{"abstract":"Simplex leaving row includes nonlimiting coefficients.","category":"Optimization solver contracts","checks":8,"contract":"Given finite Python integer/float nonnegative RHS values and nonzero pivot coefficients, return basis index of the minimum exact represented rhs/coefficient over positive coefficients; tie by smallest basis index; None means unbounded.","evaluation_group":"model-522c42bd64f0266f","failed_approach":"Filtering negative coefficients fixes feasibility but row-order tie breaking violates the stated anti-cycling rule.","family":"z-optimization-simplex-ratio","id":"FA-12011","implementations":{"attempt":{"sha256":"0575b96bf1a5f90dd9b0f1e169ed175e3e33891e0f6e274358b244144df621ed","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(rows):\n    eligible=[r for r in rows if r[2]>0]\n    return min(eligible,key=lambda r:r[1]/r[2])[0] if eligible else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('negative coefficient', solve([(1,N,-1),(2,2*N,1)]), 2)\ncheck('basis tie', solve([(8,2*N,2),(3,N,1)]), 3)\ncheck('strict minimum', solve([(8,3*N,1),(3,N,1)]), 3)\ncheck('unbounded', solve([(1,N,-1)]), None)\ncheck('degenerate tie', solve([(9,0,1),(2,0,2)]), 2)\ncheck('empty tableau', solve([]), None)\ncheck('nearby large ratios remain distinct', solve([(0,2**54+N,1),(1,2**54+N-1,1)]), 1)\ncheck('tiny positive ratio remains distinct from zero', solve([(0,1e-300,1e300),(1,0,1)]), 1)\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":"4d05b2227608cdef524f363e2cad2b585702668bb0a54ca50f5a0f655abba482","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(rows):\n    return min(rows, key=lambda r:r[1]/r[2])[0] if rows else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('negative coefficient', solve([(1,N,-1),(2,2*N,1)]), 2)\ncheck('basis tie', solve([(8,2*N,2),(3,N,1)]), 3)\ncheck('strict minimum', solve([(8,3*N,1),(3,N,1)]), 3)\ncheck('unbounded', solve([(1,N,-1)]), None)\ncheck('degenerate tie', solve([(9,0,1),(2,0,2)]), 2)\ncheck('empty tableau', solve([]), None)\ncheck('nearby large ratios remain distinct', solve([(0,2**54+N,1),(1,2**54+N-1,1)]), 1)\ncheck('tiny positive ratio remains distinct from zero', solve([(0,1e-300,1e300),(1,0,1)]), 1)\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":"3608f4163263db28d8fcd6b75606a762b9f77febfc11c84d6eb7d91b0aacd9b5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(rows):\n    eligible=[r for r in rows if r[2]>0]\n    return min(eligible,key=lambda r:(Fraction(r[1])/Fraction(r[2]),r[0]))[0] if eligible else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('negative coefficient', solve([(1,N,-1),(2,2*N,1)]), 2)\ncheck('basis tie', solve([(8,2*N,2),(3,N,1)]), 3)\ncheck('strict minimum', solve([(8,3*N,1),(3,N,1)]), 3)\ncheck('unbounded', solve([(1,N,-1)]), None)\ncheck('degenerate tie', solve([(9,0,1),(2,0,2)]), 2)\ncheck('empty tableau', solve([]), None)\ncheck('nearby large ratios remain distinct', solve([(0,2**54+N,1),(1,2**54+N-1,1)]), 1)\ncheck('tiny positive ratio remains distinct from zero', solve([(0,1e-300,1e300),(1,0,1)]), 1)\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":"Controlled finite inputs and explicit one-step contracts; this is not a production solver or a numerical stability benchmark. 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":"z-optimization-simplex-ratio","generated_at":"2026-09-29T14:38:53.035301+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"This deterministic solver-step model isolates an algorithmic invariant used by iterative optimization implementations.","repair":"Consider strictly positive coefficients, compare exact ratios, and break ratio ties by smallest basis index.","root_cause":"Ratio selection includes negative pivot column coefficients.","sha256":"329fb6d8f832052f33739ff71df6e7b2f7fb25a0ed390f36e629e848711ea147","title":"Simplex leaving row includes nonlimiting coefficients · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.196,"exit_code":1,"observations":[{"actual":2,"check":"negative coefficient","expected":2,"passed":true},{"actual":8,"check":"basis tie","expected":3,"passed":false},{"actual":3,"check":"strict minimum","expected":3,"passed":true},{"actual":null,"check":"unbounded","expected":null,"passed":true},{"actual":9,"check":"degenerate tie","expected":2,"passed":false},{"actual":null,"check":"empty tableau","expected":null,"passed":true},{"actual":0,"check":"nearby large ratios remain distinct","expected":1,"passed":false},{"actual":0,"check":"tiny positive ratio remains distinct from zero","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"negative coefficient\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"basis tie\", \"actual\": 8, \"expected\": 3, \"passed\": false}, {\"check\": \"strict minimum\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"unbounded\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"degenerate tie\", \"actual\": 9, \"expected\": 2, \"passed\": false}, {\"check\": \"empty tableau\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"nearby large ratios remain distinct\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"tiny positive ratio remains distinct from zero\", \"actual\": 0, \"expected\": 1, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.078,"exit_code":1,"observations":[{"actual":1,"check":"negative coefficient","expected":2,"passed":false},{"actual":8,"check":"basis tie","expected":3,"passed":false},{"actual":3,"check":"strict minimum","expected":3,"passed":true},{"actual":1,"check":"unbounded","expected":null,"passed":false},{"actual":9,"check":"degenerate tie","expected":2,"passed":false},{"actual":null,"check":"empty tableau","expected":null,"passed":true},{"actual":0,"check":"nearby large ratios remain distinct","expected":1,"passed":false},{"actual":0,"check":"tiny positive ratio remains distinct from zero","expected":1,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"negative coefficient\", \"actual\": 1, \"expected\": 2, \"passed\": false}, {\"check\": \"basis tie\", \"actual\": 8, \"expected\": 3, \"passed\": false}, {\"check\": \"strict minimum\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"unbounded\", \"actual\": 1, \"expected\": null, \"passed\": false}, {\"check\": \"degenerate tie\", \"actual\": 9, \"expected\": 2, \"passed\": false}, {\"check\": \"empty tableau\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"nearby large ratios remain distinct\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"tiny positive ratio remains distinct from zero\", \"actual\": 0, \"expected\": 1, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.917,"exit_code":0,"observations":[{"actual":2,"check":"negative coefficient","expected":2,"passed":true},{"actual":3,"check":"basis tie","expected":3,"passed":true},{"actual":3,"check":"strict minimum","expected":3,"passed":true},{"actual":null,"check":"unbounded","expected":null,"passed":true},{"actual":2,"check":"degenerate tie","expected":2,"passed":true},{"actual":null,"check":"empty tableau","expected":null,"passed":true},{"actual":1,"check":"nearby large ratios remain distinct","expected":1,"passed":true},{"actual":1,"check":"tiny positive ratio remains distinct from zero","expected":1,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"negative coefficient\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"basis tie\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"strict minimum\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"unbounded\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"degenerate tie\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"empty tableau\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"nearby large ratios remain distinct\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"tiny positive ratio remains distinct from zero\", \"actual\": 1, \"expected\": 1, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}