{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":8,"contract":"For paired ordinal observations return sign(tau_b)*tau_b**2 as an exact Fraction string. Every unordered observation pair contributes its coordinate comparison; normalize signed concordance squared by products of non-tied x/y pair counts. Undefined if either coordinate has no varying pairs.","contract_signature":"points","evaluation_group":"s3-na-tie-adjusted-concordance-squared","failed_approach":"Always negative also loses the observed direction.","family":"s3-numerical-aggregation-tie-adjusted-concordance-squared-concordance-square-sign","id":"FA-13721","implementations":{"attempt":{"sha256":"f5b18b4c5d1952075c68d0e6c350b40a6b6cbb3bd120d49b1c5135768ae2bf52","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(points):\n    concordant=discordant=tx=ty=0\n    for i in range(len(points)):\n        for j in range(i+1,len(points)):\n            dx=points[i][0]-points[j][0]\n            dy=points[i][1]-points[j][1]\n            if dx: tx+=1\n            if dy: ty+=1\n            concordant+=int(dx*dy>0)\n            discordant+=int(dx*dy<0)\n    if not tx or not ty: return None\n    d=concordant-discordant\n    return str(Fraction(-d*d,tx*ty))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([(1, 1), (2, 2), (3, 3)],)), '1')\ncheck('regression 2', solve(*([(1, 3), (2, 2), (3, 1)],)), '-1')\ncheck('regression 3', solve(*([(1, 1), (1, 2), (2, 2), (3, 1)],)), '-1/20')\ncheck('regression 4', solve(*([],)), None)\ncheck('regression 5', solve(*([(1, 1), (1, 2)],)), None)\ncheck('regression 6', solve(*([(1, 1), (2, 2), (2, 2), (4, 3)],)), '1')\ncheck('regression 7', solve(*([(1, 2), (3, 1), (4, 4), (2, 5)],)), '0')\ncheck(\"variable discordance direction\",solve([(0,N),(N,0)]),\"-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":"9c00be52cb6952a16db3c709a95f6a11593f8eeb5c504571763abb47f1815abb","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(points):\n    concordant=discordant=tx=ty=0\n    for i in range(len(points)):\n        for j in range(i+1,len(points)):\n            dx=points[i][0]-points[j][0]\n            dy=points[i][1]-points[j][1]\n            if dx: tx+=1\n            if dy: ty+=1\n            concordant+=int(dx*dy>0)\n            discordant+=int(dx*dy<0)\n    if not tx or not ty: return None\n    d=concordant-discordant\n    return str(Fraction(d*d,tx*ty))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([(1, 1), (2, 2), (3, 3)],)), '1')\ncheck('regression 2', solve(*([(1, 3), (2, 2), (3, 1)],)), '-1')\ncheck('regression 3', solve(*([(1, 1), (1, 2), (2, 2), (3, 1)],)), '-1/20')\ncheck('regression 4', solve(*([],)), None)\ncheck('regression 5', solve(*([(1, 1), (1, 2)],)), None)\ncheck('regression 6', solve(*([(1, 1), (2, 2), (2, 2), (4, 3)],)), '1')\ncheck('regression 7', solve(*([(1, 2), (3, 1), (4, 4), (2, 5)],)), '0')\ncheck(\"variable discordance direction\",solve([(0,N),(N,0)]),\"-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-tie-adjusted-concordance-squared-concordance-square-sign","generated_at":"2026-09-29T14:39:10.314103+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":"Squaring the numerator loses negative association direction.","sha256":"03756c965524a55fd5cd8397aafb7f97ed49954aa94ae9c40be7567f6bd2762f","title":"Tie adjusted concordance squared: Squaring the numerator loses negative association direction. · 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":41.069,"exit_code":1,"observations":[{"actual":"-1","check":"regression 1","expected":"1","passed":false},{"actual":"-1","check":"regression 2","expected":"-1","passed":true},{"actual":"-1/20","check":"regression 3","expected":"-1/20","passed":true},{"actual":null,"check":"regression 4","expected":null,"passed":true},{"actual":null,"check":"regression 5","expected":null,"passed":true},{"actual":"-1","check":"regression 6","expected":"1","passed":false},{"actual":"0","check":"regression 7","expected":"0","passed":true},{"actual":"-1","check":"variable discordance direction","expected":"-1","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"-1\", \"expected\": \"1\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": \"-1\", \"expected\": \"-1\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"-1/20\", \"expected\": \"-1/20\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"-1\", \"expected\": \"1\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"variable discordance direction\", \"actual\": \"-1\", \"expected\": \"-1\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.552,"exit_code":1,"observations":[{"actual":"1","check":"regression 1","expected":"1","passed":true},{"actual":"1","check":"regression 2","expected":"-1","passed":false},{"actual":"1/20","check":"regression 3","expected":"-1/20","passed":false},{"actual":null,"check":"regression 4","expected":null,"passed":true},{"actual":null,"check":"regression 5","expected":null,"passed":true},{"actual":"1","check":"regression 6","expected":"1","passed":true},{"actual":"0","check":"regression 7","expected":"0","passed":true},{"actual":"1","check":"variable discordance direction","expected":"-1","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"1\", \"expected\": \"-1\", \"passed\": false}, {\"check\": \"regression 3\", \"actual\": \"1/20\", \"expected\": \"-1/20\", \"passed\": false}, {\"check\": \"regression 4\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"variable discordance direction\", \"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."}}