{"abstract":"The exact integer matrix binary power result violates the stated contract at binary exponent digit test.","category":"Numerics","checks":8,"contract":"Input [square integer matrix,nonnegative exponent<=12]; return exact matrix power.","contract_signature":"x","evaluation_group":"s3-numerics-integer-matrix-binary-power","failed_approach":"The partial repair e>1 still violates the binary exponent digit test invariant.","family":"s3-numerics-integer-matrix-binary-power-binary-exponent-digit-test","id":"FA-15471","implementations":{"attempt":{"sha256":"9d6089aaaac2995893686d5df3a984ba4f15b843dd4547fd30a8d75a91cc415f","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,e=x;n=len(a)\n    def mul(a,b):return [[sum(a[i][k]*b[k][j] for k in range(n)) for j in range(n)] for i in range(n)]\n    r=[[int(i==j) for j in range(n)] for i in range(n)]\n    for _ in range(12):\n     if e==0:break\n     if e>1:r=mul(r,a)\n     a=mul(a,a)\n     e=e//2\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]], 0], [[1]]), ([[[-1, 3], [-1, -3]], 8], [[1168, 2688], [-896, -624]]), ([[[-1]], 2], [[1]]), ([[[-1]], 3], [[-1]]), ([[[-1]], 4], [[1]]), ([[[-1]], 5], [[-1]]), ([[[-1]], 6], [[1]])], [([[[-1]], 2], [[1]]), ([[[-1]], 6], [[1]]), ([[[-1]], 0], [[1]]), ([[[-1, 3], [-1, -3]], 8], [[1168, 2688], [-896, -624]]), ([[[2]], 8], [[256]]), ([[[2]], 0], [[1]]), ([[[2]], 1], [[2]]), ([[[2]], 2], [[4]])], [([[[-1]], 3], [[-1]]), ([[[2]], 2], [[4]]), ([[[-1]], 0], [[1]]), ([[[-1, 3], [-1, -3]], 8], [[1168, 2688], [-896, -624]]), ([[[1]], 7], [[1]]), ([[[1]], 8], [[1]]), ([[[3]], 0], [[1]]), ([[[3]], 1], [[3]])], [([[[-1]], 4], [[1]]), ([[[2]], 5], [[32]]), ([[[-1]], 0], [[1]]), ([[[-1, 3], [-1, -3]], 8], [[1168, 2688], [-896, -624]]), ([[[-1]], 6], [[1]]), ([[[-1]], 7], [[-1]]), ([[[-1]], 8], [[1]]), ([[[3]], 0], [[1]])], [([[[-1]], 5], [[-1]]), ([[[2]], 8], [[256]]), ([[[-1]], 0], [[1]]), ([[[-1, 3], [-1, -3]], 8], [[1168, 2688], [-896, -624]]), ([[[-3]], 5], [[-243]]), ([[[-3]], 6], [[729]]), ([[[-3]], 7], [[-2187]]), ([[[-3]], 8], [[6561]])]]\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":"d23df03000a7e52764d902da254148abd8d9ef681f51bc5156117be62b741663","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,e=x;n=len(a)\n    def mul(a,b):return [[sum(a[i][k]*b[k][j] for k in range(n)) for j in range(n)] for i in range(n)]\n    r=[[int(i==j) for j in range(n)] for i in range(n)]\n    for _ in range(12):\n     if e==0:break\n     if e%2==0:r=mul(r,a)\n     a=mul(a,a)\n     e=e//2\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]], 0], [[1]]), ([[[-1, 3], [-1, -3]], 8], [[1168, 2688], [-896, -624]]), ([[[-1]], 2], [[1]]), ([[[-1]], 3], [[-1]]), ([[[-1]], 4], [[1]]), ([[[-1]], 5], [[-1]]), ([[[-1]], 6], [[1]])], [([[[-1]], 2], [[1]]), ([[[-1]], 6], [[1]]), ([[[-1]], 0], [[1]]), ([[[-1, 3], [-1, -3]], 8], [[1168, 2688], [-896, -624]]), ([[[2]], 8], [[256]]), ([[[2]], 0], [[1]]), ([[[2]], 1], [[2]]), ([[[2]], 2], [[4]])], [([[[-1]], 3], [[-1]]), ([[[2]], 2], [[4]]), ([[[-1]], 0], [[1]]), ([[[-1, 3], [-1, -3]], 8], [[1168, 2688], [-896, -624]]), ([[[1]], 7], [[1]]), ([[[1]], 8], [[1]]), ([[[3]], 0], [[1]]), ([[[3]], 1], [[3]])], [([[[-1]], 4], [[1]]), ([[[2]], 5], [[32]]), ([[[-1]], 0], [[1]]), ([[[-1, 3], [-1, -3]], 8], [[1168, 2688], [-896, -624]]), ([[[-1]], 6], [[1]]), ([[[-1]], 7], [[-1]]), ([[[-1]], 8], [[1]]), ([[[3]], 0], [[1]])], [([[[-1]], 5], [[-1]]), ([[[2]], 8], [[256]]), ([[[-1]], 0], [[1]]), ([[[-1, 3], [-1, -3]], 8], [[1168, 2688], [-896, -624]]), ([[[-3]], 5], [[-243]]), ([[[-3]], 6], [[729]]), ([[[-3]], 7], [[-2187]]), ([[[-3]], 8], [[6561]])]]\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-integer-matrix-binary-power-binary-exponent-digit-test","generated_at":"2026-09-29T14:39:27.223680+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.","root_cause":"The binary exponent digit test step uses e%2==0 instead of e%2==1.","sha256":"d7114656384f29cfb6daa6aa77df03761857cb4d2c55948f0559ca0f8b8fd41e","title":"Integer matrix binary power: binary exponent digit test · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":41.778,"exit_code":1,"observations":[{"actual":[[1]],"check":"explicit oracle 0","expected":[[-1]],"passed":false},{"actual":[[1]],"check":"explicit oracle 1","expected":[[1]],"passed":true},{"actual":[[-136,-1032],[344,552]],"check":"explicit oracle 2","expected":[[1168,2688],[-896,-624]],"passed":false},{"actual":[[-1]],"check":"explicit oracle 3","expected":[[1]],"passed":false},{"actual":[[-1]],"check":"explicit oracle 4","expected":[[-1]],"passed":true},{"actual":[[-1]],"check":"explicit oracle 5","expected":[[1]],"passed":false},{"actual":[[-1]],"check":"explicit oracle 6","expected":[[-1]],"passed":true},{"actual":[[-1]],"check":"explicit oracle 7","expected":[[1]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[1]], \"expected\": [[-1]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [[1]], \"expected\": [[1]], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [[-136, -1032], [344, 552]], \"expected\": [[1168, 2688], [-896, -624]], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [[-1]], \"expected\": [[1]], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [[-1]], \"expected\": [[-1]], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [[-1]], \"expected\": [[1]], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [[-1]], \"expected\": [[-1]], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [[-1]], \"expected\": [[1]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.605,"exit_code":1,"observations":[{"actual":[[1]],"check":"explicit oracle 0","expected":[[-1]],"passed":false},{"actual":[[1]],"check":"explicit oracle 1","expected":[[1]],"passed":true},{"actual":[[-136,-1032],[344,552]],"check":"explicit oracle 2","expected":[[1168,2688],[-896,-624]],"passed":false},{"actual":[[-1]],"check":"explicit oracle 3","expected":[[1]],"passed":false},{"actual":[[1]],"check":"explicit oracle 4","expected":[[-1]],"passed":false},{"actual":[[-1]],"check":"explicit oracle 5","expected":[[1]],"passed":false},{"actual":[[1]],"check":"explicit oracle 6","expected":[[-1]],"passed":false},{"actual":[[-1]],"check":"explicit oracle 7","expected":[[1]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[1]], \"expected\": [[-1]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [[1]], \"expected\": [[1]], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [[-136, -1032], [344, 552]], \"expected\": [[1168, 2688], [-896, -624]], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [[-1]], \"expected\": [[1]], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [[1]], \"expected\": [[-1]], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [[-1]], \"expected\": [[1]], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [[1]], \"expected\": [[-1]], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [[-1]], \"expected\": [[1]], \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}