{"abstract":"High damping at coarse steps flips the velocity sign and the body jitters.","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":"Clamping 1 - c*dt at zero stops the flip but still over-damps relative to the contract.","family":"w2-physics_integrator_stability-damping-clamp-sleep-linear-damping-form","id":"FA-87241","implementations":{"attempt":{"sha256":"23080f7401f4d8ec33de02ddac8dc97b424ef0902ab4f9e79a21870c27331072","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 = max(0.0, 1.0 - dt * lin_damp)\n        vx *= dl\n        vy *= dl\n        w *= 1.0 / (1.0 + dt * 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 = [[[[[-0.0, 0.0], 0.99, 2.0, 0.5, 0.015625, 8.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0], [0, 0, 0]]], [-1.823636, 7.294543, 0.0, 0.0, False, 1]], [[[-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]], [[[0.02, 0.01], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 3]], [[[2.14, -0.12], 1.88, 80.0, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.007331, -0.000411, 1.780327, 0.0, False, -1]], [[[-0.02, 0.07], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0.5]]], [0.0, 0.0, 0.806428, 0.0, False, 1]], [[[0.0, -0.04], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0]]], [0.0, -0.038473, -1.442578, 0.0, False, -1]], [[[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]], [[[-3.19, -0.03], 1.71, 20.0, 0.5, 0.015625, 3.0, 0.5, 1.0, 0.015625, [[0, 8, -1], [0, 1, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-0.374853, 1.272803, 0.682904, 0.0, False, -1]]], [[[[0.02, 0.02], 1.76, 80.0, 40.0, 0.03125, 8.0, 0.5, 1.0, 0.03125, [[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, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 0]], [[[0.06, -0.1], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, 1.5]]], [0.023385, -0.038974, -2.448788, 0.0, False, -1]], [[[1.54, 3.78], -0.99, 20.0, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.03125, [[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]], [[[0.07, 0.04], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5]]], [0.043701, 0.024972, 2.822272, 0.0, False, -1]], [[[-0.04, -0.09], 0.0, 2.0, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, -1.5]]], [-0.02954, -0.066466, -5.729036, 0.0, False, -1]], [[[-0.02, -0.0], 1.5, 0.5, 5.0, 0.03125, 3.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 8, 0.5]]], [0.0, 3.0, 0.432432, 0.0, False, 2]], [[[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]], [[[0.63, 0.72], -1.08, 20.0, 0.5, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [5, 0, 2], [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, 0.1875, True, 8]]], [[[[-0.0, -0.04], 1.8, 0.5, 40.0, 0.03125, 8.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, -0.038182, 0.158025, 0.03125, False, -1]], [[[0.09, 0.02], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5]]], [0.0, 0.0, 1.297297, 0.0, False, 4]], [[[-1.31, 0.47], 0.1, 80.0, 5.0, 0.0625, 8.0, 2.0, 0.3, 0.125, [[0, 0, 0], [-2, 8, -1], [0, 0, 0], [0, 0, 0], [1, 0, 0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 5]], [[[0.05, -0.02], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, -1.5], [0, 0, 1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5]]], [0.0, 0.0, 0.011538, 0.015625, False, 5]], [[[3.31, 5.08], -0.33, 2.0, 40.0, 0.03125, 3.0, 0.5, 0.3, 0.0625, [[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, 0, 0], [0, 0, 0]]], [0.949044, 1.456539, -9.9e-05, 0.0, False, -1]], [[[0.08, -0.01], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.09375, True, 8]], [[[-0.07, 0.04], 0.0, 2.0, 0.5, 0.03125, 8.0, 0.5, 0.3, 0.09375, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0]]], [-0.043099, 0.024628, -1.518273, 0.0, False, -1]], [[[4.65, -4.7], -0.73, 20.0, 0.5, 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, 0.5]]], [0.0, 0.0, 0.484848, 0.0625, False, 3]]], [[[[4.92, 4.59], 0.62, 20.0, 0.5, 0.0625, 3.0, 0.5, 1.0, 0.1875, [[0, 0, 0], [0, 8, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 0.5]]], [-0.888889, 0.0, 0.484848, 0.0, False, 6]], [[[-5.56, 0.39], -1.79, 2.0, 40.0, 0.03125, 3.0, 0.5, 1.0, 0.0625, [[-2, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 1, 0.5], [5, -3, 0.5], [0, 0, 0]]], [2.80594, -0.31467, 0.141788, 0.0, False, -1]], [[[-0.02, 0.03], 0.27, 2.0, 40.0, 0.03125, 3.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 0]], [[[-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]], [[[4.25, 3.24], 1.04, 2.0, 0.5, 0.015625, 3.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [1, 8, -1], [0, 0, 0]]], [0.934883, 2.754778, 0.023569, 0.0, False, -1]], [[[-0.05, 0.02], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 3]], [[[5.93, 2.95], -1.5, 2.0, 0.5, 0.03125, 8.0, 0.5, 0.3, 0.09375, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [4.379353, 2.178599, -1.388111, 0.0, False, -1]], [[[-0.04, -0.04], 0.45, 20.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[0, 1, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 0]]], [[[[-4.0, -0.28], -1.66, 20.0, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[-2, 8, 2], [0, 0, 0], [-2, 0, 2], [0, 0, 0], [0, 0, 0]]], [-0.279632, 0.133877, 2.11515, 0.0, False, -1]], [[[0.05, -0.01], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 2]], [[[0.18, -1.7], -1.08, 80.0, 0.5, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.000833, -0.00787, -0.984763, 0.0625, False, -1]], [[[-0.01, 0.03], -0.14, 0.5, 0.5, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [1, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.806218, 0.806218, -0.336061, 0.0, False, 0]], [[[-4.85, -4.08], 0.8, 2.0, 0.5, 0.03125, 3.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [5, 0, 2], [0, 0, 0]]], [2.378, -1.522313, 2.690829, 0.0, False, -1]], [[[-0.03, -0.03], 0.71, 80.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, -1], [0, 0, 0], [0, 0, 0], [-2, 0, 0.5]]], [-0.333333, 0.0, 0.142857, 0.0625, False, 2]], [[[-0.02, 0.02], 1.56, 0.5, 40.0, 0.0625, 3.0, 2.0, 0.3, 0.1875, [[1, 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, 0.0, 0.1875, True, 3]], [[[-0.08, 0.04], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, -3.0], [0, 0, 0], [0, 0, 3.0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 3]]]]\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":"e9629a18936ecff78c80e5f3ed697a58785d52359aab02ab802abcab938bba90","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 - dt * lin_damp\n        vx *= dl\n        vy *= dl\n        w *= 1.0 / (1.0 + dt * 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 = [[[[[-0.0, 0.0], 0.99, 2.0, 0.5, 0.015625, 8.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0], [0, 0, 0]]], [-1.823636, 7.294543, 0.0, 0.0, False, 1]], [[[-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]], [[[0.02, 0.01], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 3]], [[[2.14, -0.12], 1.88, 80.0, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.007331, -0.000411, 1.780327, 0.0, False, -1]], [[[-0.02, 0.07], 0.0, 2.0, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0.5]]], [0.0, 0.0, 0.806428, 0.0, False, 1]], [[[0.0, -0.04], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0]]], [0.0, -0.038473, -1.442578, 0.0, False, -1]], [[[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]], [[[-3.19, -0.03], 1.71, 20.0, 0.5, 0.015625, 3.0, 0.5, 1.0, 0.015625, [[0, 8, -1], [0, 1, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [-0.374853, 1.272803, 0.682904, 0.0, False, -1]]], [[[[0.02, 0.02], 1.76, 80.0, 40.0, 0.03125, 8.0, 0.5, 1.0, 0.03125, [[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, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 0]], [[[0.06, -0.1], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, 1.5]]], [0.023385, -0.038974, -2.448788, 0.0, False, -1]], [[[1.54, 3.78], -0.99, 20.0, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.03125, [[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]], [[[0.07, 0.04], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5]]], [0.043701, 0.024972, 2.822272, 0.0, False, -1]], [[[-0.04, -0.09], 0.0, 2.0, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, -1.5]]], [-0.02954, -0.066466, -5.729036, 0.0, False, -1]], [[[-0.02, -0.0], 1.5, 0.5, 5.0, 0.03125, 3.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 8, 0.5]]], [0.0, 3.0, 0.432432, 0.0, False, 2]], [[[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]], [[[0.63, 0.72], -1.08, 20.0, 0.5, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [5, 0, 2], [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, 0.1875, True, 8]]], [[[[-0.0, -0.04], 1.8, 0.5, 40.0, 0.03125, 8.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, -0.038182, 0.158025, 0.03125, False, -1]], [[[0.09, 0.02], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 0.3, 0.0625, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5]]], [0.0, 0.0, 1.297297, 0.0, False, 4]], [[[-1.31, 0.47], 0.1, 80.0, 5.0, 0.0625, 8.0, 2.0, 0.3, 0.125, [[0, 0, 0], [-2, 8, -1], [0, 0, 0], [0, 0, 0], [1, 0, 0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 5]], [[[0.05, -0.02], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, -1.5], [0, 0, 1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5]]], [0.0, 0.0, 0.011538, 0.015625, False, 5]], [[[3.31, 5.08], -0.33, 2.0, 40.0, 0.03125, 3.0, 0.5, 0.3, 0.0625, [[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, 0, 0], [0, 0, 0]]], [0.949044, 1.456539, -9.9e-05, 0.0, False, -1]], [[[0.08, -0.01], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.09375, True, 8]], [[[-0.07, 0.04], 0.0, 2.0, 0.5, 0.03125, 8.0, 0.5, 0.3, 0.09375, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0]]], [-0.043099, 0.024628, -1.518273, 0.0, False, -1]], [[[4.65, -4.7], -0.73, 20.0, 0.5, 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, 0.5]]], [0.0, 0.0, 0.484848, 0.0625, False, 3]]], [[[[4.92, 4.59], 0.62, 20.0, 0.5, 0.0625, 3.0, 0.5, 1.0, 0.1875, [[0, 0, 0], [0, 8, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 0, 0.5]]], [-0.888889, 0.0, 0.484848, 0.0, False, 6]], [[[-5.56, 0.39], -1.79, 2.0, 40.0, 0.03125, 3.0, 0.5, 1.0, 0.0625, [[-2, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 1, 0.5], [5, -3, 0.5], [0, 0, 0]]], [2.80594, -0.31467, 0.141788, 0.0, False, -1]], [[[-0.02, 0.03], 0.27, 2.0, 40.0, 0.03125, 3.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 0]], [[[-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]], [[[4.25, 3.24], 1.04, 2.0, 0.5, 0.015625, 3.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [1, 8, -1], [0, 0, 0]]], [0.934883, 2.754778, 0.023569, 0.0, False, -1]], [[[-0.05, 0.02], 0.0, 0.5, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 3]], [[[5.93, 2.95], -1.5, 2.0, 0.5, 0.03125, 8.0, 0.5, 0.3, 0.09375, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [4.379353, 2.178599, -1.388111, 0.0, False, -1]], [[[-0.04, -0.04], 0.45, 20.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[0, 1, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 0]]], [[[[-4.0, -0.28], -1.66, 20.0, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[-2, 8, 2], [0, 0, 0], [-2, 0, 2], [0, 0, 0], [0, 0, 0]]], [-0.279632, 0.133877, 2.11515, 0.0, False, -1]], [[[0.05, -0.01], 0.0, 0.5, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[0, 0, 0.5], [0, 0, -0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 2]], [[[0.18, -1.7], -1.08, 80.0, 0.5, 0.0625, 3.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.000833, -0.00787, -0.984763, 0.0625, False, -1]], [[[-0.01, 0.03], -0.14, 0.5, 0.5, 0.0625, 3.0, 0.5, 1.0, 0.0625, [[0, 0, 0], [1, 1, -1], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.806218, 0.806218, -0.336061, 0.0, False, 0]], [[[-4.85, -4.08], 0.8, 2.0, 0.5, 0.03125, 3.0, 2.0, 0.3, 0.0625, [[0, 0, 0], [0, 0, 0], [5, 0, 2], [0, 0, 0]]], [2.378, -1.522313, 2.690829, 0.0, False, -1]], [[[-0.03, -0.03], 0.71, 80.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, -1], [0, 0, 0], [0, 0, 0], [-2, 0, 0.5]]], [-0.333333, 0.0, 0.142857, 0.0625, False, 2]], [[[-0.02, 0.02], 1.56, 0.5, 40.0, 0.0625, 3.0, 2.0, 0.3, 0.1875, [[1, 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, 0.0, 0.1875, True, 3]], [[[-0.08, 0.04], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, -3.0], [0, 0, 0], [0, 0, 3.0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 3]]]]\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-linear-damping-form","generated_at":"2026-09-29T14:50:56.991283+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":"dl = 1 - dt*lin_damp can become negative.","sha256":"0d8965d9a675224363a213aa990ce48a8ff34ce070094260ef114477ffb535ab","title":"Linear damping uses the explicit 1 - c*dt factor · 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":42.575,"exit_code":1,"observations":[{"actual":[-1.818298,7.273193,0.0,0.0,false,1],"check":"case 0","expected":[-1.823636,7.294543,0.0,0.0,false,1],"passed":false},{"actual":[0.36358,2.977887,1.230769,0.0,false,0],"check":"case 1","expected":[0.363645,2.977879,1.230769,0.0,false,0],"passed":false},{"actual":[0.0,0.0,0.0,0.03125,true,3],"check":"case 2","expected":[0.0,0.0,0.0,0.03125,true,3],"passed":true},{"actual":[0.0,0.0,1.780327,0.0,false,-1],"check":"case 3","expected":[0.007331,-0.000411,1.780327,0.0,false,-1],"passed":false},{"actual":[0.0,0.0,0.806428,0.0,false,1],"check":"case 4","expected":[0.0,0.0,0.806428,0.0,false,1],"passed":true},{"actual":[0.0,-0.038462,-1.442578,0.0,false,-1],"check":"case 5","expected":[0.0,-0.038473,-1.442578,0.0,false,-1],"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":[-0.249045,0.845626,0.682904,0.0,false,-1],"check":"case 7","expected":[-0.374853,1.272803,0.682904,0.0,false,-1],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [-1.818298, 7.273193, 0.0, 0.0, false, 1], \"expected\": [-1.823636, 7.294543, 0.0, 0.0, false, 1], \"passed\": false}, {\"check\": \"case 1\", \"actual\": [0.36358, 2.977887, 1.230769, 0.0, false, 0], \"expected\": [0.363645, 2.977879, 1.230769, 0.0, false, 0], \"passed\": false}, {\"check\": \"case 2\", \"actual\": [0.0, 0.0, 0.0, 0.03125, true, 3], \"expected\": [0.0, 0.0, 0.0, 0.03125, true, 3], \"passed\": true}, {\"check\": \"case 3\", \"actual\": [0.0, 0.0, 1.780327, 0.0, false, -1], \"expected\": [0.007331, -0.000411, 1.780327, 0.0, false, -1], \"passed\": false}, {\"check\": \"case 4\", \"actual\": [0.0, 0.0, 0.806428, 0.0, false, 1], \"expected\": [0.0, 0.0, 0.806428, 0.0, false, 1], \"passed\": true}, {\"check\": \"case 5\", \"actual\": [0.0, -0.038462, -1.442578, 0.0, false, -1], \"expected\": [0.0, -0.038473, -1.442578, 0.0, false, -1], \"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\": [-0.249045, 0.845626, 0.682904, 0.0, false, -1], \"expected\": [-0.374853, 1.272803, 0.682904, 0.0, false, -1], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.815,"exit_code":1,"observations":[{"actual":[-1.818298,7.273193,0.0,0.0,false,1],"check":"case 0","expected":[-1.823636,7.294543,0.0,0.0,false,1],"passed":false},{"actual":[0.36358,2.977887,1.230769,0.0,false,0],"check":"case 1","expected":[0.363645,2.977879,1.230769,0.0,false,0],"passed":false},{"actual":[0.0,0.0,0.0,0.03125,true,3],"check":"case 2","expected":[0.0,0.0,0.0,0.03125,true,3],"passed":true},{"actual":[-0.000131,7e-06,1.780327,0.0,false,-1],"check":"case 3","expected":[0.007331,-0.000411,1.780327,0.0,false,-1],"passed":false},{"actual":[0.0,0.0,0.806428,0.0,false,1],"check":"case 4","expected":[0.0,0.0,0.806428,0.0,false,1],"passed":true},{"actual":[0.0,-0.038462,-1.442578,0.0,false,-1],"check":"case 5","expected":[0.0,-0.038473,-1.442578,0.0,false,-1],"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":[-0.249045,0.845626,0.682904,0.0,false,-1],"check":"case 7","expected":[-0.374853,1.272803,0.682904,0.0,false,-1],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"case 0\", \"actual\": [-1.818298, 7.273193, 0.0, 0.0, false, 1], \"expected\": [-1.823636, 7.294543, 0.0, 0.0, false, 1], \"passed\": false}, {\"check\": \"case 1\", \"actual\": [0.36358, 2.977887, 1.230769, 0.0, false, 0], \"expected\": [0.363645, 2.977879, 1.230769, 0.0, false, 0], \"passed\": false}, {\"check\": \"case 2\", \"actual\": [0.0, 0.0, 0.0, 0.03125, true, 3], \"expected\": [0.0, 0.0, 0.0, 0.03125, true, 3], \"passed\": true}, {\"check\": \"case 3\", \"actual\": [-0.000131, 7e-06, 1.780327, 0.0, false, -1], \"expected\": [0.007331, -0.000411, 1.780327, 0.0, false, -1], \"passed\": false}, {\"check\": \"case 4\", \"actual\": [0.0, 0.0, 0.806428, 0.0, false, 1], \"expected\": [0.0, 0.0, 0.806428, 0.0, false, 1], \"passed\": true}, {\"check\": \"case 5\", \"actual\": [0.0, -0.038462, -1.442578, 0.0, false, -1], \"expected\": [0.0, -0.038473, -1.442578, 0.0, false, -1], \"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\": [-0.249045, 0.845626, 0.682904, 0.0, false, -1], \"expected\": [-0.374853, 1.272803, 0.682904, 0.0, false, -1], \"passed\": false}], \"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."}}