{"abstract":"Positions overshoot toward the central body every step.","category":"Orbital propagation","checks":7,"contract":"Input [r0, v0, mu, T, steps]; planar two-body. Velocity Verlet with h=T/steps: p += h v + h^2 a/2; a_new = a(p); v += h (a + a_new)/2; carry a_new. Return final [x,y,vx,vy] rounded to 6 plus specific energy v^2/2-mu/|r| rounded to 6.","evaluation_group":"w2-orbital_propagation-verlet_two_body","failed_approach":"Using 0.5*h*a has the wrong dimension for a position update.","family":"w2-orbital_propagation-verlet_two_body-drift-half-factor","id":"FA-69546","implementations":{"attempt":{"sha256":"1506bfe65eddfc4fa74e8210f2270674ef2bf2742f43d59bbbf5e0ff96d44b38","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    r0,v0,mu,T,steps=x\n    h=T/steps\n    def acc(q):\n        rr=(q[0]**2+q[1]**2)**1.5\n        return [-mu*q[0]/rr,-mu*q[1]/rr]\n    p=list(r0); v=list(v0)\n    a=acc(p)\n    for _ in range(steps):\n        p=[p[i]+h*v[i]+0.5*h*a[i] for i in range(2)]\n        an=acc(p)\n        v=[v[i]+0.5*h*(a[i]+an[i]) for i in range(2)]\n        a=an\n    en=(v[0]**2+v[1]**2)/2-mu/math.sqrt(p[0]**2+p[1]**2)\n    return [round(c,6) for c in p+v]+[round(en,6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489])], [('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856])], [('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, 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":"49d792cc3fac70d8fd211030a4d1c9759aebb60dc9acca6548b8755a0edd0303","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    r0,v0,mu,T,steps=x\n    h=T/steps\n    def acc(q):\n        rr=(q[0]**2+q[1]**2)**1.5\n        return [-mu*q[0]/rr,-mu*q[1]/rr]\n    p=list(r0); v=list(v0)\n    a=acc(p)\n    for _ in range(steps):\n        p=[p[i]+h*v[i]+h*h*a[i] for i in range(2)]\n        an=acc(p)\n        v=[v[i]+0.5*h*(a[i]+an[i]) for i in range(2)]\n        a=an\n    en=(v[0]**2+v[1]**2)/2-mu/math.sqrt(p[0]**2+p[1]**2)\n    return [round(c,6) for c in p+v]+[round(en,6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489])], [('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856])], [('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, 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":"1f28a6014b215676f2f2a79a2e1707b4fc1e7dcaa1cf29a1bf9e877a2fdbeb0c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nN = 1\nobservations = []\ndef solve(x):\n    r0,v0,mu,T,steps=x\n    h=T/steps\n    def acc(q):\n        rr=(q[0]**2+q[1]**2)**1.5\n        return [-mu*q[0]/rr,-mu*q[1]/rr]\n    p=list(r0); v=list(v0)\n    a=acc(p)\n    for _ in range(steps):\n        p=[p[i]+h*v[i]+0.5*h*h*a[i] for i in range(2)]\n        an=acc(p)\n        v=[v[i]+0.5*h*(a[i]+an[i]) for i in range(2)]\n        a=an\n    en=(v[0]**2+v[1]**2)/2-mu/math.sqrt(p[0]**2+p[1]**2)\n    return [round(c,6) for c in p+v]+[round(en,6)]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489])], [('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856])], [('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]', [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30], [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038]), ('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049])], [('velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]', [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25], [-2.100327, 1.143517, -0.394254, -0.35669, -0.276826]), ('velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]', [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10], [-0.160223, -0.731051, 1.375248, 0.033556, -0.389962]), ('velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]', [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6], [6111.297912, 3317.130164, -3.439136, 6.583207, -29.740489]), ('velocity verlet two-body propagation [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8]', [[2.0, 0.0], [0.0, 0.5], 1.0, 4.0, 8], [-0.104683, 0.976244, -0.959856, -0.601306, -0.377049]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]', [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12], [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856]), ('velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]', [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20], [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351]), ('velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]', [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15], [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038])]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, 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 toy two-body model with stipulated constants and conventions; not flight dynamics software or a validated SGP4 implementation. 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-orbital_propagation-verlet_two_body-drift-half-factor","generated_at":"2026-09-29T14:48:12.493982+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Orbit determination and mission planning chain many small conversions; one wrong branch or unit silently moves a spacecraft by kilometres.","repair":"Use 0.5*h*h*a.","root_cause":"The drift uses h^2 a instead of h^2 a/2.","sha256":"9b655b95dc5851d341b94a447c457b2b877a7e864682c1fbd34f9b13e0114a12","title":"Velocity Verlet two-body propagation: Position drift omits the one-half acceleration factor · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":39.255,"exit_code":1,"observations":[{"actual":[5711.537898,4260.468281,-4.475625,6.065216,-27.530685],"check":"velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]","expected":[5585.861325,4220.456543,-4.545757,6.021781,-28.471856],"passed":false},{"actual":[4260.757337,6703.776146,-5.601079,5.436802,-19.715795],"check":"velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]","expected":[4100.742247,6612.678063,-5.690094,5.333971,-20.813351],"passed":false},{"actual":[-6693.93796,7000.084916,-4.249688,-4.083833,-23.785338],"check":"velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]","expected":[-6596.602558,6758.244077,-4.170275,-4.186438,-24.748038],"passed":false},{"actual":[-1.58811,-1.314714,-0.535358,-0.259116,-0.308164],"check":"velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]","expected":[-0.993552,0.151005,-0.14987,-0.983712,-0.499988],"passed":false},{"actual":[-0.485751,-4.115111,-0.132602,-1.05214,0.32096],"check":"velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 1.0, 5.0, 25]","expected":[-2.100327,1.143517,-0.394254,-0.35669,-0.276826],"passed":false},{"actual":[-1.129637,1.756435,-0.809542,2.398682,2.725668],"check":"velocity verlet two-body propagation [[-1.5, 0.5], [0.1, -0.7], 1.0, 2.0, 10]","expected":[-0.160223,-0.731051,1.375248,0.033556,-0.389962],"passed":false},{"actual":[6170.769208,3336.240484,-3.419715,6.592828,-29.242012],"check":"velocity verlet two-body propagation [[6800.0, 1200.0], [-1.1, 7.4], 398600.4418, 300.0, 6]","expected":[6111.297912,3317.130164,-3.439136,6.583207,-29.740489],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 7.546], 398600.4418, 600.0, 12]\", \"actual\": [5711.537898, 4260.468281, -4.475625, 6.065216, -27.530685], \"expected\": [5585.861325, 4220.456543, -4.545757, 6.021781, -28.471856], \"passed\": false}, {\"check\": \"velocity verlet two-body propagation [[7000.0, 0.0], [0.0, 8.5], 398600.4418, 900.0, 20]\", \"actual\": [4260.757337, 6703.776146, -5.601079, 5.436802, -19.715795], \"expected\": [4100.742247, 6612.678063, -5.690094, 5.333971, -20.813351], \"passed\": false}, {\"check\": \"velocity verlet two-body propagation [[0.0, 9000.0], [-6.2, 0.8], 398600.4418, 1200.0, 15]\", \"actual\": [-6693.93796, 7000.084916, -4.249688, -4.083833, -23.785338], \"expected\": [-6596.602558, 6758.244077, -4.170275, -4.186438, -24.748038], \"passed\": false}, {\"check\": \"velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.0], 1.0, 3.0, 30]\", \"actual\": [-1.58811, -1.314714, -0.535358, -0.259116, -0.308164], \"expected\": [-0.993552, 0.151005, -0.14987, -0.983712, -0.499988], \"passed\": false}, {\"check\": \"velocity verlet two-body propagation [[1.0, 0.0], [0.0, 1.2], 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