{"abstract":"Relative error is dominated by a 2*pi factor.","category":"Physics integrator stability","checks":8,"contract":"solve(xs, dt, omega): integrator frequency diagnostic. Upward crossings are samples with x[i-1]<0<=x[i], timed by linear interpolation. Period is the mean interval (last-first)/(count-1); relative error vs 2*pi/omega. Fewer than two crossings gives [None, count, None]. Return [period, count, error] rounded to 6.","evaluation_group":"w2-physics_integrator_stability-zero-crossing-period","failed_approach":"pi/omega is the half period.","family":"w2-physics_integrator_stability-zero-crossing-period-reference-period","id":"FA-87296","implementations":{"attempt":{"sha256":"e645e2fc6c3dfc1993718c5553bfeaf6b957a71039b1d1724e04880fcbad12b1","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(xs, dt, omega):\n    ts = []\n    for i in range(1, len(xs)):\n        a, b = xs[i - 1], xs[i]\n        if a < 0 <= b:\n            frac = -a / (b - a)\n            ts.append((i - 1 + frac) * dt)\n    if len(ts) < 2:\n        return [None, len(ts), None]\n    period = (ts[-1] - ts[0]) / (len(ts) - 1)\n    ref = math.pi / omega\n    return [round(period, 6), len(ts), round((period - ref) / ref, 6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[[[0.014, -0.488, -0.823, -0.928, -0.752, -0.382, 0.014, 0.485, 0.758, 0.797, 0.609, 0.243, -0.085, -0.47, -0.635, -0.672, -0.536, -0.267, 0.094, 0.396, 0.572, 0.57, 0.411, 0.193, -0.146, -0.39, -0.492, -0.459, -0.307, -0.026, 0.217, 0.381, 0.449, 0.431, 0.259, 0.13, -0.203, -0.364, -0.385], 0.125, 4.227], [1.446397, 3, -0.026939]], [[[-0.082, -0.546, -0.881, -0.981, -0.842, -0.495, -0.004, 0.435, 0.768, 0.94, 0.85], 0.125, 3.973], [None, 1, None]], [[[-0.157, -0.354, -0.537, -0.694, -0.821, -0.909, -0.965, -0.982, -0.957, -0.899, -0.777, -0.642, -0.509, -0.329, -0.077, 0.066, 0.298, 0.474, 0.579, 0.721, 0.837, 0.931, 0.946, 0.934, 0.903, 0.754, 0.706, 0.532, 0.37], 0.05, 4.035], [None, 1, None]], [[[-0.982, -0.868, -0.655, -0.382, -0.029, 0.261, 0.569, 0.826, 0.963, 0.996, 0.942, 0.728, 0.495, 0.137, -0.124, -0.479, -0.718, -0.94, -0.984, -0.971, -0.815, -0.573, -0.4, 0.056, 0.347, 0.586, 0.868, 0.976, 0.975, 0.849, 0.649, 0.358, 0.039, -0.279], 0.25, 1.314], [4.694298, 2, -0.018283]], [[[-0.506, -0.297, -0.076, 0.135, 0.36, 0.549, 0.702, 0.847, 0.916, 0.953, 0.938, 0.873, 0.756, 0.641, 0.488, 0.29, 0.083, -0.164, -0.355, -0.505, -0.711, -0.811, -0.87, -0.884, -0.875, -0.809, -0.705, -0.583], 0.1, 2.222], [None, 1, None]], [[[-0.996, -0.793, -0.388, 0.134, 0.56, 0.832, 0.845, 0.666, 0.306, -0.118, -0.51, -0.737, -0.721, -0.538, -0.141, 0.138, 0.492, 0.642, 0.605, 0.406, 0.165, -0.141, -0.462, -0.553, -0.483, -0.275, -0.004, 0.223], 0.125, 4.228], [1.454645, 3, -0.021159]], [[[0.977, -0.065, -0.968, -0.204, 0.883, 0.472, -0.609, -0.652, 0.532, 0.791, -0.188, -0.864, -0.051, 0.844, 0.497, -0.642, -0.528, 0.547, 0.79, -0.35, -0.705, 0.213, 0.671, 0.508, -0.528, -0.582, 0.109, 0.698, -0.453, -0.687, -0.293, 0.533, 0.0, -0.44, -0.539, 0.624, 0.282, -0.55, -0.586, 0.295], 0.25, 5.546], [1.108671, 9, -0.021405]], [[[-0.981, -0.904, -0.463, 0.134, 0.714, 0.994, 0.852, 0.37, -0.184, -0.786, -0.999, -0.817, -0.396, 0.217, 0.816, 0.997, 0.831, 0.172, -0.235, -0.913, -0.987, -0.687, -0.191, 0.507, 0.853, 0.935, 0.831, 0.108, -0.661, -0.982, -0.967, -0.674, -0.003, 0.527, 0.989, 0.998], 0.125, 5.059], [1.217921, 4, -0.019372]]], [[[[0.045, -0.043, -0.133, -0.217, -0.299, -0.379, -0.463, -0.542, -0.605, -0.673, -0.734, -0.781, -0.828, -0.863, -0.894, -0.926, -0.942, -0.953, -0.956, 0.0, -0.936, -0.915], 0.05, 1.751], [None, 1, None]], [[[-0.425, -0.944, -0.194, 0.722, 0.59, -0.255, -0.74, -0.107, 0.57, 0.553, -0.097, -0.577, -0.147, 0.454], 0.25, 4.911], [1.2541, 3, -0.019783]], [[[0.577, -0.503, -0.961, 0.0, 0.735, 0.821, -0.096, -0.89, -0.599, 0.293, 0.882, 0.27, -0.691, -0.829, -0.079, 0.762, 0.626, -0.255, -0.768], 0.25, 4.575], [1.386742, 3, 0.009734]], [[[0.221, 0.117, 0.014, -0.083, -0.18, -0.269, -0.351, -0.412, -0.477, -0.546, -0.588, -0.634, -0.663, -0.691, -0.713, -0.719, -0.719, -0.712, -0.695, -0.675, -0.648, -0.606, -0.565, -0.525, -0.465, -0.424, -0.382, -0.319, 0.0, -0.186, -0.134, -0.057, -0.026, 0.046, 0.083, 0.103], 0.1, 1.021], [0.436111, 2, -0.929133]], [[[0.598, 0.444, 0.282, 0.1, -0.054, -0.227, -0.393, -0.519, -0.64, -0.741, -0.821, -0.87, -0.883, -0.872, 0.0, -0.781, -0.714, -0.591, -0.444, -0.356, -0.197, -0.101], 0.05, 3.483], [None, 1, None]], [[[0.877, 0.977, 0.997, 0.935, 0.796, 0.586, 0.338, 0.07, -0.221, -0.509, -0.724, -0.872, -0.984, -0.99, -0.943, -0.8, -0.569, -0.289, 0.003, 0.279, 0.533, 0.725, 0.872, 0.982, 0.999, 0.949], 0.05, 5.66], [None, 1, None]], [[[0.144, 0.442, 0.68, 0.836, 0.896, 0.861, 0.737, 0.526, 0.311, 0.059, -0.239, -0.422, -0.588, -0.695, -0.705, -0.663, -0.539, -0.391, -0.114, 0.034, 0.204, 0.352, 0.522, 0.559, 0.544, 0.476, 0.383, 0.171, 0.101, -0.116, -0.203, -0.371, -0.436, -0.437, -0.406, -0.341, -0.233, -0.158], 0.125, 2.578], [None, 1, None]], [[[-0.26, -0.635, 0.0, -0.981, -0.883, -0.608, -0.253, 0.194], 0.125, 3.422], [0.570749, 2, -0.689154]]], [[[[0.172, 0.032, -0.109, -0.229, -0.347, -0.446, -0.539, 0.0, -0.678, -0.719, -0.735, -0.746], 0.125, 1.122], [None, 1, None]], [[[-0.958, -0.915, -0.449, 0.251, 0.801, 0.969, 0.683, 0.131, -0.526, -0.913, -0.847, -0.422, 0.209, 0.666, 0.904, 0.594, 0.028, -0.59, -0.799, -0.804, -0.222, 0.054, 0.675, 0.839, 0.576, 0.287, -0.577, -0.769, -0.769, -0.464, 0.137, 0.597, 0.789, 0.47, 0.186, -0.526], 0.125, 5.507], [1.130442, 4, -0.009205]], [[[-0.745, -0.947, -0.997, -0.894, -0.633, -0.308, 0.087, 0.49, 0.766, 0.95, 0.0, 0.895, 0.599, 0.314], 0.125, 3.14], [None, 1, None]], [[[0.994, 0.734, 0.153, -0.46, -0.899, -0.981, -0.687, -0.107, 0.566, 0.962, 0.945, 0.592, 0.108, -0.696, -0.989, -0.951, -0.63, -0.031, 0.787, 0.962, 0.922, 0.611, -0.166, -0.659, -0.982, -0.83, -0.303, 0.254, 0.875, 0.988, 0.858, 0.34, -0.095, -0.851, -1.0], 0.125, 5.091], [1.211562, 3, -0.018322]], [[[0.933, 0.714, -0.336, -1.0, -0.474, 0.686, 0.977, 0.163, -0.857, -0.786, 0.203, 0.999, 0.61, -0.354], 0.25, 4.554], [1.34653, 2, -0.024046]], [[[-0.67, -0.229, 0.24, 0.683, 0.931, 0.958, 0.736, 0.419, -0.111, -0.486, -0.857, -0.946, -0.798, -0.441, -0.101, 0.333, 0.67, 0.917, 0.818, 0.648, 0.149, -0.167, -0.548, -0.843, -0.877, -0.593, -0.274, 0.011, 0.501, 0.829, 0.851, 0.749, 0.322, -0.025, -0.2, -0.622, -0.835, -0.827, -0.482, -0.355], 0.1, 4.89], [1.273657, 3, -0.008754]], [[[0.146, 0.404, 0.623, 0.8, 0.913, 0.95, 0.914, 0.81, 0.674, 0.445, 0.209, 0.0, -0.264, -0.502, -0.642, -0.79, -0.842, -0.843, -0.752, -0.648, -0.463, -0.346, -0.071, 0.0, 0.377, 0.471, 0.69], 0.05, 5.411], [None, 1, None]], [[[0.782, 0.803, -0.322, -0.961, -0.145, 0.88, 0.545, -0.505, -0.847, 0.072, 0.838, 0.362, -0.691, -0.784, 0.139, 0.828, 0.292, -0.698, -0.556, 0.501, 0.616, 0.209, -0.752, -0.433, 0.497, 0.68, -0.345, -0.619, -0.392, 0.649, 0.317], 0.25, 5.143], [1.211755, 6, -0.008138]]], [[[[0.446, -0.255, -0.799, -0.921, -0.57, -0.003, 0.55, 0.838, 0.0, 0.178, -0.29, -0.676, -0.721, -0.282, 0.142, 0.554, 0.66, 0.386, 0.005, -0.48, -0.578], 0.125, 5.696], [1.082459, 2, -0.018701]], [[[0.17, -0.189, -0.512, -0.778, -0.932, -0.975, -0.881, -0.695, -0.427, -0.064, 0.23, 0.606, 0.824, 0.915, 0.921, 0.77, 0.593, 0.335, -0.033, -0.265, -0.599, -0.803, -0.885, -0.841, -0.724, -0.577, -0.279, 0.064, 0.313, 0.612, 0.818, 0.848, 0.822, 0.647, 0.408, 0.182, -0.285, -0.361, -0.715, -0.814], 0.1, 3.544], [1.759572, 2, -0.007522]], [[[-0.383, 0.145, 0.62, 0.903, 0.941, 0.0, 0.326, -0.143, -0.616, -0.843], 0.25, 2.108], [None, 1, None]], [[[0.858, 0.449, -0.091, -0.626, -0.935, -0.95, -0.646, -0.138, 0.351, 0.779, 0.951, 0.853, 0.417, -0.165, -0.466, -0.893, -0.909, -0.615, -0.173, 0.405, 0.663, 0.871, 0.73, 0.457, 0.073, -0.637, -0.735, -0.873, -0.5, -0.341, 0.277, 0.496], 0.1, 5.594], [1.113479, 3, -0.008656]], [[[-0.999, -0.701, -0.121, 0.435, 0.786, 0.722, 0.316, -0.166, -0.522, -0.638, -0.445], 0.25, 2.736], [None, 1, None]], [[[-0.7, -0.579, -0.447, -0.299, -0.148, 0.0, 0.129, 0.281, 0.391, 0.518, 0.612, 0.708, 0.784, 0.827, 0.847, 0.86], 0.05, 3.021], [None, 1, None]], [[[-0.579, -0.039, 0.483, 0.839, 0.9, 0.661, 0.255, -0.229, -0.645, -0.794, -0.7, -0.33, 0.098, 0.427, 0.688, 0.65, 0.484, 0.095, -0.27, -0.552, -0.606, -0.527, -0.266, 0.002, 0.311, 0.527, 0.441, 0.213, -0.017, -0.21, 0.0, -0.447, -0.35, -0.167, 0.014, 0.289], 0.125, 4.584], [1.026498, 5, -0.251102]], [[[-0.99, -0.835, -0.27, 0.432, 0.933, 0.924, 0.426, -0.302, -0.851, -0.998, -0.569, 0.0, 0.659, 0.995, 0.801, 0.131, -0.48, -0.924, -0.901, -0.51, 0.414, 0.939, 0.984, 0.724, -0.13, -0.791, -0.997, -0.898, 0.029, 0.738, 0.869, 0.938, 0.438], 0.25, 2.87], [2.132008, 4, -0.026153]]], [[[[0.212, -0.01, -0.226, -0.421, -0.599, -0.737, 0.0, -0.904, -0.923, -0.893, -0.823, -0.702, -0.549, -0.373, -0.238, -0.017, 0.166, 0.362, 0.478, 0.658, 0.725, 0.779, 0.802, 0.777, 0.736, 0.664, 0.487], 0.05, 4.381], [0.454645, 2, -0.682995]], [[[-0.246, -0.857, -0.926, -0.39, 0.337, 0.857, 0.82, 0.304, -0.411, -0.827, 0.0, -0.282, 0.545, 0.833, 0.722, 0.078, -0.454, -0.804, -0.558, 0.016], 0.25, 3.207], [1.286306, 4, -0.343457]], [[[0.632, 0.493, 0.349, 0.192, 0.032, -0.124, -0.27, -0.39, -0.517, -0.625, -0.72, -0.795, -0.836, -0.867, -0.869, -0.852, -0.798, -0.748, -0.649, -0.542, -0.48, -0.312, -0.243, -0.067], 0.05, 3.185], [None, 0, None]], [[[-0.75, -0.926, -0.998, -0.961, -0.821, -0.6, -0.282, 0.054, 0.36, 0.657, 0.863], 0.1, 3.277], [None, 1, None]], [[[0.002, -0.778, -0.845, -0.252, 0.499, 0.777, 0.406, -0.306, -0.662, -0.474, 0.033, 0.522, 0.466, 0.041, -0.331, -0.443, -0.117, 0.236, 0.396, 0.223, -0.189, -0.35, -0.278, 0.113, 0.247], 0.25, 3.783], [1.61462, 4, -0.027864]], [[[-0.401, 0.525, 0.905, 0.442, -0.373, -0.776, -0.497, 0.202, 0.657, 0.424, -0.109, -0.559, -0.42, -0.039, 0.436, 0.44, -0.081, -0.375, -0.333, -0.118], 0.25, 3.964], [1.581132, 3, -0.002479]], [[[0.989, 0.612, -0.023, -0.671, -0.904, -0.67, -0.092, 0.435, 0.806, 0.739, 0.322, -0.319, -0.683, 0.0, -0.283, 0.093, 0.497, 0.641, 0.444, 0.121, -0.289, -0.589, -0.444, -0.108, 0.369, 0.484, 0.511, 0.106, -0.224, -0.463, -0.472, -0.292, 0.086, 0.244, 0.414, 0.19, 0.1, -0.321], 0.125, 5.793], [0.799935, 5, -0.262472]], [[[0.996, 0.809, 0.426, -0.058, -0.471, -0.802, -0.887, -0.736, -0.425, -0.086, 0.322, 0.651, 0.786, 0.7], 0.1, 5.023], [None, 1, None]]]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"case %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":"982f002355988072de252dbc2bead9c8d082e66d75a627587b865ef915600c48","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(xs, dt, omega):\n    ts = []\n    for i in range(1, len(xs)):\n        a, b = xs[i - 1], xs[i]\n        if a < 0 <= b:\n            frac = -a / (b - a)\n            ts.append((i - 1 + frac) * dt)\n    if len(ts) < 2:\n        return [None, len(ts), None]\n    period = (ts[-1] - ts[0]) / (len(ts) - 1)\n    ref = 1 / omega\n    return [round(period, 6), len(ts), round((period - ref) / ref, 6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[[[0.014, -0.488, -0.823, -0.928, -0.752, -0.382, 0.014, 0.485, 0.758, 0.797, 0.609, 0.243, -0.085, -0.47, -0.635, -0.672, -0.536, -0.267, 0.094, 0.396, 0.572, 0.57, 0.411, 0.193, -0.146, -0.39, -0.492, -0.459, -0.307, -0.026, 0.217, 0.381, 0.449, 0.431, 0.259, 0.13, -0.203, -0.364, -0.385], 0.125, 4.227], [1.446397, 3, -0.026939]], [[[-0.082, -0.546, -0.881, -0.981, -0.842, -0.495, -0.004, 0.435, 0.768, 0.94, 0.85], 0.125, 3.973], [None, 1, None]], [[[-0.157, -0.354, -0.537, -0.694, -0.821, -0.909, -0.965, -0.982, -0.957, -0.899, -0.777, -0.642, -0.509, -0.329, -0.077, 0.066, 0.298, 0.474, 0.579, 0.721, 0.837, 0.931, 0.946, 0.934, 0.903, 0.754, 0.706, 0.532, 0.37], 0.05, 4.035], [None, 1, None]], [[[-0.982, -0.868, -0.655, -0.382, -0.029, 0.261, 0.569, 0.826, 0.963, 0.996, 0.942, 0.728, 0.495, 0.137, -0.124, -0.479, -0.718, -0.94, -0.984, -0.971, -0.815, -0.573, -0.4, 0.056, 0.347, 0.586, 0.868, 0.976, 0.975, 0.849, 0.649, 0.358, 0.039, -0.279], 0.25, 1.314], [4.694298, 2, -0.018283]], [[[-0.506, -0.297, -0.076, 0.135, 0.36, 0.549, 0.702, 0.847, 0.916, 0.953, 0.938, 0.873, 0.756, 0.641, 0.488, 0.29, 0.083, -0.164, -0.355, -0.505, -0.711, -0.811, -0.87, -0.884, -0.875, -0.809, -0.705, -0.583], 0.1, 2.222], [None, 1, None]], [[[-0.996, -0.793, -0.388, 0.134, 0.56, 0.832, 0.845, 0.666, 0.306, -0.118, -0.51, -0.737, -0.721, -0.538, -0.141, 0.138, 0.492, 0.642, 0.605, 0.406, 0.165, -0.141, -0.462, -0.553, -0.483, -0.275, -0.004, 0.223], 0.125, 4.228], [1.454645, 3, -0.021159]], [[[0.977, -0.065, -0.968, -0.204, 0.883, 0.472, -0.609, -0.652, 0.532, 0.791, -0.188, -0.864, -0.051, 0.844, 0.497, -0.642, -0.528, 0.547, 0.79, -0.35, -0.705, 0.213, 0.671, 0.508, -0.528, -0.582, 0.109, 0.698, -0.453, -0.687, -0.293, 0.533, 0.0, -0.44, -0.539, 0.624, 0.282, -0.55, -0.586, 0.295], 0.25, 5.546], [1.108671, 9, -0.021405]], [[[-0.981, -0.904, -0.463, 0.134, 0.714, 0.994, 0.852, 0.37, -0.184, -0.786, -0.999, -0.817, -0.396, 0.217, 0.816, 0.997, 0.831, 0.172, -0.235, -0.913, -0.987, -0.687, -0.191, 0.507, 0.853, 0.935, 0.831, 0.108, -0.661, -0.982, -0.967, -0.674, -0.003, 0.527, 0.989, 0.998], 0.125, 5.059], [1.217921, 4, -0.019372]]], [[[[0.045, -0.043, -0.133, -0.217, -0.299, -0.379, -0.463, -0.542, -0.605, -0.673, -0.734, -0.781, -0.828, -0.863, -0.894, -0.926, -0.942, -0.953, -0.956, 0.0, -0.936, -0.915], 0.05, 1.751], [None, 1, None]], [[[-0.425, -0.944, -0.194, 0.722, 0.59, -0.255, -0.74, -0.107, 0.57, 0.553, -0.097, -0.577, -0.147, 0.454], 0.25, 4.911], [1.2541, 3, -0.019783]], [[[0.577, -0.503, -0.961, 0.0, 0.735, 0.821, -0.096, -0.89, -0.599, 0.293, 0.882, 0.27, -0.691, -0.829, -0.079, 0.762, 0.626, -0.255, -0.768], 0.25, 4.575], [1.386742, 3, 0.009734]], [[[0.221, 0.117, 0.014, -0.083, -0.18, -0.269, -0.351, -0.412, -0.477, -0.546, -0.588, -0.634, -0.663, -0.691, -0.713, -0.719, -0.719, -0.712, -0.695, -0.675, -0.648, -0.606, -0.565, -0.525, -0.465, -0.424, -0.382, -0.319, 0.0, -0.186, -0.134, -0.057, -0.026, 0.046, 0.083, 0.103], 0.1, 1.021], [0.436111, 2, -0.929133]], [[[0.598, 0.444, 0.282, 0.1, -0.054, -0.227, -0.393, -0.519, -0.64, -0.741, -0.821, -0.87, -0.883, -0.872, 0.0, -0.781, -0.714, -0.591, -0.444, -0.356, -0.197, -0.101], 0.05, 3.483], [None, 1, None]], [[[0.877, 0.977, 0.997, 0.935, 0.796, 0.586, 0.338, 0.07, -0.221, -0.509, -0.724, -0.872, -0.984, -0.99, -0.943, -0.8, -0.569, -0.289, 0.003, 0.279, 0.533, 0.725, 0.872, 0.982, 0.999, 0.949], 0.05, 5.66], [None, 1, None]], [[[0.144, 0.442, 0.68, 0.836, 0.896, 0.861, 0.737, 0.526, 0.311, 0.059, -0.239, -0.422, -0.588, -0.695, -0.705, -0.663, -0.539, -0.391, -0.114, 0.034, 0.204, 0.352, 0.522, 0.559, 0.544, 0.476, 0.383, 0.171, 0.101, -0.116, -0.203, -0.371, -0.436, -0.437, -0.406, -0.341, -0.233, -0.158], 0.125, 2.578], [None, 1, None]], [[[-0.26, -0.635, 0.0, -0.981, -0.883, -0.608, -0.253, 0.194], 0.125, 3.422], [0.570749, 2, -0.689154]]], [[[[0.172, 0.032, -0.109, -0.229, -0.347, -0.446, -0.539, 0.0, -0.678, -0.719, -0.735, -0.746], 0.125, 1.122], [None, 1, None]], [[[-0.958, -0.915, -0.449, 0.251, 0.801, 0.969, 0.683, 0.131, -0.526, -0.913, -0.847, -0.422, 0.209, 0.666, 0.904, 0.594, 0.028, -0.59, -0.799, -0.804, -0.222, 0.054, 0.675, 0.839, 0.576, 0.287, -0.577, -0.769, -0.769, -0.464, 0.137, 0.597, 0.789, 0.47, 0.186, -0.526], 0.125, 5.507], [1.130442, 4, -0.009205]], [[[-0.745, -0.947, -0.997, -0.894, -0.633, -0.308, 0.087, 0.49, 0.766, 0.95, 0.0, 0.895, 0.599, 0.314], 0.125, 3.14], [None, 1, None]], [[[0.994, 0.734, 0.153, -0.46, -0.899, -0.981, -0.687, -0.107, 0.566, 0.962, 0.945, 0.592, 0.108, -0.696, -0.989, -0.951, -0.63, -0.031, 0.787, 0.962, 0.922, 0.611, -0.166, -0.659, -0.982, -0.83, -0.303, 0.254, 0.875, 0.988, 0.858, 0.34, -0.095, -0.851, -1.0], 0.125, 5.091], [1.211562, 3, -0.018322]], [[[0.933, 0.714, -0.336, -1.0, -0.474, 0.686, 0.977, 0.163, -0.857, -0.786, 0.203, 0.999, 0.61, -0.354], 0.25, 4.554], [1.34653, 2, -0.024046]], [[[-0.67, -0.229, 0.24, 0.683, 0.931, 0.958, 0.736, 0.419, -0.111, -0.486, -0.857, -0.946, -0.798, -0.441, -0.101, 0.333, 0.67, 0.917, 0.818, 0.648, 0.149, -0.167, -0.548, -0.843, -0.877, -0.593, -0.274, 0.011, 0.501, 0.829, 0.851, 0.749, 0.322, -0.025, -0.2, -0.622, -0.835, -0.827, -0.482, -0.355], 0.1, 4.89], [1.273657, 3, -0.008754]], [[[0.146, 0.404, 0.623, 0.8, 0.913, 0.95, 0.914, 0.81, 0.674, 0.445, 0.209, 0.0, -0.264, -0.502, -0.642, -0.79, -0.842, -0.843, -0.752, -0.648, -0.463, -0.346, -0.071, 0.0, 0.377, 0.471, 0.69], 0.05, 5.411], [None, 1, None]], [[[0.782, 0.803, -0.322, -0.961, -0.145, 0.88, 0.545, -0.505, -0.847, 0.072, 0.838, 0.362, -0.691, -0.784, 0.139, 0.828, 0.292, -0.698, -0.556, 0.501, 0.616, 0.209, -0.752, -0.433, 0.497, 0.68, -0.345, -0.619, -0.392, 0.649, 0.317], 0.25, 5.143], [1.211755, 6, -0.008138]]], [[[[0.446, -0.255, -0.799, -0.921, -0.57, -0.003, 0.55, 0.838, 0.0, 0.178, -0.29, -0.676, -0.721, -0.282, 0.142, 0.554, 0.66, 0.386, 0.005, -0.48, -0.578], 0.125, 5.696], [1.082459, 2, -0.018701]], [[[0.17, -0.189, -0.512, -0.778, -0.932, -0.975, -0.881, -0.695, -0.427, -0.064, 0.23, 0.606, 0.824, 0.915, 0.921, 0.77, 0.593, 0.335, -0.033, -0.265, -0.599, -0.803, -0.885, -0.841, -0.724, -0.577, -0.279, 0.064, 0.313, 0.612, 0.818, 0.848, 0.822, 0.647, 0.408, 0.182, -0.285, -0.361, -0.715, -0.814], 0.1, 3.544], [1.759572, 2, -0.007522]], [[[-0.383, 0.145, 0.62, 0.903, 0.941, 0.0, 0.326, -0.143, -0.616, -0.843], 0.25, 2.108], [None, 1, None]], [[[0.858, 0.449, -0.091, -0.626, -0.935, -0.95, -0.646, -0.138, 0.351, 0.779, 0.951, 0.853, 0.417, -0.165, -0.466, -0.893, -0.909, -0.615, -0.173, 0.405, 0.663, 0.871, 0.73, 0.457, 0.073, -0.637, -0.735, -0.873, -0.5, -0.341, 0.277, 0.496], 0.1, 5.594], [1.113479, 3, -0.008656]], [[[-0.999, -0.701, -0.121, 0.435, 0.786, 0.722, 0.316, -0.166, -0.522, -0.638, -0.445], 0.25, 2.736], [None, 1, None]], [[[-0.7, -0.579, -0.447, -0.299, -0.148, 0.0, 0.129, 0.281, 0.391, 0.518, 0.612, 0.708, 0.784, 0.827, 0.847, 0.86], 0.05, 3.021], [None, 1, None]], [[[-0.579, -0.039, 0.483, 0.839, 0.9, 0.661, 0.255, -0.229, -0.645, -0.794, -0.7, -0.33, 0.098, 0.427, 0.688, 0.65, 0.484, 0.095, -0.27, -0.552, -0.606, -0.527, -0.266, 0.002, 0.311, 0.527, 0.441, 0.213, -0.017, -0.21, 0.0, -0.447, -0.35, -0.167, 0.014, 0.289], 0.125, 4.584], [1.026498, 5, -0.251102]], [[[-0.99, -0.835, -0.27, 0.432, 0.933, 0.924, 0.426, -0.302, -0.851, -0.998, -0.569, 0.0, 0.659, 0.995, 0.801, 0.131, -0.48, -0.924, -0.901, -0.51, 0.414, 0.939, 0.984, 0.724, -0.13, -0.791, -0.997, -0.898, 0.029, 0.738, 0.869, 0.938, 0.438], 0.25, 2.87], [2.132008, 4, -0.026153]]], [[[[0.212, -0.01, -0.226, -0.421, -0.599, -0.737, 0.0, -0.904, -0.923, -0.893, -0.823, -0.702, -0.549, -0.373, -0.238, -0.017, 0.166, 0.362, 0.478, 0.658, 0.725, 0.779, 0.802, 0.777, 0.736, 0.664, 0.487], 0.05, 4.381], [0.454645, 2, -0.682995]], [[[-0.246, -0.857, -0.926, -0.39, 0.337, 0.857, 0.82, 0.304, -0.411, -0.827, 0.0, -0.282, 0.545, 0.833, 0.722, 0.078, -0.454, -0.804, -0.558, 0.016], 0.25, 3.207], [1.286306, 4, -0.343457]], [[[0.632, 0.493, 0.349, 0.192, 0.032, -0.124, -0.27, -0.39, -0.517, -0.625, -0.72, -0.795, -0.836, -0.867, -0.869, -0.852, -0.798, -0.748, -0.649, -0.542, -0.48, -0.312, -0.243, -0.067], 0.05, 3.185], [None, 0, None]], [[[-0.75, -0.926, -0.998, -0.961, -0.821, -0.6, -0.282, 0.054, 0.36, 0.657, 0.863], 0.1, 3.277], [None, 1, None]], [[[0.002, -0.778, -0.845, -0.252, 0.499, 0.777, 0.406, -0.306, -0.662, -0.474, 0.033, 0.522, 0.466, 0.041, -0.331, -0.443, -0.117, 0.236, 0.396, 0.223, -0.189, -0.35, -0.278, 0.113, 0.247], 0.25, 3.783], [1.61462, 4, -0.027864]], [[[-0.401, 0.525, 0.905, 0.442, -0.373, -0.776, -0.497, 0.202, 0.657, 0.424, -0.109, -0.559, -0.42, -0.039, 0.436, 0.44, -0.081, -0.375, -0.333, -0.118], 0.25, 3.964], [1.581132, 3, -0.002479]], [[[0.989, 0.612, -0.023, -0.671, -0.904, -0.67, -0.092, 0.435, 0.806, 0.739, 0.322, -0.319, -0.683, 0.0, -0.283, 0.093, 0.497, 0.641, 0.444, 0.121, -0.289, -0.589, -0.444, -0.108, 0.369, 0.484, 0.511, 0.106, -0.224, -0.463, -0.472, -0.292, 0.086, 0.244, 0.414, 0.19, 0.1, -0.321], 0.125, 5.793], [0.799935, 5, -0.262472]], [[[0.996, 0.809, 0.426, -0.058, -0.471, -0.802, -0.887, -0.736, -0.425, -0.086, 0.322, 0.651, 0.786, 0.7], 0.1, 5.023], [None, 1, None]]]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"case %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":"ad313a3c04ddd4e70b145bc0f5b8a198ad57622e757cfd317182c518b228ce21","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(xs, dt, omega):\n    ts = []\n    for i in range(1, len(xs)):\n        a, b = xs[i - 1], xs[i]\n        if a < 0 <= b:\n            frac = -a / (b - a)\n            ts.append((i - 1 + frac) * dt)\n    if len(ts) < 2:\n        return [None, len(ts), None]\n    period = (ts[-1] - ts[0]) / (len(ts) - 1)\n    ref = 2 * math.pi / omega\n    return [round(period, 6), len(ts), round((period - ref) / ref, 6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[[[0.014, -0.488, -0.823, -0.928, -0.752, -0.382, 0.014, 0.485, 0.758, 0.797, 0.609, 0.243, -0.085, -0.47, -0.635, -0.672, -0.536, -0.267, 0.094, 0.396, 0.572, 0.57, 0.411, 0.193, -0.146, -0.39, -0.492, -0.459, -0.307, -0.026, 0.217, 0.381, 0.449, 0.431, 0.259, 0.13, -0.203, -0.364, -0.385], 0.125, 4.227], [1.446397, 3, -0.026939]], [[[-0.082, -0.546, -0.881, -0.981, -0.842, -0.495, -0.004, 0.435, 0.768, 0.94, 0.85], 0.125, 3.973], [None, 1, None]], [[[-0.157, -0.354, -0.537, -0.694, -0.821, -0.909, -0.965, -0.982, -0.957, -0.899, -0.777, -0.642, -0.509, -0.329, -0.077, 0.066, 0.298, 0.474, 0.579, 0.721, 0.837, 0.931, 0.946, 0.934, 0.903, 0.754, 0.706, 0.532, 0.37], 0.05, 4.035], [None, 1, None]], [[[-0.982, -0.868, -0.655, -0.382, -0.029, 0.261, 0.569, 0.826, 0.963, 0.996, 0.942, 0.728, 0.495, 0.137, -0.124, -0.479, -0.718, -0.94, -0.984, -0.971, -0.815, -0.573, -0.4, 0.056, 0.347, 0.586, 0.868, 0.976, 0.975, 0.849, 0.649, 0.358, 0.039, -0.279], 0.25, 1.314], [4.694298, 2, -0.018283]], [[[-0.506, -0.297, -0.076, 0.135, 0.36, 0.549, 0.702, 0.847, 0.916, 0.953, 0.938, 0.873, 0.756, 0.641, 0.488, 0.29, 0.083, -0.164, -0.355, -0.505, -0.711, -0.811, -0.87, -0.884, -0.875, -0.809, -0.705, -0.583], 0.1, 2.222], [None, 1, None]], [[[-0.996, -0.793, -0.388, 0.134, 0.56, 0.832, 0.845, 0.666, 0.306, -0.118, -0.51, -0.737, -0.721, -0.538, -0.141, 0.138, 0.492, 0.642, 0.605, 0.406, 0.165, -0.141, -0.462, -0.553, -0.483, -0.275, -0.004, 0.223], 0.125, 4.228], [1.454645, 3, -0.021159]], [[[0.977, -0.065, -0.968, -0.204, 0.883, 0.472, -0.609, -0.652, 0.532, 0.791, -0.188, -0.864, -0.051, 0.844, 0.497, -0.642, -0.528, 0.547, 0.79, -0.35, -0.705, 0.213, 0.671, 0.508, -0.528, -0.582, 0.109, 0.698, -0.453, -0.687, -0.293, 0.533, 0.0, -0.44, -0.539, 0.624, 0.282, -0.55, -0.586, 0.295], 0.25, 5.546], [1.108671, 9, -0.021405]], [[[-0.981, -0.904, -0.463, 0.134, 0.714, 0.994, 0.852, 0.37, -0.184, -0.786, -0.999, -0.817, -0.396, 0.217, 0.816, 0.997, 0.831, 0.172, -0.235, -0.913, -0.987, -0.687, -0.191, 0.507, 0.853, 0.935, 0.831, 0.108, -0.661, -0.982, -0.967, -0.674, -0.003, 0.527, 0.989, 0.998], 0.125, 5.059], [1.217921, 4, -0.019372]]], [[[[0.045, -0.043, -0.133, -0.217, -0.299, -0.379, -0.463, -0.542, -0.605, -0.673, -0.734, -0.781, -0.828, -0.863, -0.894, -0.926, -0.942, -0.953, -0.956, 0.0, -0.936, -0.915], 0.05, 1.751], [None, 1, None]], [[[-0.425, -0.944, -0.194, 0.722, 0.59, -0.255, -0.74, -0.107, 0.57, 0.553, -0.097, -0.577, -0.147, 0.454], 0.25, 4.911], [1.2541, 3, -0.019783]], [[[0.577, -0.503, -0.961, 0.0, 0.735, 0.821, -0.096, -0.89, -0.599, 0.293, 0.882, 0.27, -0.691, -0.829, -0.079, 0.762, 0.626, -0.255, -0.768], 0.25, 4.575], [1.386742, 3, 0.009734]], [[[0.221, 0.117, 0.014, -0.083, -0.18, -0.269, -0.351, -0.412, -0.477, -0.546, -0.588, -0.634, -0.663, -0.691, -0.713, -0.719, -0.719, -0.712, -0.695, -0.675, -0.648, -0.606, -0.565, -0.525, -0.465, -0.424, -0.382, -0.319, 0.0, -0.186, -0.134, -0.057, -0.026, 0.046, 0.083, 0.103], 0.1, 1.021], [0.436111, 2, -0.929133]], [[[0.598, 0.444, 0.282, 0.1, -0.054, -0.227, -0.393, -0.519, -0.64, -0.741, -0.821, -0.87, -0.883, -0.872, 0.0, -0.781, -0.714, -0.591, -0.444, -0.356, -0.197, -0.101], 0.05, 3.483], [None, 1, None]], [[[0.877, 0.977, 0.997, 0.935, 0.796, 0.586, 0.338, 0.07, -0.221, -0.509, -0.724, -0.872, -0.984, -0.99, -0.943, -0.8, -0.569, -0.289, 0.003, 0.279, 0.533, 0.725, 0.872, 0.982, 0.999, 0.949], 0.05, 5.66], [None, 1, None]], [[[0.144, 0.442, 0.68, 0.836, 0.896, 0.861, 0.737, 0.526, 0.311, 0.059, -0.239, -0.422, -0.588, -0.695, -0.705, -0.663, -0.539, -0.391, -0.114, 0.034, 0.204, 0.352, 0.522, 0.559, 0.544, 0.476, 0.383, 0.171, 0.101, -0.116, -0.203, -0.371, -0.436, -0.437, -0.406, -0.341, -0.233, -0.158], 0.125, 2.578], [None, 1, None]], [[[-0.26, -0.635, 0.0, -0.981, -0.883, -0.608, -0.253, 0.194], 0.125, 3.422], [0.570749, 2, -0.689154]]], [[[[0.172, 0.032, -0.109, -0.229, -0.347, -0.446, -0.539, 0.0, -0.678, -0.719, -0.735, -0.746], 0.125, 1.122], [None, 1, None]], [[[-0.958, -0.915, -0.449, 0.251, 0.801, 0.969, 0.683, 0.131, -0.526, -0.913, -0.847, -0.422, 0.209, 0.666, 0.904, 0.594, 0.028, -0.59, -0.799, -0.804, -0.222, 0.054, 0.675, 0.839, 0.576, 0.287, -0.577, -0.769, -0.769, -0.464, 0.137, 0.597, 0.789, 0.47, 0.186, -0.526], 0.125, 5.507], [1.130442, 4, -0.009205]], [[[-0.745, -0.947, -0.997, -0.894, -0.633, -0.308, 0.087, 0.49, 0.766, 0.95, 0.0, 0.895, 0.599, 0.314], 0.125, 3.14], [None, 1, None]], [[[0.994, 0.734, 0.153, -0.46, -0.899, -0.981, -0.687, -0.107, 0.566, 0.962, 0.945, 0.592, 0.108, -0.696, -0.989, -0.951, -0.63, -0.031, 0.787, 0.962, 0.922, 0.611, -0.166, -0.659, -0.982, -0.83, -0.303, 0.254, 0.875, 0.988, 0.858, 0.34, -0.095, -0.851, -1.0], 0.125, 5.091], [1.211562, 3, -0.018322]], [[[0.933, 0.714, -0.336, -1.0, -0.474, 0.686, 0.977, 0.163, -0.857, -0.786, 0.203, 0.999, 0.61, -0.354], 0.25, 4.554], [1.34653, 2, -0.024046]], [[[-0.67, -0.229, 0.24, 0.683, 0.931, 0.958, 0.736, 0.419, -0.111, -0.486, -0.857, -0.946, -0.798, -0.441, -0.101, 0.333, 0.67, 0.917, 0.818, 0.648, 0.149, -0.167, -0.548, -0.843, -0.877, -0.593, -0.274, 0.011, 0.501, 0.829, 0.851, 0.749, 0.322, -0.025, -0.2, -0.622, -0.835, -0.827, -0.482, -0.355], 0.1, 4.89], [1.273657, 3, -0.008754]], [[[0.146, 0.404, 0.623, 0.8, 0.913, 0.95, 0.914, 0.81, 0.674, 0.445, 0.209, 0.0, -0.264, -0.502, -0.642, -0.79, -0.842, -0.843, -0.752, -0.648, -0.463, -0.346, -0.071, 0.0, 0.377, 0.471, 0.69], 0.05, 5.411], [None, 1, None]], [[[0.782, 0.803, -0.322, -0.961, -0.145, 0.88, 0.545, -0.505, -0.847, 0.072, 0.838, 0.362, -0.691, -0.784, 0.139, 0.828, 0.292, -0.698, -0.556, 0.501, 0.616, 0.209, -0.752, -0.433, 0.497, 0.68, -0.345, -0.619, -0.392, 0.649, 0.317], 0.25, 5.143], [1.211755, 6, -0.008138]]], [[[[0.446, -0.255, -0.799, -0.921, -0.57, -0.003, 0.55, 0.838, 0.0, 0.178, -0.29, -0.676, -0.721, -0.282, 0.142, 0.554, 0.66, 0.386, 0.005, -0.48, -0.578], 0.125, 5.696], [1.082459, 2, -0.018701]], [[[0.17, -0.189, -0.512, -0.778, -0.932, -0.975, -0.881, -0.695, -0.427, -0.064, 0.23, 0.606, 0.824, 0.915, 0.921, 0.77, 0.593, 0.335, -0.033, -0.265, -0.599, -0.803, -0.885, -0.841, -0.724, -0.577, -0.279, 0.064, 0.313, 0.612, 0.818, 0.848, 0.822, 0.647, 0.408, 0.182, -0.285, -0.361, -0.715, -0.814], 0.1, 3.544], [1.759572, 2, -0.007522]], [[[-0.383, 0.145, 0.62, 0.903, 0.941, 0.0, 0.326, -0.143, -0.616, -0.843], 0.25, 2.108], [None, 1, None]], [[[0.858, 0.449, -0.091, -0.626, -0.935, -0.95, -0.646, -0.138, 0.351, 0.779, 0.951, 0.853, 0.417, -0.165, -0.466, -0.893, -0.909, -0.615, -0.173, 0.405, 0.663, 0.871, 0.73, 0.457, 0.073, -0.637, -0.735, -0.873, -0.5, -0.341, 0.277, 0.496], 0.1, 5.594], [1.113479, 3, -0.008656]], [[[-0.999, -0.701, -0.121, 0.435, 0.786, 0.722, 0.316, -0.166, -0.522, -0.638, -0.445], 0.25, 2.736], [None, 1, None]], [[[-0.7, -0.579, -0.447, -0.299, -0.148, 0.0, 0.129, 0.281, 0.391, 0.518, 0.612, 0.708, 0.784, 0.827, 0.847, 0.86], 0.05, 3.021], [None, 1, None]], [[[-0.579, -0.039, 0.483, 0.839, 0.9, 0.661, 0.255, -0.229, -0.645, -0.794, -0.7, -0.33, 0.098, 0.427, 0.688, 0.65, 0.484, 0.095, -0.27, -0.552, -0.606, -0.527, -0.266, 0.002, 0.311, 0.527, 0.441, 0.213, -0.017, -0.21, 0.0, -0.447, -0.35, -0.167, 0.014, 0.289], 0.125, 4.584], [1.026498, 5, -0.251102]], [[[-0.99, -0.835, -0.27, 0.432, 0.933, 0.924, 0.426, -0.302, -0.851, -0.998, -0.569, 0.0, 0.659, 0.995, 0.801, 0.131, -0.48, -0.924, -0.901, -0.51, 0.414, 0.939, 0.984, 0.724, -0.13, -0.791, -0.997, -0.898, 0.029, 0.738, 0.869, 0.938, 0.438], 0.25, 2.87], [2.132008, 4, -0.026153]]], [[[[0.212, -0.01, -0.226, -0.421, -0.599, -0.737, 0.0, -0.904, -0.923, -0.893, -0.823, -0.702, -0.549, -0.373, -0.238, -0.017, 0.166, 0.362, 0.478, 0.658, 0.725, 0.779, 0.802, 0.777, 0.736, 0.664, 0.487], 0.05, 4.381], [0.454645, 2, -0.682995]], [[[-0.246, -0.857, -0.926, -0.39, 0.337, 0.857, 0.82, 0.304, -0.411, -0.827, 0.0, -0.282, 0.545, 0.833, 0.722, 0.078, -0.454, -0.804, -0.558, 0.016], 0.25, 3.207], [1.286306, 4, -0.343457]], [[[0.632, 0.493, 0.349, 0.192, 0.032, -0.124, -0.27, -0.39, -0.517, -0.625, -0.72, -0.795, -0.836, -0.867, -0.869, -0.852, -0.798, -0.748, -0.649, -0.542, -0.48, -0.312, -0.243, -0.067], 0.05, 3.185], [None, 0, None]], [[[-0.75, -0.926, -0.998, -0.961, -0.821, -0.6, -0.282, 0.054, 0.36, 0.657, 0.863], 0.1, 3.277], [None, 1, None]], [[[0.002, -0.778, -0.845, -0.252, 0.499, 0.777, 0.406, -0.306, -0.662, -0.474, 0.033, 0.522, 0.466, 0.041, -0.331, -0.443, -0.117, 0.236, 0.396, 0.223, -0.189, -0.35, -0.278, 0.113, 0.247], 0.25, 3.783], [1.61462, 4, -0.027864]], [[[-0.401, 0.525, 0.905, 0.442, -0.373, -0.776, -0.497, 0.202, 0.657, 0.424, -0.109, -0.559, -0.42, -0.039, 0.436, 0.44, -0.081, -0.375, -0.333, -0.118], 0.25, 3.964], [1.581132, 3, -0.002479]], [[[0.989, 0.612, -0.023, -0.671, -0.904, -0.67, -0.092, 0.435, 0.806, 0.739, 0.322, -0.319, -0.683, 0.0, -0.283, 0.093, 0.497, 0.641, 0.444, 0.121, -0.289, -0.589, -0.444, -0.108, 0.369, 0.484, 0.511, 0.106, -0.224, -0.463, -0.472, -0.292, 0.086, 0.244, 0.414, 0.19, 0.1, -0.321], 0.125, 5.793], [0.799935, 5, -0.262472]], [[[0.996, 0.809, 0.426, -0.058, -0.471, -0.802, -0.887, -0.736, -0.425, -0.086, 0.322, 0.651, 0.786, 0.7], 0.1, 5.023], [None, 1, None]]]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"case %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 with stipulated toy conventions and rounded float output; not a production physics engine or a proof of numerical stability. 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":"w2-physics_integrator_stability-zero-crossing-period-reference-period","generated_at":"2026-09-29T14:50:57.352075+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Game and robotics physics loops depend on integrator update order, step control and stabilization terms; a wrong decision point turns a stable simulation into drifting or exploding motion.","repair":"Period of angular frequency omega is 2*pi/omega.","root_cause":"ref = 1/omega.","sha256":"ee09f7d49485557f0d666e5e39f14efad0408a7e7595dd96c20c80eed1963286","title":"Reference period uses one over omega · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.587,"exit_code":1,"observations":[{"actual":[1.446397,3,0.946121],"check":"case 0","expected":[1.446397,3,-0.026939],"passed":false},{"actual":[null,1,null],"check":"case 1","expected":[null,1,null],"passed":true},{"actual":[null,1,null],"check":"case 2","expected":[null,1,null],"passed":true},{"actual":[4.694298,2,0.963433],"check":"case 3","expected":[4.694298,2,-0.018283],"passed":false},{"actual":[null,1,null],"check":"case 4","expected":[null,1,null],"passed":true},{"actual":[1.454645,3,0.957682],"check":"case 5","expected":[1.454645,3,-0.021159],"passed":false},{"actual":[1.108671,9,0.957189],"check":"case 6","expected":[1.108671,9,-0.021405],"passed":false},{"actual":[1.217921,4,0.961255],"check":"case 7","expected":[1.217921,4,-0.019372],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [1.446397, 3, 0.946121], \"expected\": [1.446397, 3, -0.026939], \"passed\": false}, {\"check\": \"case 1\", \"actual\": [null, 1, null], \"expected\": [null, 1, null], \"passed\": true}, {\"check\": \"case 2\", \"actual\": [null, 1, null], \"expected\": [null, 1, null], \"passed\": true}, {\"check\": \"case 3\", \"actual\": [4.694298, 2, 0.963433], \"expected\": [4.694298, 2, -0.018283], \"passed\": false}, {\"check\": \"case 4\", \"actual\": [null, 1, null], \"expected\": [null, 1, null], \"passed\": true}, {\"check\": \"case 5\", \"actual\": [1.454645, 3, 0.957682], \"expected\": [1.454645, 3, -0.021159], \"passed\": false}, {\"check\": \"case 6\", \"actual\": [1.108671, 9, 0.957189], \"expected\": [1.108671, 9, -0.021405], \"passed\": false}, {\"check\": \"case 7\", \"actual\": [1.217921, 4, 0.961255], \"expected\": [1.217921, 4, -0.019372], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.296,"exit_code":1,"observations":[{"actual":[1.446397,3,5.113919],"check":"case 0","expected":[1.446397,3,-0.026939],"passed":false},{"actual":[null,1,null],"check":"case 1","expected":[null,1,null],"passed":true},{"actual":[null,1,null],"check":"case 2","expected":[null,1,null],"passed":true},{"actual":[4.694298,2,5.168308],"check":"case 3","expected":[4.694298,2,-0.018283],"passed":false},{"actual":[null,1,null],"check":"case 4","expected":[null,1,null],"passed":true},{"actual":[1.454645,3,5.150241],"check":"case 5","expected":[1.454645,3,-0.021159],"passed":false},{"actual":[1.108671,9,5.148691],"check":"case 6","expected":[1.108671,9,-0.021405],"passed":false},{"actual":[1.217921,4,5.161465],"check":"case 7","expected":[1.217921,4,-0.019372],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [1.446397, 3, 5.113919], \"expected\": [1.446397, 3, -0.026939], \"passed\": false}, {\"check\": \"case 1\", \"actual\": [null, 1, null], \"expected\": [null, 1, null], \"passed\": true}, {\"check\": \"case 2\", \"actual\": [null, 1, null], \"expected\": [null, 1, null], \"passed\": true}, {\"check\": \"case 3\", \"actual\": [4.694298, 2, 5.168308], \"expected\": [4.694298, 2, -0.018283], \"passed\": false}, {\"check\": \"case 4\", \"actual\": [null, 1, null], \"expected\": [null, 1, null], \"passed\": true}, {\"check\": \"case 5\", \"actual\": [1.454645, 3, 5.150241], \"expected\": [1.454645, 3, -0.021159], \"passed\": false}, {\"check\": \"case 6\", \"actual\": [1.108671, 9, 5.148691], \"expected\": [1.108671, 9, -0.021405], \"passed\": false}, {\"check\": \"case 7\", \"actual\": [1.217921, 4, 5.161465], \"expected\": [1.217921, 4, -0.019372], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":39.777,"exit_code":0,"observations":[{"actual":[1.446397,3,-0.026939],"check":"case 0","expected":[1.446397,3,-0.026939],"passed":true},{"actual":[null,1,null],"check":"case 1","expected":[null,1,null],"passed":true},{"actual":[null,1,null],"check":"case 2","expected":[null,1,null],"passed":true},{"actual":[4.694298,2,-0.018283],"check":"case 3","expected":[4.694298,2,-0.018283],"passed":true},{"actual":[null,1,null],"check":"case 4","expected":[null,1,null],"passed":true},{"actual":[1.454645,3,-0.021159],"check":"case 5","expected":[1.454645,3,-0.021159],"passed":true},{"actual":[1.108671,9,-0.021405],"check":"case 6","expected":[1.108671,9,-0.021405],"passed":true},{"actual":[1.217921,4,-0.019372],"check":"case 7","expected":[1.217921,4,-0.019372],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [1.446397, 3, -0.026939], \"expected\": [1.446397, 3, -0.026939], \"passed\": true}, {\"check\": \"case 1\", \"actual\": [null, 1, null], \"expected\": [null, 1, null], \"passed\": true}, {\"check\": \"case 2\", \"actual\": [null, 1, null], \"expected\": [null, 1, null], \"passed\": true}, {\"check\": \"case 3\", \"actual\": [4.694298, 2, -0.018283], \"expected\": [4.694298, 2, -0.018283], \"passed\": true}, {\"check\": \"case 4\", \"actual\": [null, 1, null], \"expected\": [null, 1, null], \"passed\": true}, {\"check\": \"case 5\", \"actual\": [1.454645, 3, -0.021159], \"expected\": [1.454645, 3, -0.021159], \"passed\": true}, {\"check\": \"case 6\", \"actual\": [1.108671, 9, -0.021405], \"expected\": [1.108671, 9, -0.021405], \"passed\": true}, {\"check\": \"case 7\", \"actual\": [1.217921, 4, -0.019372], \"expected\": [1.217921, 4, -0.019372], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}