{"abstract":"Removing a dead zone creates a command discontinuity.","category":"Discrete control systems","checks":6,"contract":"For symmetric nonnegative width d, output zero for abs(x)<=d, otherwise sign(x)*(abs(x)-d). This is an unscaled integer dead-zone model.","evaluation_group":"model-4869f52ab0413f0b","failed_approach":"Subtracting width without sign handling distorts negative commands.","family":"z-control_systems-deadzone-offset","id":"FA-11971","implementations":{"attempt":{"sha256":"52f3faf9993a35fa73adbcc112f3d1c2aa8b6958d6af87dab9b16f5cdff388cd","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x, d):\n    return 0 if abs(x)<=d else x-d\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('positive beyond', solve(3*N, N), 2*N)\ncheck('negative beyond', solve(-3*N, N), -2*N)\ncheck('positive edge', solve(N, N), 0)\ncheck('negative edge', solve(-N, N), 0)\ncheck('center', solve(0, N), 0)\ncheck('zero width', solve(-N, 0), -N)\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":"356e8289519a1c0b3c9057704f36858462e0c863e0da6df9afe11e78af9400e1","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x, d):\n    return 0 if abs(x)<=d else x\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('positive beyond', solve(3*N, N), 2*N)\ncheck('negative beyond', solve(-3*N, N), -2*N)\ncheck('positive edge', solve(N, N), 0)\ncheck('negative edge', solve(-N, N), 0)\ncheck('center', solve(0, N), 0)\ncheck('zero width', solve(-N, 0), -N)\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":"a12f726c4194d711ad9195aa37bf114fdd0d9caa3db2dabf1faf593f53de295e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x, d):\n    return max(0,x-d) if x>=0 else min(0,x+d)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('positive beyond', solve(3*N, N), 2*N)\ncheck('negative beyond', solve(-3*N, N), -2*N)\ncheck('positive edge', solve(N, N), 0)\ncheck('negative edge', solve(-N, N), 0)\ncheck('center', solve(0, N), 0)\ncheck('zero width', solve(-N, 0), -N)\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":"Integer-valued controlled examples only; no physical plant, stability guarantee, timing jitter, or hardware behavior is modeled. 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-control_systems-deadzone-offset","generated_at":"2026-09-29T14:38:52.653776+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"An offline discrete controller model isolates this state or arithmetic fault; it makes no physical plant or safety claim.","repair":"Subtract the dead-zone width from magnitude and retain sign.","root_cause":"Outside the dead zone the original magnitude is returned unchanged.","sha256":"ab2ab3fc9c21cd27938d9049b6451d3378bd3c1a0031e7d837fafabb8ca2fc29","title":"Removing a dead zone creates a command discontinuity · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":43.622,"exit_code":1,"observations":[{"actual":2,"check":"positive beyond","expected":2,"passed":true},{"actual":-4,"check":"negative beyond","expected":-2,"passed":false},{"actual":0,"check":"positive edge","expected":0,"passed":true},{"actual":0,"check":"negative edge","expected":0,"passed":true},{"actual":0,"check":"center","expected":0,"passed":true},{"actual":-1,"check":"zero width","expected":-1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"positive beyond\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"negative beyond\", \"actual\": -4, \"expected\": -2, \"passed\": false}, {\"check\": \"positive edge\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"negative edge\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"center\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"zero width\", \"actual\": -1, \"expected\": -1, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.744,"exit_code":1,"observations":[{"actual":3,"check":"positive beyond","expected":2,"passed":false},{"actual":-3,"check":"negative beyond","expected":-2,"passed":false},{"actual":0,"check":"positive edge","expected":0,"passed":true},{"actual":0,"check":"negative edge","expected":0,"passed":true},{"actual":0,"check":"center","expected":0,"passed":true},{"actual":-1,"check":"zero width","expected":-1,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"positive beyond\", \"actual\": 3, \"expected\": 2, \"passed\": false}, {\"check\": \"negative beyond\", \"actual\": -3, \"expected\": -2, \"passed\": false}, {\"check\": \"positive edge\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"negative edge\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"center\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"zero width\", \"actual\": -1, \"expected\": -1, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.202,"exit_code":0,"observations":[{"actual":2,"check":"positive beyond","expected":2,"passed":true},{"actual":-2,"check":"negative beyond","expected":-2,"passed":true},{"actual":0,"check":"positive edge","expected":0,"passed":true},{"actual":0,"check":"negative edge","expected":0,"passed":true},{"actual":0,"check":"center","expected":0,"passed":true},{"actual":-1,"check":"zero width","expected":-1,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"positive beyond\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"negative beyond\", \"actual\": -2, \"expected\": -2, \"passed\": true}, {\"check\": \"positive edge\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"negative edge\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"center\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"zero width\", \"actual\": -1, \"expected\": -1, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}