{"abstract":"The exact combinadic unrank result violates the stated contract at greedy upper bound.","category":"Numerics","checks":8,"contract":"Input [k,r], k>=1 and r>=0; unique increasing combination of k nonnegative integers with colex rank r. Bounds: 1<=k<=5 and 0<=r<=49.","contract_signature":"x","evaluation_group":"s3-numerics-combinadic-unrank","failed_approach":"The partial repair j-1 still violates the greedy upper bound invariant.","family":"s3-numerics-combinadic-unrank-greedy-upper-bound","id":"FA-15171","implementations":{"attempt":{"sha256":"6dd8b23f0b0e7dc3e75d98ecbd6db5a9eb171e1002af606704570994e62e41e8","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    k,r=x;out=[];ceiling=r+k+1\n    for j in range(k,0,-1):\n     a=j-1\n     for _ in range(200):\n      if a<j or math.comb(a,j)<=r:break\n      a-=1\n     out.append(a)\n     r=r-(math.comb(a,j) if a>=j else 0)\n     ceiling=a\n    return out[::-1]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, 0], [0, 1]), ([1, 1], [1]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 2], [2]), ([1, 3], [3]), ([1, 4], [4]), ([1, 5], [5])], [([2, 2], [1, 2]), ([1, 4], [4]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 17], [17]), ([1, 18], [18]), ([1, 19], [19]), ([1, 20], [20])], [([2, 5], [2, 3]), ([1, 7], [7]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 34], [34]), ([1, 35], [35]), ([1, 36], [36]), ([1, 37], [37])], [([2, 9], [3, 4]), ([1, 10], [10]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([2, 1], [0, 2]), ([2, 2], [1, 2]), ([2, 3], [0, 3]), ([2, 4], [1, 3])], [([2, 14], [4, 5]), ([1, 13], [13]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([2, 18], [3, 6]), ([2, 19], [4, 6]), ([2, 20], [5, 6]), ([2, 21], [0, 7])]]\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":"788520b07d0aa2f14a5105858635e73dc8e41d41fdb0d6714c0d811f3b9d6073","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    k,r=x;out=[];ceiling=r+k+1\n    for j in range(k,0,-1):\n     a=ceiling-2\n     for _ in range(200):\n      if a<j or math.comb(a,j)<=r:break\n      a-=1\n     out.append(a)\n     r=r-(math.comb(a,j) if a>=j else 0)\n     ceiling=a\n    return out[::-1]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, 0], [0, 1]), ([1, 1], [1]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 2], [2]), ([1, 3], [3]), ([1, 4], [4]), ([1, 5], [5])], [([2, 2], [1, 2]), ([1, 4], [4]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 17], [17]), ([1, 18], [18]), ([1, 19], [19]), ([1, 20], [20])], [([2, 5], [2, 3]), ([1, 7], [7]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 34], [34]), ([1, 35], [35]), ([1, 36], [36]), ([1, 37], [37])], [([2, 9], [3, 4]), ([1, 10], [10]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([2, 1], [0, 2]), ([2, 2], [1, 2]), ([2, 3], [0, 3]), ([2, 4], [1, 3])], [([2, 14], [4, 5]), ([1, 13], [13]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([2, 18], [3, 6]), ([2, 19], [4, 6]), ([2, 20], [5, 6]), ([2, 21], [0, 7])]]\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-combinadic-unrank-greedy-upper-bound","generated_at":"2026-09-29T14:39:24.071031+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 greedy upper bound step uses ceiling-2 instead of ceiling-1.","sha256":"abc1e69707d4140f7495edd7f4d8e5951d30e57f97590285fe8e315fd9d07a48","title":"Combinadic unrank: greedy upper bound · 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":46.797,"exit_code":1,"observations":[{"actual":[0,1],"check":"explicit oracle 0","expected":[0,1],"passed":true},{"actual":[0],"check":"explicit oracle 1","expected":[1],"passed":false},{"actual":[0],"check":"explicit oracle 2","expected":[0],"passed":true},{"actual":[0,1,2,3,4],"check":"explicit oracle 3","expected":[0,3,5,6,7],"passed":false},{"actual":[0],"check":"explicit oracle 4","expected":[2],"passed":false},{"actual":[0],"check":"explicit oracle 5","expected":[3],"passed":false},{"actual":[0],"check":"explicit oracle 6","expected":[4],"passed":false},{"actual":[0],"check":"explicit oracle 7","expected":[5],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [0, 1], \"expected\": [0, 1], \"passed\": true}, {\"check\": \"explicit oracle 1\", \"actual\": [0], \"expected\": [1], \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": [0], \"expected\": [0], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [0, 1, 2, 3, 4], \"expected\": [0, 3, 5, 6, 7], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [0], \"expected\": [2], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [0], \"expected\": [3], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [0], \"expected\": [4], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [0], \"expected\": [5], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.434,"exit_code":1,"observations":[{"actual":[-1,1],"check":"explicit oracle 0","expected":[0,1],"passed":false},{"actual":[1],"check":"explicit oracle 1","expected":[1],"passed":true},{"actual":[0],"check":"explicit oracle 2","expected":[0],"passed":true},{"actual":[-1,1,3,5,7],"check":"explicit oracle 3","expected":[0,3,5,6,7],"passed":false},{"actual":[2],"check":"explicit oracle 4","expected":[2],"passed":true},{"actual":[3],"check":"explicit oracle 5","expected":[3],"passed":true},{"actual":[4],"check":"explicit oracle 6","expected":[4],"passed":true},{"actual":[5],"check":"explicit oracle 7","expected":[5],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [-1, 1], \"expected\": [0, 1], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [1], \"expected\": [1], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [0], \"expected\": [0], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [-1, 1, 3, 5, 7], \"expected\": [0, 3, 5, 6, 7], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [2], \"expected\": [2], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [3], \"expected\": [3], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [4], \"expected\": [4], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [5], \"expected\": [5], \"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."}}