{"abstract":"The exact bounded diophantine result violates the stated contract at remaining right hand side.","category":"Numerics","checks":8,"contract":"Input [a,b,c,L], positive a,b and nonnegative L; lexicographically ordered nonnegative solutions a*u+b*v=c with u,v<=L.","evaluation_group":"s3-numerics-bounded-diophantine","failed_approach":"The partial repair c+a*u still violates the remaining right hand side invariant.","family":"s3-numerics-bounded-diophantine-remaining-right-hand-side","id":"FA-14396","implementations":{"attempt":{"sha256":"4c8ef737c48c465cbdb777086be6a7b20adfe0faa2dab7bd1ee747392d8839c0","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,b,c,L=x\n    out=[]\n    for u in range(L+1):\n     t=c+a*u\n     if t%b != 0: continue\n     v=t//b\n     if 0<=v<=L: out.append([u,v])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, 1, 1, 1], [[0, 1]]), ([1, 1, -2, 2], []), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, -2, 1], []), ([1, 1, -2, 3], []), ([1, 1, -2, 4], []), ([1, 1, -2, 5], [])], [([2, 1, 1, 2], [[0, 1]]), ([1, 1, -2, 5], []), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 0, 5], [[0, 0]]), ([1, 1, 1, 0], []), ([1, 1, 1, 1], [[0, 1], [1, 0]]), ([1, 1, 1, 2], [[0, 1], [1, 0]])], [([2, 1, 1, 3], [[0, 1]]), ([1, 1, -1, 3], []), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 3, 4], [[0, 3], [1, 2], [2, 1], [3, 0]]), ([1, 1, 3, 5], [[0, 3], [1, 2], [2, 1], [3, 0]]), ([1, 1, 4, 0], []), ([1, 1, 4, 1], [])], [([2, 1, 1, 4], [[0, 1]]), ([1, 1, 0, 1], [[0, 0]]), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 6, 3], [[3, 3]]), ([1, 1, 6, 4], [[2, 4], [3, 3], [4, 2]]), ([1, 1, 6, 5], [[1, 5], [2, 4], [3, 3], [4, 2], [5, 1]]), ([1, 1, 7, 0], [])], [([2, 1, 1, 5], [[0, 1]]), ([1, 1, 0, 4], [[0, 0]]), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 9, 2], []), ([1, 1, 9, 3], []), ([1, 1, 9, 4], []), ([1, 1, 9, 5], [[4, 5], [5, 4]])]]\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":"b1ebb186ee42392e91c318f9705c164e9d56fa788b1f5c66d049f945f186aff6","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,b,c,L=x\n    out=[]\n    for u in range(L+1):\n     t=c-u\n     if t%b != 0: continue\n     v=t//b\n     if 0<=v<=L: out.append([u,v])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, 1, 1, 1], [[0, 1]]), ([1, 1, -2, 2], []), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, -2, 1], []), ([1, 1, -2, 3], []), ([1, 1, -2, 4], []), ([1, 1, -2, 5], [])], [([2, 1, 1, 2], [[0, 1]]), ([1, 1, -2, 5], []), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 0, 5], [[0, 0]]), ([1, 1, 1, 0], []), ([1, 1, 1, 1], [[0, 1], [1, 0]]), ([1, 1, 1, 2], [[0, 1], [1, 0]])], [([2, 1, 1, 3], [[0, 1]]), ([1, 1, -1, 3], []), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 3, 4], [[0, 3], [1, 2], [2, 1], [3, 0]]), ([1, 1, 3, 5], [[0, 3], [1, 2], [2, 1], [3, 0]]), ([1, 1, 4, 0], []), ([1, 1, 4, 1], [])], [([2, 1, 1, 4], [[0, 1]]), ([1, 1, 0, 1], [[0, 0]]), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 6, 3], [[3, 3]]), ([1, 1, 6, 4], [[2, 4], [3, 3], [4, 2]]), ([1, 1, 6, 5], [[1, 5], [2, 4], [3, 3], [4, 2], [5, 1]]), ([1, 1, 7, 0], [])], [([2, 1, 1, 5], [[0, 1]]), ([1, 1, 0, 4], [[0, 0]]), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 9, 2], []), ([1, 1, 9, 3], []), ([1, 1, 9, 4], []), ([1, 1, 9, 5], [[4, 5], [5, 4]])]]\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":"0ada95cbc52b378173b5a115d068fbfe3259483758acbf1e8a5832279ff0daf6","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,b,c,L=x\n    out=[]\n    for u in range(L+1):\n     t=c-a*u\n     if t%b != 0: continue\n     v=t//b\n     if 0<=v<=L: out.append([u,v])\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2, 1, 1, 1], [[0, 1]]), ([1, 1, -2, 2], []), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, -2, 1], []), ([1, 1, -2, 3], []), ([1, 1, -2, 4], []), ([1, 1, -2, 5], [])], [([2, 1, 1, 2], [[0, 1]]), ([1, 1, -2, 5], []), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 0, 5], [[0, 0]]), ([1, 1, 1, 0], []), ([1, 1, 1, 1], [[0, 1], [1, 0]]), ([1, 1, 1, 2], [[0, 1], [1, 0]])], [([2, 1, 1, 3], [[0, 1]]), ([1, 1, -1, 3], []), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 3, 4], [[0, 3], [1, 2], [2, 1], [3, 0]]), ([1, 1, 3, 5], [[0, 3], [1, 2], [2, 1], [3, 0]]), ([1, 1, 4, 0], []), ([1, 1, 4, 1], [])], [([2, 1, 1, 4], [[0, 1]]), ([1, 1, 0, 1], [[0, 0]]), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 6, 3], [[3, 3]]), ([1, 1, 6, 4], [[2, 4], [3, 3], [4, 2]]), ([1, 1, 6, 5], [[1, 5], [2, 4], [3, 3], [4, 2], [5, 1]]), ([1, 1, 7, 0], [])], [([2, 1, 1, 5], [[0, 1]]), ([1, 1, 0, 4], [[0, 0]]), ([1, 1, -2, 0], []), ([4, 4, 14, 5], []), ([1, 1, 9, 2], []), ([1, 1, 9, 3], []), ([1, 1, 9, 4], []), ([1, 1, 9, 5], [[4, 5], [5, 4]])]]\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-bounded-diophantine-remaining-right-hand-side","generated_at":"2026-09-29T14:39:16.450024+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 c-a*u at the remaining right hand side step.","root_cause":"The remaining right hand side step uses c-u instead of c-a*u.","sha256":"87e42f0f803da2dce0c9e8c4c6a03039dc9286d519f0e8049d2b239f75006b79","title":"Bounded diophantine: remaining right hand side · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.407,"exit_code":1,"observations":[{"actual":[[0,1]],"check":"explicit oracle 0","expected":[[0,1]],"passed":true},{"actual":[[2,0]],"check":"explicit oracle 1","expected":[],"passed":false},{"actual":[],"check":"explicit oracle 2","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 3","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 4","expected":[],"passed":true},{"actual":[[2,0],[3,1]],"check":"explicit oracle 5","expected":[],"passed":false},{"actual":[[2,0],[3,1],[4,2]],"check":"explicit oracle 6","expected":[],"passed":false},{"actual":[[2,0],[3,1],[4,2],[5,3]],"check":"explicit oracle 7","expected":[],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[0, 1]], \"expected\": [[0, 1]], \"passed\": true}, {\"check\": \"explicit oracle 1\", \"actual\": [[2, 0]], \"expected\": [], \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [[2, 0], [3, 1]], \"expected\": [], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [[2, 0], [3, 1], [4, 2]], \"expected\": [], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [[2, 0], [3, 1], [4, 2], [5, 3]], \"expected\": [], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.106,"exit_code":1,"observations":[{"actual":[[0,1],[1,0]],"check":"explicit oracle 0","expected":[[0,1]],"passed":false},{"actual":[],"check":"explicit oracle 1","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 2","expected":[],"passed":true},{"actual":[[2,3]],"check":"explicit oracle 3","expected":[],"passed":false},{"actual":[],"check":"explicit oracle 4","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 5","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 6","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 7","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[0, 1], [1, 0]], \"expected\": [[0, 1]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [[2, 3]], \"expected\": [], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.487,"exit_code":0,"observations":[{"actual":[[0,1]],"check":"explicit oracle 0","expected":[[0,1]],"passed":true},{"actual":[],"check":"explicit oracle 1","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 2","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 3","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 4","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 5","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 6","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 7","expected":[],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[0, 1]], \"expected\": [[0, 1]], \"passed\": true}, {\"check\": \"explicit oracle 1\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}