{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":8,"contract":"Return probability that two distinct uniformly chosen observation indices carry equal integer labels, as an exact Fraction string. Fewer than two observations returns None. Labels themselves are nominal; repeated indices are excluded.","contract_signature":"xs","evaluation_group":"s3-na-empirical-distinct-draw-collision","failed_approach":"A singleton does not provide two distinct draw indices even if its label would match itself.","family":"s3-numerical-aggregation-empirical-distinct-draw-collision-collision-singleton-identity","id":"FA-13366","implementations":{"attempt":{"sha256":"f042191be172429405f4231f647c6f62d6a7e47b01e8ad99c63c500f0b330359","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(xs):\n    counts=Counter(xs)\n    n=len(xs)\n    if n<2: return \"1\"\n    return str(Fraction(sum(v*(v-1) for v in counts.values()),n*(n-1)))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([1, 1, 2],)), '1/3')\ncheck('regression 2', solve(*([1, 2, 3],)), '0')\ncheck('regression 3', solve(*([],)), None)\ncheck('regression 4', solve(*([9],)), None)\ncheck('regression 5', solve(*([2, 2, 2, 2],)), '1')\ncheck('regression 6', solve(*([0, 0, 1, 1, 1, 2],)), '4/15')\ncheck('regression 7', solve(*([-1, -1, 0, 0],)), '1/3')\ncheck(\"variable collision multiplicity\",solve([0]*N+[1]),str(Fraction(N*(N-1),(N+1)*N)))\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":"9712f951d4b4a5ace585e643620b8dd9003d823ad5e5323df1832a2c1ebd46f5","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(xs):\n    counts=Counter(xs)\n    n=len(xs)\n    if n<2: return \"0\"\n    return str(Fraction(sum(v*(v-1) for v in counts.values()),n*(n-1)))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([1, 1, 2],)), '1/3')\ncheck('regression 2', solve(*([1, 2, 3],)), '0')\ncheck('regression 3', solve(*([],)), None)\ncheck('regression 4', solve(*([9],)), None)\ncheck('regression 5', solve(*([2, 2, 2, 2],)), '1')\ncheck('regression 6', solve(*([0, 0, 1, 1, 1, 2],)), '4/15')\ncheck('regression 7', solve(*([-1, -1, 0, 0],)), '1/3')\ncheck(\"variable collision multiplicity\",solve([0]*N+[1]),str(Fraction(N*(N-1),(N+1)*N)))\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-empirical-distinct-draw-collision-collision-singleton-identity","generated_at":"2026-09-29T14:39:06.394231+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":"A singleton is assigned zero rather than an undefined distinct-draw probability.","sha256":"40fb871b1db740766c5d0ef825a81799f110238a705224b3efa3de7b9cb55cf9","title":"Empirical distinct draw collision: A singleton is assigned zero rather than an undefined distinct-draw probability. · 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":47.075,"exit_code":1,"observations":[{"actual":"1/3","check":"regression 1","expected":"1/3","passed":true},{"actual":"0","check":"regression 2","expected":"0","passed":true},{"actual":"1","check":"regression 3","expected":null,"passed":false},{"actual":"1","check":"regression 4","expected":null,"passed":false},{"actual":"1","check":"regression 5","expected":"1","passed":true},{"actual":"4/15","check":"regression 6","expected":"4/15","passed":true},{"actual":"1/3","check":"regression 7","expected":"1/3","passed":true},{"actual":"0","check":"variable collision multiplicity","expected":"0","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"1/3\", \"expected\": \"1/3\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"1\", \"expected\": null, \"passed\": false}, {\"check\": \"regression 4\", \"actual\": \"1\", \"expected\": null, \"passed\": false}, {\"check\": \"regression 5\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"4/15\", \"expected\": \"4/15\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": \"1/3\", \"expected\": \"1/3\", \"passed\": true}, {\"check\": \"variable collision multiplicity\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.557,"exit_code":1,"observations":[{"actual":"1/3","check":"regression 1","expected":"1/3","passed":true},{"actual":"0","check":"regression 2","expected":"0","passed":true},{"actual":"0","check":"regression 3","expected":null,"passed":false},{"actual":"0","check":"regression 4","expected":null,"passed":false},{"actual":"1","check":"regression 5","expected":"1","passed":true},{"actual":"4/15","check":"regression 6","expected":"4/15","passed":true},{"actual":"1/3","check":"regression 7","expected":"1/3","passed":true},{"actual":"0","check":"variable collision multiplicity","expected":"0","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"1/3\", \"expected\": \"1/3\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": null, \"passed\": false}, {\"check\": \"regression 4\", \"actual\": \"0\", \"expected\": null, \"passed\": false}, {\"check\": \"regression 5\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"4/15\", \"expected\": \"4/15\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": \"1/3\", \"expected\": \"1/3\", \"passed\": true}, {\"check\": \"variable collision multiplicity\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}], \"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."}}