{"abstract":"The exact balanced odd radix encoding result violates the stated contract at digit significance order.","category":"Numerics","checks":8,"contract":"Input [integer, odd radix>=3]; return least-significant-first balanced digits between -(base//2) and base//2, zero=[0]. Bounds: |integer|<=100 and radix<=9.","contract_signature":"x","evaluation_group":"s3-numerics-balanced-odd-radix-encoding","failed_approach":"The partial repair sorted(out) still violates the digit significance order invariant.","family":"s3-numerics-balanced-odd-radix-encoding-digit-significance-order","id":"FA-15036","implementations":{"attempt":{"sha256":"1807c7624340ab067886423834f5e27805a516274ab129cb4e9c07ce0235f5f1","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    n,b=x\n    if n==0:return [0]\n    out=[];half=b//2\n    for _ in range(60):\n     if n==0:break\n     r=n%b\n     if r>half:r-=b\n     out.append(r)\n     n=(n-r)//b\n    return sorted(out)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([-100, 3], [-1, 0, 1, -1, -1]), ([100, 9], [1, 2, 1]), ([-100, 5], [0, 0, 1, -1]), ([-100, 7], [-2, 0, -2]), ([-100, 9], [-1, -2, -1]), ([-99, 3], [0, 0, 1, -1, -1]), ([-99, 5], [1, 0, 1, -1]), ([-99, 7], [-1, 0, -2])], [([-100, 5], [0, 0, 1, -1]), ([-100, 9], [-1, -2, -1]), ([-100, 3], [-1, 0, 1, -1, -1]), ([100, 9], [1, 2, 1]), ([-96, 5], [-1, 1, 1, -1]), ([-96, 7], [2, 0, -2]), ([-96, 9], [3, -2, -1]), ([-95, 3], [1, 1, 1, -1, -1])], [([-99, 3], [0, 0, 1, -1, -1]), ([-99, 7], [-1, 0, -2]), ([-100, 3], [-1, 0, 1, -1, -1]), ([100, 9], [1, 2, 1]), ([-92, 7], [-1, 1, -2]), ([-92, 9], [-2, -1, -1]), ([-91, 3], [-1, 0, -1, 0, -1]), ([-91, 5], [-1, 2, 1, -1])], [([-99, 5], [1, 0, 1, -1]), ([-98, 5], [2, 0, 1, -1]), ([-100, 3], [-1, 0, 1, -1, -1]), ([100, 9], [1, 2, 1]), ([-88, 9], [2, -1, -1]), ([-87, 3], [0, 1, -1, 0, -1]), ([-87, 5], [-2, -2, 2, -1]), ([-87, 7], [-3, 2, -2])], [([-99, 7], [-1, 0, -2]), ([-97, 3], [-1, 1, 1, -1, -1]), ([-100, 3], [-1, 0, 1, -1, -1]), ([100, 9], [1, 2, 1]), ([-83, 3], [1, -1, 0, 0, -1]), ([-83, 5], [2, -2, 2, -1]), ([-83, 7], [1, 2, -2]), ([-83, 9], [-2, 0, -1])]]\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":"251734831fa6c2ebb9d49ae03ae192b1f9cb91760ee05a6fd3ae1dc3de474720","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    n,b=x\n    if n==0:return [0]\n    out=[];half=b//2\n    for _ in range(60):\n     if n==0:break\n     r=n%b\n     if r>half:r-=b\n     out.append(r)\n     n=(n-r)//b\n    return out[::-1]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([-100, 3], [-1, 0, 1, -1, -1]), ([100, 9], [1, 2, 1]), ([-100, 5], [0, 0, 1, -1]), ([-100, 7], [-2, 0, -2]), ([-100, 9], [-1, -2, -1]), ([-99, 3], [0, 0, 1, -1, -1]), ([-99, 5], [1, 0, 1, -1]), ([-99, 7], [-1, 0, -2])], [([-100, 5], [0, 0, 1, -1]), ([-100, 9], [-1, -2, -1]), ([-100, 3], [-1, 0, 1, -1, -1]), ([100, 9], [1, 2, 1]), ([-96, 5], [-1, 1, 1, -1]), ([-96, 7], [2, 0, -2]), ([-96, 9], [3, -2, -1]), ([-95, 3], [1, 1, 1, -1, -1])], [([-99, 3], [0, 0, 1, -1, -1]), ([-99, 7], [-1, 0, -2]), ([-100, 3], [-1, 0, 1, -1, -1]), ([100, 9], [1, 2, 1]), ([-92, 7], [-1, 1, -2]), ([-92, 9], [-2, -1, -1]), ([-91, 3], [-1, 0, -1, 0, -1]), ([-91, 5], [-1, 2, 1, -1])], [([-99, 5], [1, 0, 1, -1]), ([-98, 5], [2, 0, 1, -1]), ([-100, 3], [-1, 0, 1, -1, -1]), ([100, 9], [1, 2, 1]), ([-88, 9], [2, -1, -1]), ([-87, 3], [0, 1, -1, 0, -1]), ([-87, 5], [-2, -2, 2, -1]), ([-87, 7], [-3, 2, -2])], [([-99, 7], [-1, 0, -2]), ([-97, 3], [-1, 1, 1, -1, -1]), ([-100, 3], [-1, 0, 1, -1, -1]), ([100, 9], [1, 2, 1]), ([-83, 3], [1, -1, 0, 0, -1]), ([-83, 5], [2, -2, 2, -1]), ([-83, 7], [1, 2, -2]), ([-83, 9], [-2, 0, -1])]]\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-balanced-odd-radix-encoding-digit-significance-order","generated_at":"2026-09-29T14:39:22.691764+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 digit significance order step uses out[::-1] instead of out.","sha256":"4b184e43987e32787a1f0750991e7351195be8fe54d178c78a9f0092a9714cf5","title":"Balanced odd radix encoding: digit significance order · 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":42.463,"exit_code":1,"observations":[{"actual":[-1,-1,-1,0,1],"check":"explicit oracle 0","expected":[-1,0,1,-1,-1],"passed":false},{"actual":[1,1,2],"check":"explicit oracle 1","expected":[1,2,1],"passed":false},{"actual":[-1,0,0,1],"check":"explicit oracle 2","expected":[0,0,1,-1],"passed":false},{"actual":[-2,-2,0],"check":"explicit oracle 3","expected":[-2,0,-2],"passed":false},{"actual":[-2,-1,-1],"check":"explicit oracle 4","expected":[-1,-2,-1],"passed":false},{"actual":[-1,-1,0,0,1],"check":"explicit oracle 5","expected":[0,0,1,-1,-1],"passed":false},{"actual":[-1,0,1,1],"check":"explicit oracle 6","expected":[1,0,1,-1],"passed":false},{"actual":[-2,-1,0],"check":"explicit oracle 7","expected":[-1,0,-2],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [-1, -1, -1, 0, 1], \"expected\": [-1, 0, 1, -1, -1], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [1, 1, 2], \"expected\": [1, 2, 1], \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": [-1, 0, 0, 1], \"expected\": [0, 0, 1, -1], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [-2, -2, 0], \"expected\": [-2, 0, -2], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [-2, -1, -1], \"expected\": [-1, -2, -1], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [-1, -1, 0, 0, 1], \"expected\": [0, 0, 1, -1, -1], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [-1, 0, 1, 1], \"expected\": [1, 0, 1, -1], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [-2, -1, 0], \"expected\": [-1, 0, -2], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.954,"exit_code":1,"observations":[{"actual":[-1,-1,1,0,-1],"check":"explicit oracle 0","expected":[-1,0,1,-1,-1],"passed":false},{"actual":[1,2,1],"check":"explicit oracle 1","expected":[1,2,1],"passed":true},{"actual":[-1,1,0,0],"check":"explicit oracle 2","expected":[0,0,1,-1],"passed":false},{"actual":[-2,0,-2],"check":"explicit oracle 3","expected":[-2,0,-2],"passed":true},{"actual":[-1,-2,-1],"check":"explicit oracle 4","expected":[-1,-2,-1],"passed":true},{"actual":[-1,-1,1,0,0],"check":"explicit oracle 5","expected":[0,0,1,-1,-1],"passed":false},{"actual":[-1,1,0,1],"check":"explicit oracle 6","expected":[1,0,1,-1],"passed":false},{"actual":[-2,0,-1],"check":"explicit oracle 7","expected":[-1,0,-2],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [-1, -1, 1, 0, -1], \"expected\": [-1, 0, 1, -1, -1], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [1, 2, 1], \"expected\": [1, 2, 1], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [-1, 1, 0, 0], \"expected\": [0, 0, 1, -1], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [-2, 0, -2], \"expected\": [-2, 0, -2], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [-1, -2, -1], \"expected\": [-1, -2, -1], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [-1, -1, 1, 0, 0], \"expected\": [0, 0, 1, -1, -1], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [-1, 1, 0, 1], \"expected\": [1, 0, 1, -1], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [-2, 0, -1], \"expected\": [-1, 0, -2], \"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."}}