{"abstract":"The exact colex combination rank result violates the stated contract at selected element traversal.","category":"Numerics","checks":8,"contract":"Input strictly increasing selected nonnegative integers; zero-based colex rank=sum choose(a_i,i+1).","evaluation_group":"s3-numerics-colex-combination-rank","failed_approach":"The partial repair range(1,len(a)) still violates the selected element traversal invariant.","family":"s3-numerics-colex-combination-rank-selected-element-traversal","id":"FA-15141","implementations":{"attempt":{"sha256":"6a8efaee542645d793afc960f265ac2b5bfecff7dc668fac14aba226bb62aaa2","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    a=x;rank=0\n    for i in range(1,len(a)):\n     top=a[i];bottom=i+1\n     term=math.comb(top,bottom) if 0<=bottom<=top else 0\n     rank=rank+term\n    return rank\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([1], 1), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0], 0), ([0, 1], 0), ([0], 0), ([1], 1), ([2], 2)], [([1], 1), ([1, 2], 2), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0, 3], 3), ([1, 2], 2), ([1, 3], 4), ([2, 3], 5)], [([2], 2), ([3], 3), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0, 4], 6), ([1, 2], 2), ([1, 3], 4), ([1, 4], 7)], [([0, 2], 1), ([2, 3], 5), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0, 1, 2, 3], 0), ([0, 1, 2, 4], 1), ([0, 1, 3, 4], 2), ([0, 2, 3, 4], 3)], [([1, 2], 2), ([2], 2), ([0], 0), ([4, 5, 6, 7, 8], 125), ([1, 2], 2), ([1, 3], 4), ([1, 4], 7), ([1, 5], 11)]]\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":"812d1cc3f7b3e03f1866e48faecd1f68701f254698d1a826d4f5674dc970ebc1","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    a=x;rank=0\n    for i in range(len(a)-1):\n     top=a[i];bottom=i+1\n     term=math.comb(top,bottom) if 0<=bottom<=top else 0\n     rank=rank+term\n    return rank\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([1], 1), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0], 0), ([0, 1], 0), ([0], 0), ([1], 1), ([2], 2)], [([1], 1), ([1, 2], 2), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0, 3], 3), ([1, 2], 2), ([1, 3], 4), ([2, 3], 5)], [([2], 2), ([3], 3), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0, 4], 6), ([1, 2], 2), ([1, 3], 4), ([1, 4], 7)], [([0, 2], 1), ([2, 3], 5), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0, 1, 2, 3], 0), ([0, 1, 2, 4], 1), ([0, 1, 3, 4], 2), ([0, 2, 3, 4], 3)], [([1, 2], 2), ([2], 2), ([0], 0), ([4, 5, 6, 7, 8], 125), ([1, 2], 2), ([1, 3], 4), ([1, 4], 7), ([1, 5], 11)]]\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"},"fixed":{"sha256":"fe05e2cee738aab18589198cba9bb996dfd040c59a128b67c7fafb9fba9e93c1","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    a=x;rank=0\n    for i in range(len(a)):\n     top=a[i];bottom=i+1\n     term=math.comb(top,bottom) if 0<=bottom<=top else 0\n     rank=rank+term\n    return rank\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([1], 1), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0], 0), ([0, 1], 0), ([0], 0), ([1], 1), ([2], 2)], [([1], 1), ([1, 2], 2), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0, 3], 3), ([1, 2], 2), ([1, 3], 4), ([2, 3], 5)], [([2], 2), ([3], 3), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0, 4], 6), ([1, 2], 2), ([1, 3], 4), ([1, 4], 7)], [([0, 2], 1), ([2, 3], 5), ([0], 0), ([4, 5, 6, 7, 8], 125), ([0, 1, 2, 3], 0), ([0, 1, 2, 4], 1), ([0, 1, 3, 4], 2), ([0, 2, 3, 4], 3)], [([1, 2], 2), ([2], 2), ([0], 0), ([4, 5, 6, 7, 8], 125), ([1, 2], 2), ([1, 3], 4), ([1, 4], 7), ([1, 5], 11)]]\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-colex-combination-rank-selected-element-traversal","generated_at":"2026-09-29T14:39:23.872139+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.","repair":"Use range(len(a)) at the selected element traversal step.","root_cause":"The selected element traversal step uses range(len(a)-1) instead of range(len(a)).","sha256":"12f05be068f5178bd4b87485263da13033d81c8c7e534918cb4acbb3e45a3f0e","title":"Colex combination rank: selected element traversal · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.631,"exit_code":1,"observations":[{"actual":0,"check":"explicit oracle 0","expected":1,"passed":false},{"actual":0,"check":"explicit oracle 1","expected":0,"passed":true},{"actual":121,"check":"explicit oracle 2","expected":125,"passed":false},{"actual":0,"check":"explicit oracle 3","expected":0,"passed":true},{"actual":0,"check":"explicit oracle 4","expected":0,"passed":true},{"actual":0,"check":"explicit oracle 5","expected":0,"passed":true},{"actual":0,"check":"explicit oracle 6","expected":1,"passed":false},{"actual":0,"check":"explicit oracle 7","expected":2,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": 121, \"expected\": 125, \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": 0, \"expected\": 2, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.227,"exit_code":1,"observations":[{"actual":0,"check":"explicit oracle 0","expected":1,"passed":false},{"actual":0,"check":"explicit oracle 1","expected":0,"passed":true},{"actual":69,"check":"explicit oracle 2","expected":125,"passed":false},{"actual":0,"check":"explicit oracle 3","expected":0,"passed":true},{"actual":0,"check":"explicit oracle 4","expected":0,"passed":true},{"actual":0,"check":"explicit oracle 5","expected":0,"passed":true},{"actual":0,"check":"explicit oracle 6","expected":1,"passed":false},{"actual":0,"check":"explicit oracle 7","expected":2,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": 69, \"expected\": 125, \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": 0, \"expected\": 2, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":46.776,"exit_code":0,"observations":[{"actual":1,"check":"explicit oracle 0","expected":1,"passed":true},{"actual":0,"check":"explicit oracle 1","expected":0,"passed":true},{"actual":125,"check":"explicit oracle 2","expected":125,"passed":true},{"actual":0,"check":"explicit oracle 3","expected":0,"passed":true},{"actual":0,"check":"explicit oracle 4","expected":0,"passed":true},{"actual":0,"check":"explicit oracle 5","expected":0,"passed":true},{"actual":1,"check":"explicit oracle 6","expected":1,"passed":true},{"actual":2,"check":"explicit oracle 7","expected":2,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 1\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": 125, \"expected\": 125, \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": 2, \"expected\": 2, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}