{
  "format": "mbs-marker-sign-audit-v1",
  "source_capture": "capture.npz",
  "source_capture_role": "audited production trajectory retained in the source study archive",
  "source_capture_publicly_distributed": false,
  "source_capture_sha256": "c40e0416131f8a56302eb00758d9da3c934194daa85c86c44d90b58619ce0a8d",
  "source_parameters": "/studies/passive-axisymmetric-cylinder/capture.parameters.json",
  "source_parameters_sha256": "16708efba81a3566cba5a7678494a8d6608b98e694639d4f4f0a83b0c899951d",
  "analysis_window_s": [
    120.0,
    200.0
  ],
  "duration_s": 80.0,
  "coordinate_conventions": {
    "quaternion": "scalar-first active body-to-world",
    "rotation_matrix": "v_lab = R v_body",
    "angular_velocity": "omega_lab = R omega_body",
    "drive_field": "B=(cos(gamma) sin(Omega t), -cos(gamma) cos(Omega t), sin(gamma)); positive about lab +z",
    "zxz": "R=Rz(phi) Rx(theta) Rz(psi)",
    "magnetic_axis_azimuth": "atan2(m_y,m_x)=phi-pi/2, so its rate is phi_dot away from a pole"
  },
  "inertia": {
    "principal_moments_kg_m2": [
      9.999999999999997e-08,
      1.0000000000000004e-07,
      1.4811621398856305e-07
    ],
    "physical_cylinder_axis_in_magnetic_body_frame": [
      0.0672040188636503,
      0.0677571546691779,
      0.9954358783164846
    ],
    "manufacturing_misalignment_deg": 5.476228447888731,
    "display_body_plus_x_local_direction": [
      -0.9952557075153424,
      -0.06579819490014263,
      0.07167059512811305
    ]
  },
  "mean_signed_rates_rad_s": {
    "drive_field_about_lab_z": 376.99111843077515,
    "cylinder_axis_lab_azimuth_net": 98.9831128647432,
    "angular_velocity_lab_z_mean": 32.02573869135203,
    "display_body_plus_x_lab_azimuth_net": 6.338926079443363,
    "magnetic_body_z_lab_azimuth_net": 6.308946297383788,
    "physical_cylinder_axis_spin_mean": -6.783716360328233,
    "magnetic_body_z_component_omega3_mean": -15.747869872247048
  },
  "mean_signed_rates_rev_s": {
    "drive_field_about_lab_z": 59.99999999999999,
    "cylinder_axis_lab_azimuth_net": 15.753651695046859,
    "angular_velocity_lab_z_mean": 5.097054618898044,
    "display_body_plus_x_lab_azimuth_net": 1.0088714194375397,
    "magnetic_body_z_lab_azimuth_net": 1.0040999889299407,
    "physical_cylinder_axis_spin_mean": -1.0796619912795993,
    "magnetic_body_z_component_omega3_mean": -2.506351333336052
  },
  "projected_azimuths": {
    "display_body_plus_x": {
      "minimum_xy_projection_norm": 0.5172845817581074,
      "net_winding_turns": 80.70971355500316,
      "net_rate_rad_s": 6.338926079443363,
      "net_rate_rev_s": 1.0088714194375397,
      "least_squares_rate_rad_s": 6.342226947137026,
      "least_squares_rate_rev_s": 1.0093967688474785,
      "mean_instantaneous_rate_rad_s": 6.338929302293979,
      "median_instantaneous_rate_rad_s": 11.863827819535981,
      "fraction_instantaneously_positive": 0.6379318103409483,
      "fraction_instantaneously_negative": 0.3620681896590517
    },
    "magnetic_body_z": {
      "minimum_xy_projection_norm": 0.0260025789849722,
      "net_winding_turns": 80.32799911439525,
      "net_rate_rad_s": 6.308946297383788,
      "net_rate_rev_s": 1.0040999889299407,
      "least_squares_rate_rad_s": 6.342194214513126,
      "least_squares_rate_rev_s": 1.0093915592885845,
      "mean_instantaneous_rate_rad_s": 6.30894612077582,
      "median_instantaneous_rate_rad_s": 55.98272787363903,
      "fraction_instantaneously_positive": 0.6709816450917745,
      "fraction_instantaneously_negative": 0.32901835490822545
    },
    "physical_cylinder_axis": {
      "minimum_xy_projection_norm": 0.012325638295350752,
      "net_winding_turns": 1260.2921356037486,
      "net_rate_rad_s": 98.9831128647432,
      "net_rate_rev_s": 15.753651695046859,
      "least_squares_rate_rad_s": 99.00444627240334,
      "least_squares_rate_rev_s": 15.757047012328965,
      "mean_instantaneous_rate_rad_s": 98.9831233976436,
      "median_instantaneous_rate_rad_s": 90.36160099717391,
      "fraction_instantaneously_positive": 0.7737361313193434,
      "fraction_instantaneously_negative": 0.2262638686806566
    }
  },
  "late_window_ranges_rev_s": {
    "magnetic_body_z_component_omega3": [
      -2.9408741339302513,
      -2.044178750474439
    ],
    "physical_cylinder_axis_spin": [
      -1.9923080421621304,
      -0.1939992759244823
    ]
  },
  "zxz_decomposition_rev_s": {
    "mean_omega3": -2.506351333336052,
    "mean_psi_dot": -14.745343082142247,
    "mean_cos_theta_times_phi_dot": 12.238991748806194,
    "mean_phi_dot_magnetic_axis_azimuth": 1.0040999608200305,
    "mean_omega_lab_z": 5.097054618898044,
    "mean_cos_theta_times_psi_dot": 4.092954658077801
  },
  "identity_residuals": {
    "max_abs_omega3_minus_psi_dot_plus_cos_theta_phi_dot_rad_s": 2.2737367544323206e-13,
    "max_abs_omega_lab_z_minus_phi_dot_plus_cos_theta_psi_dot_rad_s": 5.845834039064357e-09
  },
  "physical_axis_torque_balance": {
    "equation": "I_parallel s_dot = a dot tau_B - c s",
    "damping_coefficient_N_m_s": 9.849411219693549e-09,
    "mean_a_dot_tau_B_N_m": -6.751705783941185e-08,
    "c_times_mean_s_N_m": -6.681561203063558e-08,
    "mean_dynamic_residual_N_m": -7.0144580877633e-10
  },
  "interpretation": [
    "Both omega_body,3 and physical cylinder-axis spin remain negative throughout the late window.",
    "The magnetic body-z vector and visible body+x surface marker nevertheless accumulate positive lab-z winding, the same sign as the field, while frequently backtracking instantaneously.",
    "A body component is an instantaneous projection of the angular-velocity vector, not the azimuth rate of a drawn marker.",
    "The moving-basis effect is not omitted: the quaternion kinematics and the omega cross I omega term include it; only the reported vector components are instantaneous coordinate projections."
  ],
  "reduced_misalignment_side_note": {
    "source": "/studies/passive-axisymmetric-cylinder/hamdi-reduced-tilt.parameters.json",
    "source_sha256": "4c7f083f6fb925238a44f34888c2d01ea32b60338f0b5a7801b0db9210a8dd1e",
    "principal_moments_kg_m2": [
      9.999999999892008e-08,
      9.99999999989201e-08,
      1.4811621398231806e-07
    ],
    "manufacturing_misalignment_deg": 2.1211991681897233,
    "relative_to_original": 0.3873467274740002,
    "reduction_percent": 61.26532725259999,
    "initial_theta_rad": 0.7912605162352084,
    "initial_theta_deg": 45.3358880756202,
    "user_reported_theta_floor_rad": 0.75,
    "verification_status": "Parameter geometry verified; reported theta floor not independently simulated in this audit."
  }
}