1, -1, 0, 2], -2], [-15, 23, -12, 2]), ([[-1, -1, 0, 2], -1], [-2, 5, -6, 2]), ([[-1, -1, 0, 2], 0], [-1, -1, 0, 2])], [([[-1, -1, -1, -1], 1], [-4, -6, -4, -1]), ([[-1, -1, -1, 1], -2], [-11, 15, -7, 1]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, 1, 1], -1], [0, 0, -2, 1]), ([[-1, -1, 1, 1], 0], [-1, -1, 1, 1]), ([[-1, -1, 1, 1], 1], [0, 4, 4, 1]), ([[-1, -1, 1, 1], 2], [9, 15, 7, 1])], [([[-1, -1, -1, -1], 2], [-15, -17, -7, -1]), ([[-1, -1, -1, 1], 1], [-2, 0, 2, 1]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, 2, 0], 1], [0, 3, 2, 0]), ([[-1, -1, 2, 0], 2], [5, 7, 2, 0]), ([[-1, -1, 2, 1], -2], [1, 3, -4, 1]), ([[-1, -1, 2, 1], -1], [1, -2, -1, 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":"020a4b6a5d5a2777408bd57bb2b23fb5c2d2f85b6a257823b444bae7ee0d3f13","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,h=x\n    n=len(A);r=[0]*n\n    for i in range(n):\n     for j in range(i+1):\n      r[j]+=(A[i]) * (math.comb(i,j) if j<=i else 0) * (h**(i-j) if j<=i else 0)\n    return r\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, -1, -1], -1], [0, -2, 2, -1]), ([[-1, -1, -1, -1], 0], [-1, -1, -1, -1]), ([[-1, -1, -1, -1], 1], [-4, -6, -4, -1]), ([[-1, -1, -1, -1], 2], [-15, -17, -7, -1]), ([[-1, -1, -1, 0], -2], [-3, 3, -1, 0]), ([[-1, -1, -1, 0], -1], [-1, 1, -1, 0])], [([[-1, -1, -1, -1], -1], [0, -2, 2, -1]), ([[-1, -1, -1, -1], 2], [-15, -17, -7, -1]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, -1, 2], 0], [-1, -1, -1, 2]), ([[-1, -1, -1, 2], 1], [-1, 3, 5, 2]), ([[-1, -1, -1, 2], 2], [9, 19, 11, 2]), ([[-1, -1, 0, -1], -2], [9, -13, 6, -1])], [([[-1, -1, -1, -1], 0], [-1, -1, -1, -1]), ([[-1, -1, -1, 0], 0], [-1, -1, -1, 0]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, 0, 1], 2], [5, 11, 6, 1]), ([[-1, -1, 0, 2], -2], [-15, 23, -12, 2]), ([[-1, -1, 0, 2], -1], [-2, 5, -6, 2]), ([[-1, -1, 0, 2], 0], [-1, -1, 0, 2])], [([[-1, -1, -1, -1], 1], [-4, -6, -4, -1]), ([[-1, -1, -1, 1], -2], [-11, 15, -7, 1]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, 1, 1], -1], [0, 0, -2, 1]), ([[-1, -1, 1, 1], 0], [-1, -1, 1, 1]), ([[-1, -1, 1, 1], 1], [0, 4, 4, 1]), ([[-1, -1, 1, 1], 2], [9, 15, 7, 1])], [([[-1, -1, -1, -1], 2], [-15, -17, -7, -1]), ([[-1, -1, -1, 1], 1], [-2, 0, 2, 1]), ([[-1, -1, -1, -1], -2], [5, -9, 5, -1]), ([[2, 2, 2, 2], 2], [30, 34, 14, 2]), ([[-1, -1, 2, 0], 1], [0, 3, 2, 0]), ([[-1, -1, 2, 0], 2], [5, 7, 2, 0]), ([[-1, -1, 2, 1], -2], [1, 3, -4, 1]), ([[-1, -1, 2, 1], -1], [1, -2, -1, 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-polynomial-taylor-shift-target-degree-triangle","generated_at":"2026-09-29T14:39:19.073010+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 range(i+1) at the target degree triangle step.","root_cause":"The target degree triangle step uses range(i) instead of range(i+1).","sha256":"53b23d23aa50a6c1ff21c7b69d781622d3d008486ab8cf0afb27f30572beadf5","title":"Polynomial taylor shift: target degree triangle · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.524,"exit_code":1,"observations":[{"actual":[0,-9,5,-1],"check":"explicit oracle 0","expected":[5,-9,5,-1],"passed":false},{"actual":[0,34,14,2],"check":"explicit oracle 1","expected":[30,34,14,2],"passed":false},{"actual":[0,-2,2,-1],"check":"explicit oracle 2","expected":[0,-2,2,-1],"passed":true},{"actual":[0,-1,-1,-1],"check":"explicit oracle 3","expected":[-1,-1,-1,-1],"passed":false},{"actual":[0,-6,-4,-1],"check":"explicit oracle 4","expected":[-4,-6,-4,-1],"passed":false},{"actual":[0,-17,-7,-1],"check":"explicit oracle 5","expected":[-15,-17,-7,-1],"passed":false},{"actual":[0,3,-1,0],"check":"explicit oracle 6","expected":[-3,3,-1,0],"passed":false},{"actual":[0,1,-1,0],"check":"explicit oracle 7","expected":[-1,1,-1,0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [0, -9, 5, -1], \"expected\": [5, -9, 5, -1], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [0, 34, 14, 2], \"expected\": [30, 34, 14, 2], \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": [0, -2, 2, -1], \"expected\": [0, -2, 2, -1], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [0, -1, -1, -1], \"expected\": [-1, -1, -1, -1], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [0, -6, -4, -1], \"expected\": [-4, -6, -4, -1], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [0, -17, -7, -1], \"expected\": [-15, -17, -7, -1], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [0, 3, -1, 0], \"expected\": [-3, 3, -1, 0], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [0, 1, -1, 0], \"expected\": [-1, 1, -1, 0], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.708,"exit_code":1,"observations":[{"actual":[6,-8,6,0],"check":"explicit oracle 0","expected":[5,-9,5,-1],"passed":false},{"actual":[28,32,12,0],"check":"explicit oracle 1","expected":[30,34,14,2],"passed":false},{"actual":[1,-1,3,0],"check":"explicit oracle 2","expected":[0,-2,2,-1],"passed":false},{"actual":[0,0,0,0],"check":"explicit oracle 3","expected":[-1,-1,-1,-1],"passed":false},{"actual":[-3,-5,-3,0],"check":"explicit oracle 4","expected":[-4,-6,-4,-1],"passed":false},{"actual":[-14,-16,-6,0],"check":"explicit oracle 5","expected":[-15,-17,-7,-1],"passed":false},{"actual":[-2,4,0,0],"check":"explicit oracle 6","expected":[-3,3,-1,0],"passed":false},{"actual":[0,2,0,0],"check":"explicit oracle 7","expected":[-1,1,-1,0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [6, -8, 6, 0], \"expected\": [5, -9, 5, -1], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [28, 32, 12, 0], \"expected\": [30, 34, 14, 2], \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": [1, -1, 3, 0], \"expected\": [0, -2, 2, -1], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [0, 0, 0, 0], \"expected\": [-1, -1, -1, -1], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [-3, -5, -3, 0], \"expected\": [-4, -6, -4, -1], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [-14, -16, -6, 0], \"expected\": [-15, -17, -7, -1], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [-2, 4, 0, 0], \"expected\": [-3, 3, -1, 0], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [0, 2, 0, 0], \"expected\": [-1, 1, -1, 0], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.737,"exit_code":0,"observations":[{"actual":[5,-9,5,-1],"check":"explicit oracle 0","expected":[5,-9,5,-1],"passed":true},{"actual":[30,34,14,2],"check":"explicit oracle 1","expected":[30,34,14,2],"passed":true},{"actual":[0,-2,2,-1],"check":"explicit oracle 2","expected":[0,-2,2,-1],"passed":true},{"actual":[-1,-1,-1,-1],"check":"explicit oracle 3","expected":[-1,-1,-1,-1],"passed":true},{"actual":[-4,-6,-4,-1],"check":"explicit oracle 4","expected":[-4,-6,-4,-1],"passed":true},{"actual":[-15,-17,-7,-1],"check":"explicit oracle 5","expected":[-15,-17,-7,-1],"passed":true},{"actual":[-3,3,-1,0],"check":"explicit oracle 6","expected":[-3,3,-1,0],"passed":true},{"actual":[-1,1,-1,0],"check":"explicit oracle 7","expected":[-1,1,-1,0],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [5, -9, 5, -1], \"expected\": [5, -9, 5, -1], \"passed\": true}, {\"check\": \"explicit oracle 1\", \"actual\": [30, 34, 14, 2], \"expected\": [30, 34, 14, 2], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [0, -2, 2, -1], \"expected\": [0, -2, 2, -1], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [-1, -1, -1, -1], \"expected\": [-1, -1, -1, -1], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [-4, -6, -4, -1], \"expected\": [-4, -6, -4, -1], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [-15, -17, -7, -1], \"expected\": [-15, -17, -7, -1], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [-3, 3, -1, 0], \"expected\": [-3, 3, -1, 0], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [-1, 1, -1, 0], \"expected\": [-1, 1, -1, 0], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}