{
  "experiment": "polarization-alignment-check",
  "status": "exact_initial_same_depth_angular_energy",
  "equation": "V(theta)/omega_M = -q*d*M*theta^2/[2*(d+1)] + O(theta^4), with current grade M=particle index-1",
  "rows": [
    {
      "depth": 2,
      "particle_index": 76,
      "current_grade": 75,
      "partner_rank": 2,
      "q": 0.333333333,
      "theta_squared_coefficient_over_smaller_mass": -8.333333333,
      "finite_angle_coefficient": -8.333118927,
      "relative_error": 2.573e-05
    },
    {
      "depth": 2,
      "particle_index": 81,
      "current_grade": 80,
      "partner_rank": 2,
      "q": 0.333333333,
      "theta_squared_coefficient_over_smaller_mass": -8.888888889,
      "finite_angle_coefficient": -8.888644911,
      "relative_error": 2.745e-05
    },
    {
      "depth": 2,
      "particle_index": 95,
      "current_grade": 94,
      "partner_rank": 2,
      "q": 0.333333333,
      "theta_squared_coefficient_over_smaller_mass": -10.444444444,
      "finite_angle_coefficient": -10.444107509,
      "relative_error": 3.226e-05
    },
    {
      "depth": 3,
      "particle_index": 1,
      "current_grade": 0,
      "partner_rank": 2,
      "q": 0.333333333,
      "theta_squared_coefficient_over_smaller_mass": -0.0,
      "finite_angle_coefficient": 0.0,
      "relative_error": 0.0
    },
    {
      "depth": 3,
      "particle_index": 4,
      "current_grade": 3,
      "partner_rank": 2,
      "q": 0.333333333,
      "theta_squared_coefficient_over_smaller_mass": -0.375,
      "finite_angle_coefficient": -0.374999616,
      "relative_error": 1.025e-06
    },
    {
      "depth": 3,
      "particle_index": 16,
      "current_grade": 15,
      "partner_rank": 2,
      "q": 0.333333333,
      "theta_squared_coefficient_over_smaller_mass": -1.875,
      "finite_angle_coefficient": -1.874989828,
      "relative_error": 5.425e-06
    },
    {
      "depth": 3,
      "particle_index": 17,
      "current_grade": 16,
      "partner_rank": 2,
      "q": 0.333333333,
      "theta_squared_coefficient_over_smaller_mass": -2.0,
      "finite_angle_coefficient": -1.999988417,
      "relative_error": 5.792e-06
    },
    {
      "depth": 4,
      "particle_index": 3,
      "current_grade": 2,
      "partner_rank": 4,
      "q": 0.2,
      "theta_squared_coefficient_over_smaller_mass": -0.16,
      "finite_angle_coefficient": -0.159999887,
      "relative_error": 7.04e-07
    },
    {
      "depth": 4,
      "particle_index": 20,
      "current_grade": 19,
      "partner_rank": 4,
      "q": 0.2,
      "theta_squared_coefficient_over_smaller_mass": -1.52,
      "finite_angle_coefficient": -1.519988701,
      "relative_error": 7.433e-06
    },
    {
      "depth": 4,
      "particle_index": 72,
      "current_grade": 71,
      "partner_rank": 4,
      "q": 0.2,
      "theta_squared_coefficient_over_smaller_mass": -5.68,
      "finite_angle_coefficient": -5.679840868,
      "relative_error": 2.802e-05
    },
    {
      "depth": 5,
      "particle_index": 10,
      "current_grade": 9,
      "partner_rank": 4,
      "q": 0.2,
      "theta_squared_coefficient_over_smaller_mass": -0.75,
      "finite_angle_coefficient": -0.749997326,
      "relative_error": 3.566e-06
    },
    {
      "depth": 5,
      "particle_index": 15,
      "current_grade": 14,
      "partner_rank": 4,
      "q": 0.2,
      "theta_squared_coefficient_over_smaller_mass": -1.166666667,
      "finite_angle_coefficient": -1.166660132,
      "relative_error": 5.601e-06
    },
    {
      "depth": 5,
      "particle_index": 22,
      "current_grade": 21,
      "partner_rank": 4,
      "q": 0.2,
      "theta_squared_coefficient_over_smaller_mass": -1.75,
      "finite_angle_coefficient": -1.74998521,
      "relative_error": 8.451e-06
    },
    {
      "depth": 6,
      "particle_index": 13,
      "current_grade": 12,
      "partner_rank": 8,
      "q": 0.111111111,
      "theta_squared_coefficient_over_smaller_mass": -0.571428571,
      "finite_angle_coefficient": -0.571425715,
      "relative_error": 4.998e-06
    },
    {
      "depth": 6,
      "particle_index": 35,
      "current_grade": 34,
      "partner_rank": 8,
      "q": 0.111111111,
      "theta_squared_coefficient_over_smaller_mass": -1.619047619,
      "finite_angle_coefficient": -1.619024376,
      "relative_error": 1.436e-05
    },
    {
      "depth": 10,
      "particle_index": 23,
      "current_grade": 22,
      "partner_rank": 32,
      "q": 0.03030303,
      "theta_squared_coefficient_over_smaller_mass": -0.303030303,
      "finite_angle_coefficient": -0.303027309,
      "relative_error": 9.882e-06
    }
  ],
  "sources": {
    "experiments/polarization-alignment-check.py": "155dd8f2db5395c96ec0803ea95417b29a96102d34ffedec08ceb0f1ee0b5740"
  },
  "scope": "Prepared same-depth distinct-grade cores. The depth-three index-one state has M=0 and zero mass-current pair term. No cross-depth neutrino coupling, scattering rate, or full stability."
}