{"abstract":"Sample count replaces zero-lag energy normalization.","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. 0<=lag<=len(values); use the uncentered lagged product sum divided by full-signal energy. A zero-energy signal returns None. Exact operational definition: str(Fraction(sum(a*b for a,b in zip(values,values[lag:])),sum(v*v for v in values))) if any(values) else None","evaluation_group":"model-ed242fd699352cc9","failed_approach":"Truncated-tail energy changes the normalization across lags.","family":"xn-autocorrelation-zero-lag-normalized","id":"FA-6471","implementations":{"attempt":{"sha256":"fc18919c6065336e0606c21625abddcf073e60b278293a0e2ade05d470e3d2a3","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(values, lag):\n    return str(Fraction(sum(a*b for a,b in zip(values,values[lag:])),sum(v*v for v in values[lag:]))) if any(values[lag:]) else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2, 3], 1)', solve(*([1, 2, 3], 1)), '4/7')\ncheck('fixture 2: ([1, 2, 3], 0)', solve(*([1, 2, 3], 0)), '1')\ncheck('fixture 3: ([2, 0], 1)', solve(*([2, 0], 1)), '0')\ncheck('fixture 4: ([0, 0], 0)', solve(*([0, 0], 0)), None)\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":"29648dc96cacc26002b2429bea359c23773dbfa227137cb2665179153c6e0e82","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(values, lag):\n    return str(Fraction(sum(a*b for a,b in zip(values,values[lag:])),len(values))) if values else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2, 3], 1)', solve(*([1, 2, 3], 1)), '4/7')\ncheck('fixture 2: ([1, 2, 3], 0)', solve(*([1, 2, 3], 0)), '1')\ncheck('fixture 3: ([2, 0], 1)', solve(*([2, 0], 1)), '0')\ncheck('fixture 4: ([0, 0], 0)', solve(*([0, 0], 0)), None)\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":"010f1a0926edeb87553e2d0535e92d1d03ccb23e23b331868722b8623538a60c","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(values, lag):\n    return str(Fraction(sum(a*b for a,b in zip(values,values[lag:])),sum(v*v for v in values))) if any(values) else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 2, 3], 1)', solve(*([1, 2, 3], 1)), '4/7')\ncheck('fixture 2: ([1, 2, 3], 0)', solve(*([1, 2, 3], 0)), '1')\ncheck('fixture 3: ([2, 0], 1)', solve(*([2, 0], 1)), '0')\ncheck('fixture 4: ([0, 0], 0)', solve(*([0, 0], 0)), None)\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-autocorrelation-zero-lag-normalized","generated_at":"2026-09-29T14:38:02.414932+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 str(Fraction(sum(a*b for a,b in zip(values,values[lag:])),sum(v*v for v in values))) if any(values) else None","root_cause":"Sample count replaces zero-lag energy normalization.","sha256":"4ea8b3be5bb2b3d1f4fcc7e75d128a5da427d12b6db1c187e78feb0bcf29e88b","title":"Autocorrelation zero lag normalized · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":120.957,"exit_code":1,"observations":[{"actual":"8/13","check":"fixture 1: ([1, 2, 3], 1)","expected":"4/7","passed":false},{"actual":"1","check":"fixture 2: ([1, 2, 3], 0)","expected":"1","passed":true},{"actual":null,"check":"fixture 3: ([2, 0], 1)","expected":"0","passed":false},{"actual":null,"check":"fixture 4: ([0, 0], 0)","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3], 1)\", \"actual\": \"8/13\", \"expected\": \"4/7\", \"passed\": false}, {\"check\": \"fixture 2: ([1, 2, 3], 0)\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"fixture 3: ([2, 0], 1)\", \"actual\": null, \"expected\": \"0\", \"passed\": false}, {\"check\": \"fixture 4: ([0, 0], 0)\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.394,"exit_code":1,"observations":[{"actual":"8/3","check":"fixture 1: ([1, 2, 3], 1)","expected":"4/7","passed":false},{"actual":"14/3","check":"fixture 2: ([1, 2, 3], 0)","expected":"1","passed":false},{"actual":"0","check":"fixture 3: ([2, 0], 1)","expected":"0","passed":true},{"actual":"0","check":"fixture 4: ([0, 0], 0)","expected":null,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3], 1)\", \"actual\": \"8/3\", \"expected\": \"4/7\", \"passed\": false}, {\"check\": \"fixture 2: ([1, 2, 3], 0)\", \"actual\": \"14/3\", \"expected\": \"1\", \"passed\": false}, {\"check\": \"fixture 3: ([2, 0], 1)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"fixture 4: ([0, 0], 0)\", \"actual\": \"0\", \"expected\": null, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.415,"exit_code":0,"observations":[{"actual":"4/7","check":"fixture 1: ([1, 2, 3], 1)","expected":"4/7","passed":true},{"actual":"1","check":"fixture 2: ([1, 2, 3], 0)","expected":"1","passed":true},{"actual":"0","check":"fixture 3: ([2, 0], 1)","expected":"0","passed":true},{"actual":null,"check":"fixture 4: ([0, 0], 0)","expected":null,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 2, 3], 1)\", \"actual\": \"4/7\", \"expected\": \"4/7\", \"passed\": true}, {\"check\": \"fixture 2: ([1, 2, 3], 0)\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"fixture 3: ([2, 0], 1)\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"fixture 4: ([0, 0], 0)\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}