{"abstract":"The exact combinadic unrank result violates the stated contract at increasing combination output.","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 out[:-1][::-1] still violates the increasing combination output invariant.","family":"s3-numerics-combinadic-unrank-increasing-combination-output","id":"FA-15186","implementations":{"attempt":{"sha256":"9d1721190ea5495ff7949c6147a5dbd64d8a595fc0672b6eb47d694a9598d74a","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-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][::-1]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, 0], [0, 1]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 1], [1]), ([1, 2], [2]), ([1, 3], [3]), ([1, 4], [4]), ([1, 5], [5])], [([2, 1], [0, 2]), ([1, 3], [3]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 17], [17]), ([1, 18], [18]), ([1, 19], [19]), ([1, 20], [20])], [([2, 2], [1, 2]), ([1, 6], [6]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 34], [34]), ([1, 35], [35]), ([1, 36], [36]), ([1, 37], [37])], [([2, 3], [0, 3]), ([1, 9], [9]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([2, 1], [0, 2]), ([2, 2], [1, 2]), ([2, 4], [1, 3]), ([2, 5], [2, 3])], [([2, 4], [1, 3]), ([1, 12], [12]), ([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":"2a568ca04b2f07c21f26d849b26377bde5a48a49317e0119265c989c980bc80e","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-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\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, 0], [0, 1]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 1], [1]), ([1, 2], [2]), ([1, 3], [3]), ([1, 4], [4]), ([1, 5], [5])], [([2, 1], [0, 2]), ([1, 3], [3]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 17], [17]), ([1, 18], [18]), ([1, 19], [19]), ([1, 20], [20])], [([2, 2], [1, 2]), ([1, 6], [6]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([1, 34], [34]), ([1, 35], [35]), ([1, 36], [36]), ([1, 37], [37])], [([2, 3], [0, 3]), ([1, 9], [9]), ([1, 0], [0]), ([5, 49], [0, 3, 5, 6, 7]), ([2, 1], [0, 2]), ([2, 2], [1, 2]), ([2, 4], [1, 3]), ([2, 5], [2, 3])], [([2, 4], [1, 3]), ([1, 12], [12]), ([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-increasing-combination-output","generated_at":"2026-09-29T14:39:24.117201+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 increasing combination output step uses out instead of out[::-1].","sha256":"0e4c4e765b09565c0152c3044cc4706fb03bf2d60fb76afb2ecd5bd89c3e35fd","title":"Combinadic unrank: increasing combination output · 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":46.462,"exit_code":1,"observations":[{"actual":[1],"check":"explicit oracle 0","expected":[0,1],"passed":false},{"actual":[],"check":"explicit oracle 1","expected":[0],"passed":false},{"actual":[3,5,6,7],"check":"explicit oracle 2","expected":[0,3,5,6,7],"passed":false},{"actual":[],"check":"explicit oracle 3","expected":[1],"passed":false},{"actual":[],"check":"explicit oracle 4","expected":[2],"passed":false},{"actual":[],"check":"explicit oracle 5","expected":[3],"passed":false},{"actual":[],"check":"explicit oracle 6","expected":[4],"passed":false},{"actual":[],"check":"explicit oracle 7","expected":[5],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [1], \"expected\": [0, 1], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [], \"expected\": [0], \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": [3, 5, 6, 7], \"expected\": [0, 3, 5, 6, 7], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [], \"expected\": [1], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [], \"expected\": [2], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [], \"expected\": [3], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [], \"expected\": [4], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [], \"expected\": [5], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.948,"exit_code":1,"observations":[{"actual":[1,0],"check":"explicit oracle 0","expected":[0,1],"passed":false},{"actual":[0],"check":"explicit oracle 1","expected":[0],"passed":true},{"actual":[7,6,5,3,0],"check":"explicit oracle 2","expected":[0,3,5,6,7],"passed":false},{"actual":[1],"check":"explicit oracle 3","expected":[1],"passed":true},{"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, 0], \"expected\": [0, 1], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [0], \"expected\": [0], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [7, 6, 5, 3, 0], \"expected\": [0, 3, 5, 6, 7], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [1], \"expected\": [1], \"passed\": true}, {\"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."}}