{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":8,"contract":"Treat samples as frequency vectors over nominal integer labels. Return squared cosine dot**2/(sum count_a**2 * sum count_b**2) as exact Fraction string. A zero norm on either side returns None.","contract_signature":"a, b","evaluation_group":"s3-na-frequency-cosine-squared","failed_approach":"Combining norms in one side of the product misnormalizes the angle.","family":"s3-numerical-aggregation-frequency-cosine-squared-cosine-shared-norm","id":"FA-14121","implementations":{"attempt":{"sha256":"4585d7ae7dda84de10c9a8d7b9e4a1f871b4a29ca942b6f7e0fb73c31228b59b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom collections import Counter, defaultdict\nimport math\nimport itertools\nN = 1\nobservations = []\ndef solve(a, b):\n    ca,cb=Counter(a),Counter(b)\n    keys=set(ca)|set(cb)\n    dot=sum(ca[k]*cb[k] for k in keys)\n    na=sum(v*v for v in ca.values())\n    nb=sum(v*v for v in ca.values())+sum(v*v for v in cb.values())\n    return str(Fraction(dot*dot,na*nb)) if na and nb else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([1, 1, 2], [1, 2, 2])), '16/25')\ncheck('regression 2', solve(*([1, 2], [1, 2])), '1')\ncheck('regression 3', solve(*([], [])), None)\ncheck('regression 4', solve(*([0], [1])), '0')\ncheck('regression 5', solve(*([1, 1, 1, 2], [1, 2])), '4/5')\ncheck('regression 6', solve(*([-1, 0, 0], [0, 0, 1, 1])), '2/5')\ncheck('regression 7', solve(*([2, 2], [])), None)\ncheck(\"variable cosine concentration\",solve([0]*N+[1],[0]),str(Fraction(N*N,N*N+1)))\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":"28dcd5386aea01bd8ec0850cec769f5fe87cf187a415a04d8e314832b2465fe4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom collections import Counter, defaultdict\nimport math\nimport itertools\nN = 1\nobservations = []\ndef solve(a, b):\n    ca,cb=Counter(a),Counter(b)\n    keys=set(ca)|set(cb)\n    dot=sum(ca[k]*cb[k] for k in keys)\n    na=sum(v*v for v in ca.values())\n    nb=na\n    return str(Fraction(dot*dot,na*nb)) if na and nb else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([1, 1, 2], [1, 2, 2])), '16/25')\ncheck('regression 2', solve(*([1, 2], [1, 2])), '1')\ncheck('regression 3', solve(*([], [])), None)\ncheck('regression 4', solve(*([0], [1])), '0')\ncheck('regression 5', solve(*([1, 1, 1, 2], [1, 2])), '4/5')\ncheck('regression 6', solve(*([-1, 0, 0], [0, 0, 1, 1])), '2/5')\ncheck('regression 7', solve(*([2, 2], [])), None)\ncheck(\"variable cosine concentration\",solve([0]*N+[1],[0]),str(Fraction(N*N,N*N+1)))\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":"Small offline integer/rational inputs only; no performance, statistical inference, or production-library conformance claim. 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-numerical-aggregation-frequency-cosine-squared-cosine-shared-norm","generated_at":"2026-09-29T14:39:14.060407+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Exact bounded examples isolate a reduction defect without floating-point or external-service effects.","root_cause":"Both norms are computed from the first sample.","sha256":"70ddb099d218007bedf119cc3608c562167baa2cedbfcdf0e33f187adb1bf546","title":"Frequency cosine squared: Both norms are computed from the first sample. · 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":44.953,"exit_code":1,"observations":[{"actual":"8/25","check":"regression 1","expected":"16/25","passed":false},{"actual":"1/2","check":"regression 2","expected":"1","passed":false},{"actual":null,"check":"regression 3","expected":null,"passed":true},{"actual":"0","check":"regression 4","expected":"0","passed":true},{"actual":"2/15","check":"regression 5","expected":"4/5","passed":false},{"actual":"16/65","check":"regression 6","expected":"2/5","passed":false},{"actual":"0","check":"regression 7","expected":null,"passed":false},{"actual":"1/6","check":"variable cosine concentration","expected":"1/2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"8/25\", \"expected\": \"16/25\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": \"1/2\", \"expected\": \"1\", \"passed\": false}, {\"check\": \"regression 3\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"2/15\", \"expected\": \"4/5\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": \"16/65\", \"expected\": \"2/5\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": null, \"passed\": false}, {\"check\": \"variable cosine concentration\", \"actual\": \"1/6\", \"expected\": \"1/2\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.746,"exit_code":1,"observations":[{"actual":"16/25","check":"regression 1","expected":"16/25","passed":true},{"actual":"1","check":"regression 2","expected":"1","passed":true},{"actual":null,"check":"regression 3","expected":null,"passed":true},{"actual":"0","check":"regression 4","expected":"0","passed":true},{"actual":"4/25","check":"regression 5","expected":"4/5","passed":false},{"actual":"16/25","check":"regression 6","expected":"2/5","passed":false},{"actual":"0","check":"regression 7","expected":null,"passed":false},{"actual":"1/4","check":"variable cosine concentration","expected":"1/2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"16/25\", \"expected\": \"16/25\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"4/25\", \"expected\": \"4/5\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": \"16/25\", \"expected\": \"2/5\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": null, \"passed\": false}, {\"check\": \"variable cosine concentration\", \"actual\": \"1/4\", \"expected\": \"1/2\", \"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."}}