{"abstract":"Tuning angular damping has no effect.","category":"Physics integrator stability","checks":8,"contract":"solve(v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks): per frame, a sleeping body wakes (timer reset) only when that frame's kick is nonzero, else it is skipped. Add the kick [dvx,dvy,domega], damp with 1/(1+dt*c) (linear and angular coefficients), clamp speed magnitude, then accumulate sleep time while |v|<sleep_lin and |omega|<sleep_ang (else reset). When timer>=sleep_time the body sleeps and velocities are zeroed. Return [vx, vy, omega, timer, asleep, frame index slept or -1].","contract_signature":"v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks","evaluation_group":"w2-physics_integrator_stability-damping-clamp-sleep","failed_approach":"Omitting dt makes angular damping frame-rate dependent.","family":"w2-physics_integrator_stability-damping-clamp-sleep-angular-damping-coefficient","id":"FA-87266","implementations":{"attempt":{"sha256":"38bfeff4189f5e76b39f0aba4c284ce32adc30fd55ccf0d78fd145a930d78af5","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks):\n    vx, vy = v\n    w = omega\n    timer = 0.0\n    asleep = False\n    slept_at = -1\n    for f, (ax, ay, aw) in enumerate(kicks):\n        if asleep:\n            if ax or ay or aw:\n                asleep = False\n                timer = 0.0\n            else:\n                continue\n        vx += ax\n        vy += ay\n        w += aw\n        dl = 1.0 / (1.0 + dt * lin_damp)\n        vx *= dl\n        vy *= dl\n        w *= 1.0 / (1.0 + ang_damp)\n        sp = math.hypot(vx, vy)\n        if sp > max_speed:\n            s = max_speed / sp\n            vx *= s\n            vy *= s\n        if math.hypot(vx, vy) < sleep_lin and abs(w) < sleep_ang:\n            timer += dt\n        else:\n            timer = 0.0\n        if timer >= sleep_time:\n            asleep = True\n            slept_at = f\n            vx = vy = w = 0.0\n    return [round(vx, 6), round(vy, 6), round(w, 6), round(timer, 6), asleep, slept_at]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[[[0.05, 0.07], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 3]], [[[-0.01, -0.01], 1.26, 0.5, 40.0, 0.015625, 3.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 0, 0], [0, 0, 0], [0, 0, 0], [0, 8, 2]]], [0.363645, 2.977879, 1.230769, 0.0, False, 0]], [[[-0.12, -5.54], -0.33, 0.5, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.03125, [[1, 8, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.853029, 2.384603, 1.618816, 0.0, False, -1]], [[[-0.07, 0.09], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5]]], [-0.065791, 0.084588, -1.387079, 0.0, False, -1]], [[[4.02, 0.82], -0.26, 2.0, 40.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 2]]], [0.0, 0.888889, 0.571429, 0.0625, False, 6]], [[[-2.26, -0.28], 0.89, 2.0, 40.0, 0.0625, 3.0, 2.0, 0.3, 0.125, [[0, 0, 0.5], [0, 0, 0], [1, 0, -1], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 2]], [[[0.0, -0.02], -0.16, 20.0, 40.0, 0.015625, 8.0, 2.0, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.046875, True, 5]], [[[-4.46, -2.51], 0.66, 0.5, 0.5, 0.015625, 8.0, 2.0, 1.0, 0.03125, [[-2, -3, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-5.900121, -5.032456, 0.634812, 0.0, False, -1]]], [[[[2.02, -3.34], -1.78, 20.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, -3, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.229381, -0.966121, -1.672561, 0.0, False, -1]], [[[3.02, -0.11], 0.43, 0.5, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, 0.5], [1, 0, 2], [-2, -3, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [5.304661, -2.733316, 1.32246, 0.0, False, -1]], [[[-5.17, 4.65], 0.37, 20.0, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 0], [1, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 3]], [[[-2.24, -3.75], -1.0, 20.0, 0.5, 0.015625, 3.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 2], [1, 1, 0.5]]], [-0.57379, 0.469444, 1.532879, 0.0, False, -1]], [[[0.0, 0.02], 1.7, 2.0, 5.0, 0.015625, 8.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 0.5], [0, 0, 0], [0, 0, 0]]], [-1.823636, 0.015162, 1.262818, 0.0, False, -1]], [[[0.04, 0.05], -1.81, 20.0, 40.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[5, 0, 0.5], [0, 0, 0], [1, -3, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 1, 0], [0, 8, 0]]], [0.157676, 2.995853, 0.0, 0.0, False, 3]], [[[-0.05, -0.0], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5], [0, 0, -1.5]]], [-0.048092, 0.0, -2.327574, 0.0, False, -1]], [[[0.68, 3.27], 1.49, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [1, -3, 0], [0, 0, 0], [0, 0, 0]]], [1.513065, 0.155838, 1.317439, 0.0, False, -1]]], [[[[3.86, -4.4], 0.73, 80.0, 0.5, 0.0625, 3.0, 2.0, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, -1], [5, 0, -1], [0, 0, 0], [0, 0, 0]]], [0.027006, 0.0, -1.796005, 0.0, False, 1]], [[[0.04, -0.02], 1.78, 80.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [5, 0, 2], [5, 0, -1], [0, 0, 0], [0, -3, 0], [0, 0, 0], [5, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 7]], [[[0.09, -0.1], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.082005, -0.091117, 1.388111, 0.0, False, -1]], [[[-0.1, -0.05], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0]]], [-0.088419, -0.044209, 2.393944, 0.0, False, -1]], [[[0.09, 0.08], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0.5], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.323456, 0.0, False, 5]], [[[1.9, 0.51], -1.66, 0.5, 5.0, 0.015625, 8.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, -1], [0, 0, 0]]], [6.708099, 0.479217, -1.769724, 0.0, False, -1]], [[[-0.02, 0.02], -1.06, 0.5, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -3, 2], [0, 1, -1], [0, 0, 2], [0, 0, 0]]], [-0.01894, -1.912189, 1.927089, 0.0, False, -1]], [[[0.04, -0.02], 1.1, 80.0, 40.0, 0.03125, 3.0, 0.5, 0.3, 0.0625, [[0, -3, 0], [0, 0, 0], [0, 0, 0], [5, 0, -1], [0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 8]]], [[[[-0.05, 0.04], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 3.0], [0, 0, -3.0], [0, 0, -3.0]]], [-0.046618, 0.037294, -5.840587, 0.0, False, -1]], [[[-0.03, 0.05], -1.01, 80.0, 0.5, 0.03125, 8.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [5, 0, 2], [0, 0, 0], [0, 0, 0]]], [0.116618, 0.0, 1.909105, 0.0, False, 3]], [[[0.02, 0.03], -1.95, 2.0, 5.0, 0.015625, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 4]], [[[-0.05, -0.02], 1.89, 0.5, 40.0, 0.0625, 3.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [5, 0, -1], [1, 1, -1], [0, 0, 0], [1, 0, 2]]], [2.951277, 0.538484, 0.54504, 0.0, False, -1]], [[[-0.05, -0.03], 1.51, 0.5, 0.5, 0.03125, 3.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [5, 1, 0], [0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [2.524203, 1.35238, 1.824634, 0.0, False, -1]], [[[-0.01, 0.0], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [-0.008062, 0.0, 1.370126, 0.0, False, -1]], [[[-0.01, -0.03], 0.0, 0.5, 0.5, 0.0625, 8.0, 2.0, 0.3, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 1]], [[[-0.03, 0.08], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.09375, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [-0.02354, 0.062773, 0.970367, 0.0, False, -1]]], [[[[-0.05, -0.05], -0.5, 0.5, 0.5, 0.03125, 3.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [1.513799, 2.430833, 0.021357, 0.0, False, -1]], [[[0.08, -0.08], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 0], [0, 0, 0.5], [0, 0, 0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 5]], [[[4.96, -1.21], -1.7, 80.0, 0.5, 0.0625, 8.0, 2.0, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.003827, -0.000934, -1.503118, 0.0, False, -1]], [[[-4.04, -5.1], 0.88, 80.0, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 1]], [[[5.74, -4.33], -1.41, 80.0, 0.5, 0.0625, 3.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [-2, 8, 0.5], [0, 0, -1], [0, 0, 0], [5, 0, 0.5]]], [0.831913, 0.00608, -1.157167, 0.0, False, -1]], [[[0.03, -0.04], -1.19, 2.0, 5.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [5, -3, 2]]], [2.572479, -1.543487, 1.52381, 0.0, False, 0]], [[[0.04, 0.03], 0.6, 2.0, 0.5, 0.015625, 3.0, 2.0, 0.3, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.030324, 0.82896, -0.387568, 0.0, False, -1]], [[[-0.03, -0.02], 0.88, 2.0, 5.0, 0.015625, 8.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 8, 0], [5, 1, -1], [0, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, -3, 0.5], [5, 0, 0], [0, 0, 0]]], [7.375353, 2.405025, -0.324717, 0.0, False, -1]]]]\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":"5680af903536fd3a2c1fa5e4133069d0192ada7147059c6d1d778b9698a17149","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks):\n    vx, vy = v\n    w = omega\n    timer = 0.0\n    asleep = False\n    slept_at = -1\n    for f, (ax, ay, aw) in enumerate(kicks):\n        if asleep:\n            if ax or ay or aw:\n                asleep = False\n                timer = 0.0\n            else:\n                continue\n        vx += ax\n        vy += ay\n        w += aw\n        dl = 1.0 / (1.0 + dt * lin_damp)\n        vx *= dl\n        vy *= dl\n        w *= dl\n        sp = math.hypot(vx, vy)\n        if sp > max_speed:\n            s = max_speed / sp\n            vx *= s\n            vy *= s\n        if math.hypot(vx, vy) < sleep_lin and abs(w) < sleep_ang:\n            timer += dt\n        else:\n            timer = 0.0\n        if timer >= sleep_time:\n            asleep = True\n            slept_at = f\n            vx = vy = w = 0.0\n    return [round(vx, 6), round(vy, 6), round(w, 6), round(timer, 6), asleep, slept_at]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[[[[0.05, 0.07], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 3]], [[[-0.01, -0.01], 1.26, 0.5, 40.0, 0.015625, 3.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 0, 0], [0, 0, 0], [0, 0, 0], [0, 8, 2]]], [0.363645, 2.977879, 1.230769, 0.0, False, 0]], [[[-0.12, -5.54], -0.33, 0.5, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.03125, [[1, 8, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.853029, 2.384603, 1.618816, 0.0, False, -1]], [[[-0.07, 0.09], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5]]], [-0.065791, 0.084588, -1.387079, 0.0, False, -1]], [[[4.02, 0.82], -0.26, 2.0, 40.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 2]]], [0.0, 0.888889, 0.571429, 0.0625, False, 6]], [[[-2.26, -0.28], 0.89, 2.0, 40.0, 0.0625, 3.0, 2.0, 0.3, 0.125, [[0, 0, 0.5], [0, 0, 0], [1, 0, -1], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 2]], [[[0.0, -0.02], -0.16, 20.0, 40.0, 0.015625, 8.0, 2.0, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.046875, True, 5]], [[[-4.46, -2.51], 0.66, 0.5, 0.5, 0.015625, 8.0, 2.0, 1.0, 0.03125, [[-2, -3, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-5.900121, -5.032456, 0.634812, 0.0, False, -1]]], [[[[2.02, -3.34], -1.78, 20.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, -3, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.229381, -0.966121, -1.672561, 0.0, False, -1]], [[[3.02, -0.11], 0.43, 0.5, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, 0.5], [1, 0, 2], [-2, -3, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [5.304661, -2.733316, 1.32246, 0.0, False, -1]], [[[-5.17, 4.65], 0.37, 20.0, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 0], [1, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 3]], [[[-2.24, -3.75], -1.0, 20.0, 0.5, 0.015625, 3.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 2], [1, 1, 0.5]]], [-0.57379, 0.469444, 1.532879, 0.0, False, -1]], [[[0.0, 0.02], 1.7, 2.0, 5.0, 0.015625, 8.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 0.5], [0, 0, 0], [0, 0, 0]]], [-1.823636, 0.015162, 1.262818, 0.0, False, -1]], [[[0.04, 0.05], -1.81, 20.0, 40.0, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[5, 0, 0.5], [0, 0, 0], [1, -3, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 1, 0], [0, 8, 0]]], [0.157676, 2.995853, 0.0, 0.0, False, 3]], [[[-0.05, -0.0], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5], [0, 0, -1.5]]], [-0.048092, 0.0, -2.327574, 0.0, False, -1]], [[[0.68, 3.27], 1.49, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [1, -3, 0], [0, 0, 0], [0, 0, 0]]], [1.513065, 0.155838, 1.317439, 0.0, False, -1]]], [[[[3.86, -4.4], 0.73, 80.0, 0.5, 0.0625, 3.0, 2.0, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, -1], [5, 0, -1], [0, 0, 0], [0, 0, 0]]], [0.027006, 0.0, -1.796005, 0.0, False, 1]], [[[0.04, -0.02], 1.78, 80.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [5, 0, 2], [5, 0, -1], [0, 0, 0], [0, -3, 0], [0, 0, 0], [5, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 7]], [[[0.09, -0.1], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.082005, -0.091117, 1.388111, 0.0, False, -1]], [[[-0.1, -0.05], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0]]], [-0.088419, -0.044209, 2.393944, 0.0, False, -1]], [[[0.09, 0.08], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0.5], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.323456, 0.0, False, 5]], [[[1.9, 0.51], -1.66, 0.5, 5.0, 0.015625, 8.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 0, -1], [0, 0, 0]]], [6.708099, 0.479217, -1.769724, 0.0, False, -1]], [[[-0.02, 0.02], -1.06, 0.5, 0.5, 0.015625, 8.0, 2.0, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, -3, 2], [0, 1, -1], [0, 0, 2], [0, 0, 0]]], [-0.01894, -1.912189, 1.927089, 0.0, False, -1]], [[[0.04, -0.02], 1.1, 80.0, 40.0, 0.03125, 3.0, 0.5, 0.3, 0.0625, [[0, -3, 0], [0, 0, 0], [0, 0, 0], [5, 0, -1], [0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 8]]], [[[[-0.05, 0.04], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 3.0], [0, 0, -3.0], [0, 0, -3.0]]], [-0.046618, 0.037294, -5.840587, 0.0, False, -1]], [[[-0.03, 0.05], -1.01, 80.0, 0.5, 0.03125, 8.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [5, 0, 2], [0, 0, 0], [0, 0, 0]]], [0.116618, 0.0, 1.909105, 0.0, False, 3]], [[[0.02, 0.03], -1.95, 2.0, 5.0, 0.015625, 3.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 1, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 4]], [[[-0.05, -0.02], 1.89, 0.5, 40.0, 0.0625, 3.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [5, 0, -1], [1, 1, -1], [0, 0, 0], [1, 0, 2]]], [2.951277, 0.538484, 0.54504, 0.0, False, -1]], [[[-0.05, -0.03], 1.51, 0.5, 0.5, 0.03125, 3.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [5, 1, 0], [0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [2.524203, 1.35238, 1.824634, 0.0, False, -1]], [[[-0.01, 0.0], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [-0.008062, 0.0, 1.370126, 0.0, False, -1]], [[[-0.01, -0.03], 0.0, 0.5, 0.5, 0.0625, 8.0, 2.0, 0.3, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 1]], [[[-0.03, 0.08], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.09375, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [-0.02354, 0.062773, 0.970367, 0.0, False, -1]]], [[[[-0.05, -0.05], -0.5, 0.5, 0.5, 0.03125, 3.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [1.513799, 2.430833, 0.021357, 0.0, False, -1]], [[[0.08, -0.08], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 0], [0, 0, 0.5], [0, 0, 0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 5]], [[[4.96, -1.21], -1.7, 80.0, 0.5, 0.0625, 8.0, 2.0, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.003827, -0.000934, -1.503118, 0.0, False, -1]], [[[-4.04, -5.1], 0.88, 80.0, 40.0, 0.0625, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 1]], [[[5.74, -4.33], -1.41, 80.0, 0.5, 0.0625, 3.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [-2, 8, 0.5], [0, 0, -1], [0, 0, 0], [5, 0, 0.5]]], [0.831913, 0.00608, -1.157167, 0.0, False, -1]], [[[0.03, -0.04], -1.19, 2.0, 5.0, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [5, -3, 2]]], [2.572479, -1.543487, 1.52381, 0.0, False, 0]], [[[0.04, 0.03], 0.6, 2.0, 0.5, 0.015625, 3.0, 2.0, 0.3, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.030324, 0.82896, -0.387568, 0.0, False, -1]], [[[-0.03, -0.02], 0.88, 2.0, 5.0, 0.015625, 8.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [0, 8, 0], [5, 1, -1], [0, 0, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, -3, 0.5], [5, 0, 0], [0, 0, 0]]], [7.375353, 2.405025, -0.324717, 0.0, False, -1]]]]\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-damping-clamp-sleep-angular-damping-coefficient","generated_at":"2026-09-29T14:50:57.213748+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.","root_cause":"omega is multiplied by the linear factor dl.","sha256":"3f633795338090ede0a4d3674239338ff3717bab3e2317e107abbcc30d381b5d","title":"Angular velocity is damped with the linear coefficient · 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":42.512,"exit_code":1,"observations":[{"actual":[0.046993,0.065791,-0.37037,0.0,false,-1],"check":"case 0","expected":[0.0,0.0,0.0,0.0625,true,3],"passed":false},{"actual":[0.363645,2.977879,0.04878,0.0,false,0],"check":"case 1","expected":[0.363645,2.977879,1.230769,0.0,false,0],"passed":false},{"actual":[0.853029,2.384603,0.329877,0.0,false,-1],"check":"case 2","expected":[0.853029,2.384603,1.618816,0.0,false,-1],"passed":false},{"actual":[-0.065791,0.084588,0.037037,0.03125,false,-1],"check":"case 3","expected":[-0.065791,0.084588,-1.387079,0.0,false,-1],"passed":false},{"actual":[0.0,0.888889,0.04878,0.0625,false,6],"check":"case 4","expected":[0.0,0.888889,0.571429,0.0625,false,6],"passed":false},{"actual":[0.0,0.0,0.0,0.125,true,2],"check":"case 5","expected":[0.0,0.0,0.0,0.125,true,2],"passed":true},{"actual":[0.0,0.0,0.0,0.046875,true,5],"check":"case 6","expected":[0.0,0.0,0.0,0.046875,true,5],"passed":true},{"actual":[-5.900121,-5.032456,0.086914,0.0,false,-1],"check":"case 7","expected":[-5.900121,-5.032456,0.634812,0.0,false,-1],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [0.046993, 0.065791, -0.37037, 0.0, false, -1], \"expected\": [0.0, 0.0, 0.0, 0.0625, true, 3], \"passed\": false}, {\"check\": \"case 1\", \"actual\": [0.363645, 2.977879, 0.04878, 0.0, false, 0], \"expected\": [0.363645, 2.977879, 1.230769, 0.0, false, 0], \"passed\": false}, {\"check\": \"case 2\", \"actual\": [0.853029, 2.384603, 0.329877, 0.0, false, -1], \"expected\": [0.853029, 2.384603, 1.618816, 0.0, false, -1], \"passed\": false}, {\"check\": \"case 3\", \"actual\": [-0.065791, 0.084588, 0.037037, 0.03125, false, -1], \"expected\": [-0.065791, 0.084588, -1.387079, 0.0, false, -1], \"passed\": false}, {\"check\": \"case 4\", \"actual\": [0.0, 0.888889, 0.04878, 0.0625, false, 6], \"expected\": [0.0, 0.888889, 0.571429, 0.0625, false, 6], \"passed\": false}, {\"check\": \"case 5\", \"actual\": [0.0, 0.0, 0.0, 0.125, true, 2], \"expected\": [0.0, 0.0, 0.0, 0.125, true, 2], \"passed\": true}, {\"check\": \"case 6\", \"actual\": [0.0, 0.0, 0.0, 0.046875, true, 5], \"expected\": [0.0, 0.0, 0.0, 0.046875, true, 5], \"passed\": true}, {\"check\": \"case 7\", \"actual\": [-5.900121, -5.032456, 0.086914, 0.0, false, -1], \"expected\": [-5.900121, -5.032456, 0.634812, 0.0, false, -1], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.856,"exit_code":1,"observations":[{"actual":[0.0,0.0,0.0,0.0625,true,3],"check":"case 0","expected":[0.0,0.0,0.0,0.0625,true,3],"passed":true},{"actual":[0.360568,2.978253,3.177694,0.0,false,-1],"check":"case 1","expected":[0.363645,2.977879,1.230769,0.0,false,0],"passed":false},{"actual":[0.853029,2.384603,1.618816,0.0,false,-1],"check":"case 2","expected":[0.853029,2.384603,1.618816,0.0,false,-1],"passed":true},{"actual":[-0.065791,0.084588,-1.387079,0.0,false,-1],"check":"case 3","expected":[-0.065791,0.084588,-1.387079,0.0,false,-1],"passed":true},{"actual":[0.0,0.888889,1.777778,0.0,false,6],"check":"case 4","expected":[0.0,0.888889,0.571429,0.0625,false,6],"passed":false},{"actual":[0.0,0.0,0.0,0.125,true,3],"check":"case 5","expected":[0.0,0.0,0.0,0.125,true,2],"passed":false},{"actual":[0.0,0.0,0.0,0.046875,true,5],"check":"case 6","expected":[0.0,0.0,0.0,0.046875,true,5],"passed":true},{"actual":[-5.900121,-5.032456,0.634812,0.0,false,-1],"check":"case 7","expected":[-5.900121,-5.032456,0.634812,0.0,false,-1],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [0.0, 0.0, 0.0, 0.0625, true, 3], \"expected\": [0.0, 0.0, 0.0, 0.0625, true, 3], \"passed\": true}, {\"check\": \"case 1\", \"actual\": [0.360568, 2.978253, 3.177694, 0.0, false, -1], \"expected\": [0.363645, 2.977879, 1.230769, 0.0, false, 0], \"passed\": false}, {\"check\": \"case 2\", \"actual\": [0.853029, 2.384603, 1.618816, 0.0, false, -1], \"expected\": [0.853029, 2.384603, 1.618816, 0.0, false, -1], \"passed\": true}, {\"check\": \"case 3\", \"actual\": [-0.065791, 0.084588, -1.387079, 0.0, false, -1], \"expected\": [-0.065791, 0.084588, -1.387079, 0.0, false, -1], \"passed\": true}, {\"check\": \"case 4\", \"actual\": [0.0, 0.888889, 1.777778, 0.0, false, 6], \"expected\": [0.0, 0.888889, 0.571429, 0.0625, false, 6], \"passed\": false}, {\"check\": \"case 5\", \"actual\": [0.0, 0.0, 0.0, 0.125, true, 3], \"expected\": [0.0, 0.0, 0.0, 0.125, true, 2], \"passed\": false}, {\"check\": \"case 6\", \"actual\": [0.0, 0.0, 0.0, 0.046875, true, 5], \"expected\": [0.0, 0.0, 0.0, 0.046875, true, 5], \"passed\": true}, {\"check\": \"case 7\", \"actual\": [-5.900121, -5.032456, 0.634812, 0.0, false, -1], \"expected\": [-5.900121, -5.032456, 0.634812, 0.0, false, -1], \"passed\": true}], \"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."}}