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"minimum_tangent_cosine": 0.9999999572082487, "maximum_tangent_angle_degrees": 0.016761684506345995, "maximum_scaled_magnitude_error": 8.154653976702458e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 11, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999572082487, "maximum_tangent_angle_degrees": 0.016761684506345995, "maximum_scaled_magnitude_error": 8.154653976702458e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 12, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999741488936, "maximum_tangent_angle_degrees": 0.013027983458765645, "maximum_scaled_magnitude_error": 1.0375451660030336e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 13, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999741488936, "maximum_tangent_angle_degrees": 0.013027983458765645, "maximum_scaled_magnitude_error": 1.0375451660030336e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 14, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999741488936, "maximum_tangent_angle_degrees": 0.013027983458765645, "maximum_scaled_magnitude_error": 1.0375451660030336e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 15, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999741488936, "maximum_tangent_angle_degrees": 0.013027983458765645, "maximum_scaled_magnitude_error": 1.0375451660030336e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 16, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999977497902, "maximum_tangent_angle_degrees": 0.003843696921151209, "maximum_scaled_magnitude_error": 7.421784469885647e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.07943444768462381, "actual_oriented_radial_cosine": 0.9975484657006878, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 17, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999977497902, "maximum_tangent_angle_degrees": 0.003843696921151209, "maximum_scaled_magnitude_error": 7.421784469885647e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.07943444768462381, "actual_oriented_radial_cosine": 0.9975484657006878, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 18, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999977497902, "maximum_tangent_angle_degrees": 0.003843696921151209, "maximum_scaled_magnitude_error": 7.421784469885647e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.07943444768462381, "actual_oriented_radial_cosine": 0.9975484657006878, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 19, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999977497902, "maximum_tangent_angle_degrees": 0.003843696921151209, "maximum_scaled_magnitude_error": 7.421784469885647e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.07943444768462381, "actual_oriented_radial_cosine": 0.9975484657006878, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 20, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999988867545, "maximum_tangent_angle_degrees": 0.0027035418929141483, "maximum_scaled_magnitude_error": 8.335885265680323e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 14.81587019650908, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.10105166026030007, "actual_oriented_radial_cosine": 0.996763286332319, "global_oriented_radial_lower_bound": 0.0011389002276691999, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 21, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999988867545, "maximum_tangent_angle_degrees": 0.0027035418929141483, "maximum_scaled_magnitude_error": 8.335885265680323e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 14.81587019650908, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.10105166026030007, "actual_oriented_radial_cosine": 0.996763286332319, "global_oriented_radial_lower_bound": 0.0011389002276691999, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 22, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999988867545, "maximum_tangent_angle_degrees": 0.0027035418929141483, "maximum_scaled_magnitude_error": 8.335885265680323e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 14.81587019650908, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.10105166026030007, "actual_oriented_radial_cosine": 0.996763286332319, "global_oriented_radial_lower_bound": 0.0011389002276691999, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 23, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999988867545, "maximum_tangent_angle_degrees": 0.0027035418929141483, "maximum_scaled_magnitude_error": 8.335885265680323e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 14.81587019650908, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.10105166026030007, "actual_oriented_radial_cosine": 0.996763286332319, "global_oriented_radial_lower_bound": 0.0011389002276691999, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 24, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999996754528, "maximum_tangent_angle_degrees": 0.004616114405764495, "maximum_scaled_magnitude_error": 9.992007221626409e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.09150010191788682, "actual_oriented_radial_cosine": 0.9993522360372664, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 25, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999996754528, "maximum_tangent_angle_degrees": 0.004616114405764495, "maximum_scaled_magnitude_error": 9.992007221626409e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.09150010191788682, "actual_oriented_radial_cosine": 0.9993522360372664, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 26, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999996754528, "maximum_tangent_angle_degrees": 0.004616114405764495, "maximum_scaled_magnitude_error": 9.992007221626409e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.09150010191788682, "actual_oriented_radial_cosine": 0.9993522360372664, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 27, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999996754528, "maximum_tangent_angle_degrees": 0.004616114405764495, "maximum_scaled_magnitude_error": 9.992007221626409e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": 1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.09150010191788682, "actual_oriented_radial_cosine": 0.9993522360372664, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 28, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999744372614, "maximum_tangent_angle_degrees": 0.012955116435822311, "maximum_scaled_magnitude_error": 6.313325581036813e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 29, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999744372614, "maximum_tangent_angle_degrees": 0.012955116435822311, "maximum_scaled_magnitude_error": 6.313325581036813e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 30, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999744372614, "maximum_tangent_angle_degrees": 0.012955116435822311, "maximum_scaled_magnitude_error": 6.313325581036813e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 31, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999744372614, "maximum_tangent_angle_degrees": 0.012955116435822311, "maximum_scaled_magnitude_error": 6.313325581036813e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 32, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999673433593, "maximum_tangent_angle_degrees": 0.014642774882198476, "maximum_scaled_magnitude_error": 8.514148967522343e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 33, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999673433593, "maximum_tangent_angle_degrees": 0.014642774882198476, "maximum_scaled_magnitude_error": 8.514148967522343e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 34, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999673433593, "maximum_tangent_angle_degrees": 0.014642774882198476, "maximum_scaled_magnitude_error": 8.514148967522343e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 35, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999673433593, "maximum_tangent_angle_degrees": 0.014642774882198476, "maximum_scaled_magnitude_error": 8.514148967522343e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true } ], "line_density_interpretation": "Counts are proportional to both source/sink charge magnitudes; arbitrary displayed source directions do not calibrate local flux-tube cross-sectional area." }, "actual_source_symmetries": { "passed": true, "errors": [], "actual_group_order": 4, "transformations": [ { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 3, 2, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 3, 2, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 } ] }, "gauss_multipoles_kernel_checks": { "passed": true, "cpu_independent_reference_maximum_scaled_error": 8.15843973306311e-16, "gpu": { "requested": true, "passed": true, "maximum_scaled_error": 8.15843973306311e-16 }, "individual_source_gauss_fluxes": [ { "source_index": 0, "charge": 2.0, "expected": 25.132741228718345, "measured": 25.13274122871834, "absolute_error": 3.552713678800501e-15 }, { "source_index": 1, "charge": -1.0, "expected": -12.566370614359172, "measured": -12.56637061435917, "absolute_error": 1.7763568394002505e-15 }, { "source_index": 2, "charge": 1.0, "expected": 12.566370614359172, "measured": 12.56637061435917, "absolute_error": 1.7763568394002505e-15 }, { "source_index": 3, "charge": -1.0, "expected": -12.566370614359172, "measured": -12.56637061435917, "absolute_error": 1.7763568394002505e-15 } ], "enclosing_gauss_flux": { "measured": 12.566370614359169, "expected": 12.566370614359172, "absolute_error": 3.552713678800501e-15 }, "far_field": { "leading_order": "monopole", "net_charge": 1.0, "dipole_moment": [ 1.0, 0.0, 0.0 ], "quadrupole_tensor": [ [ 8.0, 0.0, 0.0 ], [ 0.0, -7.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "radii": [ 80.0, 160.0, 320.0 ], "potential_relative_errors": [ 0.004522270476770701, 0.0022873968563251468, 0.0011502254974643522 ], "field_relative_errors": [ 0.015123169467177082, 0.007491078643254215, 0.0037285885966081797 ], "measured_last_doubling_slopes": [ -1.001637776627486, -2.003260869973149 ], "expected_slopes": [ -1, -2 ] } }, "representative_refinement": { "passed": true, "selected_curve_index": 16, "integration_orientation": 1.0, "reference_rtol": 1e-11, "reference_atol": 1e-13, "reference_max_step": 0.015, "common_arclength_samples": 500, "maximum_baseline_vs_strict_position_difference": 2.401615251554697e-10, "maximum_actual_serialized_samples_vs_strict_difference": 2.4032474424812477e-10, "endpoint_assignments_agree": true }, "candidate_orbits_omitted_for_complexity": [] }, "p1x4": { "passed": true, "charges": [ 4, -1, 1, -1 ], "positions": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ -1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ] ], "actual_serialized_viewer": { "passed": true, "separate_line_traces": 60, "arrow_count": 60, "arrow_points_on_correct_curves": true, "minimum_arrow_independent_field_cosine": 1.0, "verified_actual_charge_markers": 4, "html_filename": "electric_field_3d_p1x4.html", "html_sha256": "ad8cd5b3617140fbe1a86f1b654a3e3f83ad91c67d0a8ed2374e5b973b754ab0" }, "physical_curves": { "passed": true, "errors": [], "curve_count": 60, "actual_charge_endpoint_counts": [ 48, 12, 12, 12 ], "expected_charge_endpoint_counts": [ 48, 12, 12, 12 ], "actual_infinity_curve_count": 36, "expected_infinity_curve_count": 36, "source_to_sink_counts": { "0 -> 1": 10, "0 -> 3": 10, "0 -> infinity": 28, "2 -> 1": 2, "2 -> 3": 2, "2 -> infinity": 8 }, "worst_tangent_angle_degrees": 0.03611038619539964, "curves": [ { "curve_index": 0, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998715330193, "maximum_tangent_angle_degrees": 0.02904245957573933, "maximum_scaled_magnitude_error": 6.138572218739309e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": null, "passed": true }, { "curve_index": 1, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998715330193, "maximum_tangent_angle_degrees": 0.02904245957573933, "maximum_scaled_magnitude_error": 6.138572218739309e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": null, 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{ "curve_index": 7, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.999999854604122, "maximum_tangent_angle_degrees": 0.03089681288234919, "maximum_scaled_magnitude_error": 8.118385836392981e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 8, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998438489613, "maximum_tangent_angle_degrees": 0.032019170338979594, "maximum_scaled_magnitude_error": 8.127442025013903e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 9, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998438489613, "maximum_tangent_angle_degrees": 0.032019170338979594, "maximum_scaled_magnitude_error": 8.127442025013903e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 10, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998438489613, "maximum_tangent_angle_degrees": 0.032019170338979594, "maximum_scaled_magnitude_error": 8.127442025013903e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 11, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998438489613, "maximum_tangent_angle_degrees": 0.032019170338979594, "maximum_scaled_magnitude_error": 8.127442025013903e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 12, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998549817093, "maximum_tangent_angle_degrees": 0.030856667905479255, "maximum_scaled_magnitude_error": 7.625455221339753e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": null, "passed": true }, { "curve_index": 13, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998549817093, "maximum_tangent_angle_degrees": 0.030856667905479255, "maximum_scaled_magnitude_error": 7.625455221339753e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": null, "passed": true }, { "curve_index": 14, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998549817093, "maximum_tangent_angle_degrees": 0.030856667905479255, "maximum_scaled_magnitude_error": 7.625455221339753e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": null, "passed": true }, { "curve_index": 15, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998549817093, "maximum_tangent_angle_degrees": 0.030856667905479255, "maximum_scaled_magnitude_error": 7.625455221339753e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": null, "passed": true }, { "curve_index": 16, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998013955426, "maximum_tangent_angle_degrees": 0.03611038619539964, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": null, "passed": true }, { "curve_index": 17, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998013955426, "maximum_tangent_angle_degrees": 0.03611038619539964, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": null, "passed": true }, { "curve_index": 18, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998013955426, "maximum_tangent_angle_degrees": 0.03611038619539964, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": null, "passed": true }, { "curve_index": 19, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998013955426, "maximum_tangent_angle_degrees": 0.03611038619539964, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": null, "passed": true }, { "curve_index": 20, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999975971892, "maximum_tangent_angle_degrees": 0.003971891912908968, "maximum_scaled_magnitude_error": 7.077561329304058e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14493169777054035, "actual_oriented_radial_cosine": 0.9920056998078091, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 21, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999975971892, "maximum_tangent_angle_degrees": 0.003971891912908968, "maximum_scaled_magnitude_error": 7.077561329304058e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14493169777054035, "actual_oriented_radial_cosine": 0.9920056998078091, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 22, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999975971892, "maximum_tangent_angle_degrees": 0.003971891912908968, "maximum_scaled_magnitude_error": 7.077561329304058e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14493169777054035, "actual_oriented_radial_cosine": 0.9920056998078091, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 23, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999975971892, "maximum_tangent_angle_degrees": 0.003971891912908968, "maximum_scaled_magnitude_error": 7.077561329304058e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14493169777054035, "actual_oriented_radial_cosine": 0.9920056998078091, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 24, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999989548181, "maximum_tangent_angle_degrees": 0.0026195915381654737, "maximum_scaled_magnitude_error": 8.411039969784791e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14245965555160126, "actual_oriented_radial_cosine": 0.9898011997513273, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 25, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999989548181, "maximum_tangent_angle_degrees": 0.0026195915381654737, "maximum_scaled_magnitude_error": 8.411039969784791e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14245965555160126, "actual_oriented_radial_cosine": 0.9898011997513273, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 26, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999989548181, "maximum_tangent_angle_degrees": 0.0026195915381654737, "maximum_scaled_magnitude_error": 8.411039969784791e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14245965555160126, "actual_oriented_radial_cosine": 0.9898011997513273, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 27, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999989548181, "maximum_tangent_angle_degrees": 0.0026195915381654737, "maximum_scaled_magnitude_error": 8.411039969784791e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14245965555160126, "actual_oriented_radial_cosine": 0.9898011997513273, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 28, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999993009824, "maximum_tangent_angle_degrees": 0.002142306928106704, "maximum_scaled_magnitude_error": 8.46639838662026e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.154203897000473, "actual_oriented_radial_cosine": 0.9892597829932159, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 29, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999993009824, "maximum_tangent_angle_degrees": 0.002142306928106704, "maximum_scaled_magnitude_error": 8.46639838662026e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.154203897000473, "actual_oriented_radial_cosine": 0.9892597829932159, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 30, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999993009824, "maximum_tangent_angle_degrees": 0.002142306928106704, "maximum_scaled_magnitude_error": 8.46639838662026e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.154203897000473, "actual_oriented_radial_cosine": 0.9892597829932159, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 31, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999993009824, "maximum_tangent_angle_degrees": 0.002142306928106704, "maximum_scaled_magnitude_error": 8.46639838662026e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.154203897000473, "actual_oriented_radial_cosine": 0.9892597829932159, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 32, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999995530041, "maximum_tangent_angle_degrees": 0.0017131263403488226, "maximum_scaled_magnitude_error": 9.105141613494147e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.19173555834585393, "actual_oriented_radial_cosine": 0.9899116797527524, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 33, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999995530041, "maximum_tangent_angle_degrees": 0.0017131263403488226, "maximum_scaled_magnitude_error": 9.105141613494147e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.19173555834585393, "actual_oriented_radial_cosine": 0.9899116797527524, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 34, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999995530041, "maximum_tangent_angle_degrees": 0.0017131263403488226, "maximum_scaled_magnitude_error": 9.105141613494147e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.19173555834585393, "actual_oriented_radial_cosine": 0.9899116797527524, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 35, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999995530041, "maximum_tangent_angle_degrees": 0.0017131263403488226, "maximum_scaled_magnitude_error": 9.105141613494147e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.19173555834585393, "actual_oriented_radial_cosine": 0.9899116797527524, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 36, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996528387, "maximum_tangent_angle_degrees": 0.0015097438982979465, "maximum_scaled_magnitude_error": 9.61675431498654e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.22726697696083697, "actual_oriented_radial_cosine": 0.9913011399588019, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 37, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996528387, "maximum_tangent_angle_degrees": 0.0015097438982979465, "maximum_scaled_magnitude_error": 9.61675431498654e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.22726697696083697, "actual_oriented_radial_cosine": 0.9913011399588019, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 38, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996528387, "maximum_tangent_angle_degrees": 0.0015097438982979465, "maximum_scaled_magnitude_error": 9.61675431498654e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.22726697696083697, "actual_oriented_radial_cosine": 0.9913011399588019, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 39, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996528387, "maximum_tangent_angle_degrees": 0.0015097438982979465, "maximum_scaled_magnitude_error": 9.61675431498654e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.22726697696083697, "actual_oriented_radial_cosine": 0.9913011399588019, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 40, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996988369, "maximum_tangent_angle_degrees": 0.001406172193538893, "maximum_scaled_magnitude_error": 6.774432708100706e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 7.687439319873572, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2474361092153845, "actual_oriented_radial_cosine": 0.9922664147325053, "global_oriented_radial_lower_bound": 0.012691058965047476, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 41, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996988369, "maximum_tangent_angle_degrees": 0.001406172193538893, "maximum_scaled_magnitude_error": 6.774432708100706e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 7.687439319873572, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2474361092153845, "actual_oriented_radial_cosine": 0.9922664147325053, "global_oriented_radial_lower_bound": 0.012691058965047476, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 42, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996988369, "maximum_tangent_angle_degrees": 0.001406172193538893, "maximum_scaled_magnitude_error": 6.774432708100706e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 7.687439319873572, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2474361092153845, "actual_oriented_radial_cosine": 0.9922664147325053, "global_oriented_radial_lower_bound": 0.012691058965047476, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 43, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996988369, "maximum_tangent_angle_degrees": 0.001406172193538893, "maximum_scaled_magnitude_error": 6.774432708100706e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 7.687439319873572, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2474361092153845, "actual_oriented_radial_cosine": 0.9922664147325053, "global_oriented_radial_lower_bound": 0.012691058965047476, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 44, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999801056, "maximum_tangent_angle_degrees": 0.0011428862900009628, "maximum_scaled_magnitude_error": 8.87491519887831e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2916290063549297, "actual_oriented_radial_cosine": 0.9947013592208468, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 45, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999801056, "maximum_tangent_angle_degrees": 0.0011428862900009628, "maximum_scaled_magnitude_error": 8.87491519887831e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2916290063549297, "actual_oriented_radial_cosine": 0.9947013592208468, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 46, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999801056, "maximum_tangent_angle_degrees": 0.0011428862900009628, "maximum_scaled_magnitude_error": 8.87491519887831e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2916290063549297, "actual_oriented_radial_cosine": 0.9947013592208468, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 47, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999801056, "maximum_tangent_angle_degrees": 0.0011428862900009628, "maximum_scaled_magnitude_error": 8.87491519887831e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2916290063549297, "actual_oriented_radial_cosine": 0.9947013592208468, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 48, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999997848371, "maximum_tangent_angle_degrees": 0.0037585585803450155, "maximum_scaled_magnitude_error": 6.446205416490434e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": { "passed": true, "radius": 7.687439319873575, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16851101783431047, "actual_oriented_radial_cosine": 0.9994908481177288, "global_oriented_radial_lower_bound": 0.012691058965047465, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 49, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999997848371, "maximum_tangent_angle_degrees": 0.0037585585803450155, "maximum_scaled_magnitude_error": 6.446205416490434e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": { "passed": true, "radius": 7.687439319873575, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16851101783431047, "actual_oriented_radial_cosine": 0.9994908481177288, "global_oriented_radial_lower_bound": 0.012691058965047465, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 50, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999997848371, "maximum_tangent_angle_degrees": 0.0037585585803450155, "maximum_scaled_magnitude_error": 6.446205416490434e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": { "passed": true, "radius": 7.687439319873575, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16851101783431047, "actual_oriented_radial_cosine": 0.9994908481177288, "global_oriented_radial_lower_bound": 0.012691058965047465, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 51, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999997848371, "maximum_tangent_angle_degrees": 0.0037585585803450155, "maximum_scaled_magnitude_error": 6.446205416490434e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": { "passed": true, "radius": 7.687439319873575, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16851101783431047, "actual_oriented_radial_cosine": 0.9994908481177288, "global_oriented_radial_lower_bound": 0.012691058965047465, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 52, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999955692632, "maximum_tangent_angle_degrees": 0.005393561131396758, "maximum_scaled_magnitude_error": 9.01380933083514e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16902065464387697, "actual_oriented_radial_cosine": 0.9978080106935753, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 53, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999955692632, "maximum_tangent_angle_degrees": 0.005393561131396758, "maximum_scaled_magnitude_error": 9.01380933083514e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16902065464387697, "actual_oriented_radial_cosine": 0.9978080106935753, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 54, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999955692632, "maximum_tangent_angle_degrees": 0.005393561131396758, "maximum_scaled_magnitude_error": 9.01380933083514e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16902065464387697, "actual_oriented_radial_cosine": 0.9978080106935753, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 55, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999955692632, "maximum_tangent_angle_degrees": 0.005393561131396758, "maximum_scaled_magnitude_error": 9.01380933083514e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": 3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16902065464387697, "actual_oriented_radial_cosine": 0.9978080106935753, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 56, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998879064281, "maximum_tangent_angle_degrees": 0.027128637872251622, "maximum_scaled_magnitude_error": 6.395910550517978e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 57, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998879064281, "maximum_tangent_angle_degrees": 0.027128637872251622, "maximum_scaled_magnitude_error": 6.395910550517978e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 58, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998879064281, "maximum_tangent_angle_degrees": 0.027128637872251622, "maximum_scaled_magnitude_error": 6.395910550517978e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 59, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998879064281, "maximum_tangent_angle_degrees": 0.027128637872251622, "maximum_scaled_magnitude_error": 6.395910550517978e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true } ], "line_density_interpretation": "Counts are proportional to both source/sink charge magnitudes; arbitrary displayed source directions do not calibrate local flux-tube cross-sectional area." }, "actual_source_symmetries": { "passed": true, "errors": [], "actual_group_order": 4, "transformations": [ { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 3, 2, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 3, 2, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 } ] }, "gauss_multipoles_kernel_checks": { "passed": true, "cpu_independent_reference_maximum_scaled_error": 9.634823471110655e-16, "gpu": { "requested": true, "passed": true, "maximum_scaled_error": 9.634823471110655e-16 }, "individual_source_gauss_fluxes": [ { "source_index": 0, "charge": 4.0, "expected": 50.26548245743669, "measured": 50.26548245743668, "absolute_error": 7.105427357601002e-15 }, { "source_index": 1, "charge": -1.0, "expected": -12.566370614359172, "measured": -12.56637061435917, "absolute_error": 1.7763568394002505e-15 }, { "source_index": 2, "charge": 1.0, "expected": 12.566370614359172, "measured": 12.56637061435917, "absolute_error": 1.7763568394002505e-15 }, { "source_index": 3, "charge": -1.0, "expected": -12.566370614359172, "measured": -12.566370614359172, "absolute_error": 0.0 } ], "enclosing_gauss_flux": { "measured": 37.69911184307751, "expected": 37.69911184307752, "absolute_error": 7.105427357601002e-15 }, "far_field": { "leading_order": "monopole", "net_charge": 3.0, "dipole_moment": [ 3.0, 0.0, 0.0 ], "quadrupole_tensor": [ [ 12.0, 0.0, 0.0 ], [ 0.0, -9.0, 0.0 ], [ 0.0, 0.0, -3.0 ] ], "radii": [ 80.0, 160.0, 320.0 ], "potential_relative_errors": [ 0.004560794152870437, 0.0022970292892219675, 0.001152633700309084 ], "field_relative_errors": [ 0.014963496936962755, 0.00745276106711011, 0.003719212562624949 ], "measured_last_doubling_slopes": [ -1.0016481712029066, -2.0032914450548702 ], "expected_slopes": [ -1, -2 ] } }, "representative_refinement": { "passed": true, "selected_curve_index": 20, "integration_orientation": 1.0, "reference_rtol": 1e-11, "reference_atol": 1e-13, "reference_max_step": 0.015, "common_arclength_samples": 500, "maximum_baseline_vs_strict_position_difference": 1.0732747024878172e-10, "maximum_actual_serialized_samples_vs_strict_difference": 1.0732747024878172e-10, "endpoint_assignments_agree": true }, "candidate_orbits_omitted_for_complexity": [] }, "n1x2": { "passed": true, "charges": [ 1, -2, 1, -1 ], "positions": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ -1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ] ], "actual_serialized_viewer": { "passed": true, "separate_line_traces": 36, "arrow_count": 36, "arrow_points_on_correct_curves": true, "minimum_arrow_independent_field_cosine": 0.9999999999999999, "verified_actual_charge_markers": 4, "html_filename": "electric_field_3d_n1x2.html", "html_sha256": "20427aec84869db4dac9c9686a9caaa2d181a59f78624504606b129d29bbb373" }, "physical_curves": { "passed": true, "errors": [], "curve_count": 36, "actual_charge_endpoint_counts": [ 12, 24, 12, 12 ], "expected_charge_endpoint_counts": [ 12, 24, 12, 12 ], "actual_infinity_curve_count": 12, "expected_infinity_curve_count": 12, "source_to_sink_counts": { "0 -> 1": 8, "0 -> 3": 4, "2 -> 1": 8, "2 -> 3": 4, "infinity -> 1": 8, "infinity -> 3": 4 }, "worst_tangent_angle_degrees": 0.016761684506345995, "curves": [ { "curve_index": 0, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999792514073, "maximum_tangent_angle_degrees": 0.011671641890724687, "maximum_scaled_magnitude_error": 9.473025714589406e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999964, "infinity_certificate": null, "passed": true }, { "curve_index": 1, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999792514073, "maximum_tangent_angle_degrees": 0.011671641890724687, "maximum_scaled_magnitude_error": 9.473025714589406e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999964, "infinity_certificate": null, "passed": true }, { "curve_index": 2, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999792514073, "maximum_tangent_angle_degrees": 0.011671641890724687, "maximum_scaled_magnitude_error": 9.473025714589406e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999964, "infinity_certificate": null, "passed": true }, { "curve_index": 3, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999792514073, "maximum_tangent_angle_degrees": 0.011671641890724687, "maximum_scaled_magnitude_error": 9.473025714589406e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999964, "infinity_certificate": null, "passed": true }, { "curve_index": 4, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999654683888, "maximum_tangent_angle_degrees": 0.015057263582588814, "maximum_scaled_magnitude_error": 8.184600545791209e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 5, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999654683888, "maximum_tangent_angle_degrees": 0.015057263582588814, "maximum_scaled_magnitude_error": 8.184600545791209e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 6, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999654683888, "maximum_tangent_angle_degrees": 0.015057263582588814, "maximum_scaled_magnitude_error": 8.184600545791209e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 7, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999654683888, "maximum_tangent_angle_degrees": 0.015057263582588814, "maximum_scaled_magnitude_error": 8.184600545791209e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 8, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999572082487, "maximum_tangent_angle_degrees": 0.016761684506345995, "maximum_scaled_magnitude_error": 8.154653976702458e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000103, "infinity_certificate": null, "passed": true }, { "curve_index": 9, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999572082487, "maximum_tangent_angle_degrees": 0.016761684506345995, "maximum_scaled_magnitude_error": 8.154653976702458e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000103, "infinity_certificate": null, "passed": true }, { "curve_index": 10, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999572082487, "maximum_tangent_angle_degrees": 0.016761684506345995, "maximum_scaled_magnitude_error": 8.154653976702458e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000103, "infinity_certificate": null, "passed": true }, { "curve_index": 11, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999572082487, "maximum_tangent_angle_degrees": 0.016761684506345995, "maximum_scaled_magnitude_error": 8.154653976702458e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000103, "infinity_certificate": null, "passed": true }, { "curve_index": 12, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999741488936, "maximum_tangent_angle_degrees": 0.013027983458765645, "maximum_scaled_magnitude_error": 1.0375451660030336e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000117, "infinity_certificate": null, "passed": true }, { "curve_index": 13, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999741488936, "maximum_tangent_angle_degrees": 0.013027983458765645, "maximum_scaled_magnitude_error": 1.0375451660030336e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000117, "infinity_certificate": null, "passed": true }, { "curve_index": 14, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999741488936, "maximum_tangent_angle_degrees": 0.013027983458765645, "maximum_scaled_magnitude_error": 1.0375451660030336e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000117, "infinity_certificate": null, "passed": true }, { "curve_index": 15, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999741488936, "maximum_tangent_angle_degrees": 0.013027983458765645, "maximum_scaled_magnitude_error": 1.0375451660030336e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000117, "infinity_certificate": null, "passed": true }, { "curve_index": 16, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999977497902, "maximum_tangent_angle_degrees": 0.003843696921151209, "maximum_scaled_magnitude_error": 7.421784469885647e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4103152375297012, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.07943444768462381, "actual_oriented_radial_cosine": 0.9975484657006878, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 17, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999977497902, "maximum_tangent_angle_degrees": 0.003843696921151209, "maximum_scaled_magnitude_error": 7.421784469885647e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4103152375297012, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.07943444768462381, "actual_oriented_radial_cosine": 0.9975484657006878, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 18, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999977497902, "maximum_tangent_angle_degrees": 0.003843696921151209, "maximum_scaled_magnitude_error": 7.421784469885647e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4103152375297012, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.07943444768462381, "actual_oriented_radial_cosine": 0.9975484657006878, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 19, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999977497902, "maximum_tangent_angle_degrees": 0.003843696921151209, "maximum_scaled_magnitude_error": 7.421784469885647e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4103152375297012, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.07943444768462381, "actual_oriented_radial_cosine": 0.9975484657006878, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 20, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999988867545, "maximum_tangent_angle_degrees": 0.0027035418929141483, "maximum_scaled_magnitude_error": 8.335885265680323e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4198012335262922, "infinity_certificate": { "passed": true, "radius": 14.81587019650908, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.10105166026030007, "actual_oriented_radial_cosine": 0.996763286332319, "global_oriented_radial_lower_bound": 0.0011389002276691999, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 21, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999988867545, "maximum_tangent_angle_degrees": 0.0027035418929141483, "maximum_scaled_magnitude_error": 8.335885265680323e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4198012335262922, "infinity_certificate": { "passed": true, "radius": 14.81587019650908, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.10105166026030007, "actual_oriented_radial_cosine": 0.996763286332319, "global_oriented_radial_lower_bound": 0.0011389002276691999, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 22, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999988867545, "maximum_tangent_angle_degrees": 0.0027035418929141483, "maximum_scaled_magnitude_error": 8.335885265680323e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4198012335262922, "infinity_certificate": { "passed": true, "radius": 14.81587019650908, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.10105166026030007, "actual_oriented_radial_cosine": 0.996763286332319, "global_oriented_radial_lower_bound": 0.0011389002276691999, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 23, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999988867545, "maximum_tangent_angle_degrees": 0.0027035418929141483, "maximum_scaled_magnitude_error": 8.335885265680323e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4198012335262922, "infinity_certificate": { "passed": true, "radius": 14.81587019650908, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.10105166026030007, "actual_oriented_radial_cosine": 0.996763286332319, "global_oriented_radial_lower_bound": 0.0011389002276691999, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 24, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.999999996754528, "maximum_tangent_angle_degrees": 0.004616114405764495, "maximum_scaled_magnitude_error": 9.992007221626409e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4158726375354753, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.09150010191788682, "actual_oriented_radial_cosine": 0.9993522360372664, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 25, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.999999996754528, "maximum_tangent_angle_degrees": 0.004616114405764495, "maximum_scaled_magnitude_error": 9.992007221626409e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4158726375354753, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.09150010191788682, "actual_oriented_radial_cosine": 0.9993522360372664, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 26, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.999999996754528, "maximum_tangent_angle_degrees": 0.004616114405764495, "maximum_scaled_magnitude_error": 9.992007221626409e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4158726375354753, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.09150010191788682, "actual_oriented_radial_cosine": 0.9993522360372664, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 27, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.999999996754528, "maximum_tangent_angle_degrees": 0.004616114405764495, "maximum_scaled_magnitude_error": 9.992007221626409e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4158726375354753, "infinity_certificate": { "passed": true, "radius": 14.815870196509078, "all_sources_radius": 1.0, "net_charge": -1.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.09150010191788682, "actual_oriented_radial_cosine": 0.9993522360372664, "global_oriented_radial_lower_bound": 0.0011389002276692003, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 28, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999744372614, "maximum_tangent_angle_degrees": 0.012955116435822311, "maximum_scaled_magnitude_error": 6.313325581036813e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000018, "infinity_certificate": null, "passed": true }, { "curve_index": 29, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999744372614, "maximum_tangent_angle_degrees": 0.012955116435822311, "maximum_scaled_magnitude_error": 6.313325581036813e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000018, "infinity_certificate": null, "passed": true }, { "curve_index": 30, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999744372614, "maximum_tangent_angle_degrees": 0.012955116435822311, "maximum_scaled_magnitude_error": 6.313325581036813e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000018, "infinity_certificate": null, "passed": true }, { "curve_index": 31, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999744372614, "maximum_tangent_angle_degrees": 0.012955116435822311, "maximum_scaled_magnitude_error": 6.313325581036813e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000018, "infinity_certificate": null, "passed": true }, { "curve_index": 32, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999673433593, "maximum_tangent_angle_degrees": 0.014642774882198476, "maximum_scaled_magnitude_error": 8.514148967522343e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000013, "infinity_certificate": null, "passed": true }, { "curve_index": 33, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999673433593, "maximum_tangent_angle_degrees": 0.014642774882198476, "maximum_scaled_magnitude_error": 8.514148967522343e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000013, "infinity_certificate": null, "passed": true }, { "curve_index": 34, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999673433593, "maximum_tangent_angle_degrees": 0.014642774882198476, "maximum_scaled_magnitude_error": 8.514148967522343e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000013, "infinity_certificate": null, "passed": true }, { "curve_index": 35, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999673433593, "maximum_tangent_angle_degrees": 0.014642774882198476, "maximum_scaled_magnitude_error": 8.514148967522343e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000013, "infinity_certificate": null, "passed": true } ], "line_density_interpretation": "Counts are proportional to both source/sink charge magnitudes; arbitrary displayed source directions do not calibrate local flux-tube cross-sectional area." }, "actual_source_symmetries": { "passed": true, "errors": [], "actual_group_order": 4, 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true, "passed": true, "maximum_scaled_error": 5.533265586523273e-16 }, "individual_source_gauss_fluxes": [ { "source_index": 0, "charge": 1.0, "expected": 12.566370614359172, "measured": 12.56637061435917, "absolute_error": 1.7763568394002505e-15 }, { "source_index": 1, "charge": -2.0, "expected": -25.132741228718345, "measured": -25.132741228718345, "absolute_error": 0.0 }, { "source_index": 2, "charge": 1.0, "expected": 12.566370614359172, "measured": 12.56637061435917, "absolute_error": 1.7763568394002505e-15 }, { "source_index": 3, "charge": -1.0, "expected": -12.566370614359172, "measured": -12.56637061435917, "absolute_error": 1.7763568394002505e-15 } ], "enclosing_gauss_flux": { "measured": -12.566370614359174, "expected": -12.566370614359172, "absolute_error": 1.7763568394002505e-15 }, "far_field": { "leading_order": "monopole", "net_charge": -1.0, "dipole_moment": [ 0.0, -1.0, 0.0 ], "quadrupole_tensor": [ [ 7.0, 0.0, 0.0 ], [ 0.0, -8.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "radii": [ 80.0, 160.0, 320.0 ], "potential_relative_errors": [ 0.006336117612646963, 0.003178538545036136, 0.0015918511451326611 ], "field_relative_errors": [ 0.01614870729446004, 0.008206613250709113, 0.00413672780338513 ], "measured_last_doubling_slopes": [ -0.997705420454866, -1.9954258894455676 ], "expected_slopes": [ -1, -2 ] } }, "representative_refinement": { "passed": true, "selected_curve_index": 16, "integration_orientation": -1.0, "reference_rtol": 1e-11, "reference_atol": 1e-13, "reference_max_step": 0.015, "common_arclength_samples": 500, "maximum_baseline_vs_strict_position_difference": 2.4032474424812477e-10, "maximum_actual_serialized_samples_vs_strict_difference": 2.4032474424812477e-10, "endpoint_assignments_agree": true }, "candidate_orbits_omitted_for_complexity": [] }, "n1x4": { "passed": true, "charges": [ 1, -4, 1, -1 ], "positions": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ -1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ] ], "actual_serialized_viewer": { "passed": true, "separate_line_traces": 60, "arrow_count": 60, "arrow_points_on_correct_curves": true, "minimum_arrow_independent_field_cosine": 0.9999999999999998, "verified_actual_charge_markers": 4, "html_filename": "electric_field_3d_n1x4.html", "html_sha256": "f289b0bbd9788a3e2c94c0f4199410e72fcfa388a83e367cabcd91431f6b909d" }, "physical_curves": { "passed": true, "errors": [], "curve_count": 60, "actual_charge_endpoint_counts": [ 12, 48, 12, 12 ], "expected_charge_endpoint_counts": [ 12, 48, 12, 12 ], "actual_infinity_curve_count": 36, "expected_infinity_curve_count": 36, "source_to_sink_counts": { "0 -> 1": 10, "0 -> 3": 2, "2 -> 1": 10, "2 -> 3": 2, "infinity -> 1": 28, "infinity -> 3": 8 }, "worst_tangent_angle_degrees": 0.03611038619539964, "curves": [ { "curve_index": 0, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998715330193, "maximum_tangent_angle_degrees": 0.02904245957573933, "maximum_scaled_magnitude_error": 6.138572218739309e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000003, "infinity_certificate": null, "passed": true }, { "curve_index": 1, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998715330193, "maximum_tangent_angle_degrees": 0.02904245957573933, "maximum_scaled_magnitude_error": 6.138572218739309e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000003, "infinity_certificate": null, "passed": true }, { "curve_index": 2, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998715330193, "maximum_tangent_angle_degrees": 0.02904245957573933, "maximum_scaled_magnitude_error": 6.138572218739309e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000003, "infinity_certificate": null, "passed": true }, { "curve_index": 3, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998715330193, "maximum_tangent_angle_degrees": 0.02904245957573933, "maximum_scaled_magnitude_error": 6.138572218739309e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000003, "infinity_certificate": null, "passed": true }, { "curve_index": 4, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.999999854604122, "maximum_tangent_angle_degrees": 0.03089681288234919, "maximum_scaled_magnitude_error": 8.118385836392981e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999905, "infinity_certificate": null, "passed": true }, { "curve_index": 5, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.999999854604122, "maximum_tangent_angle_degrees": 0.03089681288234919, "maximum_scaled_magnitude_error": 8.118385836392981e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999905, "infinity_certificate": null, "passed": true }, { "curve_index": 6, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.999999854604122, "maximum_tangent_angle_degrees": 0.03089681288234919, "maximum_scaled_magnitude_error": 8.118385836392981e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999905, "infinity_certificate": null, "passed": true }, { "curve_index": 7, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.999999854604122, "maximum_tangent_angle_degrees": 0.03089681288234919, "maximum_scaled_magnitude_error": 8.118385836392981e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999905, "infinity_certificate": null, "passed": true }, { "curve_index": 8, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998438489613, "maximum_tangent_angle_degrees": 0.032019170338979594, "maximum_scaled_magnitude_error": 8.127442025013903e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": null, "passed": true }, { "curve_index": 9, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998438489613, "maximum_tangent_angle_degrees": 0.032019170338979594, "maximum_scaled_magnitude_error": 8.127442025013903e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": null, "passed": true }, { "curve_index": 10, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998438489613, "maximum_tangent_angle_degrees": 0.032019170338979594, "maximum_scaled_magnitude_error": 8.127442025013903e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": null, "passed": true }, { "curve_index": 11, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998438489613, "maximum_tangent_angle_degrees": 0.032019170338979594, "maximum_scaled_magnitude_error": 8.127442025013903e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": null, "passed": true }, { "curve_index": 12, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998549817093, "maximum_tangent_angle_degrees": 0.030856667905479255, "maximum_scaled_magnitude_error": 7.625455221339753e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000138, "infinity_certificate": null, "passed": true }, { "curve_index": 13, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998549817093, "maximum_tangent_angle_degrees": 0.030856667905479255, "maximum_scaled_magnitude_error": 7.625455221339753e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000138, "infinity_certificate": null, "passed": true }, { "curve_index": 14, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998549817093, "maximum_tangent_angle_degrees": 0.030856667905479255, "maximum_scaled_magnitude_error": 7.625455221339753e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000138, "infinity_certificate": null, "passed": true }, { "curve_index": 15, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998549817093, "maximum_tangent_angle_degrees": 0.030856667905479255, "maximum_scaled_magnitude_error": 7.625455221339753e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000138, "infinity_certificate": null, "passed": true }, { "curve_index": 16, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998013955426, "maximum_tangent_angle_degrees": 0.03611038619539964, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 17, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998013955426, "maximum_tangent_angle_degrees": 0.03611038619539964, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 18, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998013955426, "maximum_tangent_angle_degrees": 0.03611038619539964, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 19, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998013955426, "maximum_tangent_angle_degrees": 0.03611038619539964, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 20, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999975971892, "maximum_tangent_angle_degrees": 0.003971891912908968, "maximum_scaled_magnitude_error": 7.077561329304058e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.2508107751499953, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14493169777054035, "actual_oriented_radial_cosine": 0.9920056998078091, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 21, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999975971892, "maximum_tangent_angle_degrees": 0.003971891912908968, "maximum_scaled_magnitude_error": 7.077561329304058e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.2508107751499953, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14493169777054035, "actual_oriented_radial_cosine": 0.9920056998078091, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 22, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999975971892, "maximum_tangent_angle_degrees": 0.003971891912908968, "maximum_scaled_magnitude_error": 7.077561329304058e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.2508107751499953, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14493169777054035, "actual_oriented_radial_cosine": 0.9920056998078091, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 23, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999975971892, "maximum_tangent_angle_degrees": 0.003971891912908968, "maximum_scaled_magnitude_error": 7.077561329304058e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.2508107751499953, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14493169777054035, "actual_oriented_radial_cosine": 0.9920056998078091, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 24, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999989548181, "maximum_tangent_angle_degrees": 0.0026195915381654737, "maximum_scaled_magnitude_error": 8.411039969784791e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.3418242743212687, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14245965555160126, "actual_oriented_radial_cosine": 0.9898011997513273, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 25, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999989548181, "maximum_tangent_angle_degrees": 0.0026195915381654737, "maximum_scaled_magnitude_error": 8.411039969784791e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.3418242743212687, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14245965555160126, "actual_oriented_radial_cosine": 0.9898011997513273, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 26, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999989548181, "maximum_tangent_angle_degrees": 0.0026195915381654737, "maximum_scaled_magnitude_error": 8.411039969784791e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.3418242743212687, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14245965555160126, "actual_oriented_radial_cosine": 0.9898011997513273, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 27, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999989548181, "maximum_tangent_angle_degrees": 0.0026195915381654737, "maximum_scaled_magnitude_error": 8.411039969784791e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.3418242743212687, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.14245965555160126, "actual_oriented_radial_cosine": 0.9898011997513273, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 28, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999993009824, "maximum_tangent_angle_degrees": 0.002142306928106704, "maximum_scaled_magnitude_error": 8.46639838662026e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.3822584156755457, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.154203897000473, "actual_oriented_radial_cosine": 0.9892597829932159, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 29, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999993009824, "maximum_tangent_angle_degrees": 0.002142306928106704, "maximum_scaled_magnitude_error": 8.46639838662026e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.3822584156755457, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.154203897000473, "actual_oriented_radial_cosine": 0.9892597829932159, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 30, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999993009824, "maximum_tangent_angle_degrees": 0.002142306928106704, "maximum_scaled_magnitude_error": 8.46639838662026e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.3822584156755457, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.154203897000473, "actual_oriented_radial_cosine": 0.9892597829932159, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 31, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999993009824, "maximum_tangent_angle_degrees": 0.002142306928106704, "maximum_scaled_magnitude_error": 8.46639838662026e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.3822584156755457, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.154203897000473, "actual_oriented_radial_cosine": 0.9892597829932159, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 32, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999995530041, "maximum_tangent_angle_degrees": 0.0017131263403488226, "maximum_scaled_magnitude_error": 9.105141613494147e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4127871505448482, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.19173555834585393, "actual_oriented_radial_cosine": 0.9899116797527524, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 33, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999995530041, "maximum_tangent_angle_degrees": 0.0017131263403488226, "maximum_scaled_magnitude_error": 9.105141613494147e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4127871505448482, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.19173555834585393, "actual_oriented_radial_cosine": 0.9899116797527524, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 34, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999995530041, "maximum_tangent_angle_degrees": 0.0017131263403488226, "maximum_scaled_magnitude_error": 9.105141613494147e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4127871505448482, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.19173555834585393, "actual_oriented_radial_cosine": 0.9899116797527524, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 35, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999995530041, "maximum_tangent_angle_degrees": 0.0017131263403488226, "maximum_scaled_magnitude_error": 9.105141613494147e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4127871505448482, "infinity_certificate": { "passed": true, "radius": 7.687439319873574, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.19173555834585393, "actual_oriented_radial_cosine": 0.9899116797527524, "global_oriented_radial_lower_bound": 0.012691058965047469, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 36, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996528387, "maximum_tangent_angle_degrees": 0.0015097438982979465, "maximum_scaled_magnitude_error": 9.61675431498654e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4168127221813585, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.22726697696083697, "actual_oriented_radial_cosine": 0.9913011399588019, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 37, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996528387, "maximum_tangent_angle_degrees": 0.0015097438982979465, "maximum_scaled_magnitude_error": 9.61675431498654e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4168127221813585, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.22726697696083697, "actual_oriented_radial_cosine": 0.9913011399588019, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 38, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996528387, "maximum_tangent_angle_degrees": 0.0015097438982979465, "maximum_scaled_magnitude_error": 9.61675431498654e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4168127221813585, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.22726697696083697, "actual_oriented_radial_cosine": 0.9913011399588019, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 39, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996528387, "maximum_tangent_angle_degrees": 0.0015097438982979465, "maximum_scaled_magnitude_error": 9.61675431498654e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4168127221813585, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.22726697696083697, "actual_oriented_radial_cosine": 0.9913011399588019, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 40, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996988369, "maximum_tangent_angle_degrees": 0.001406172193538893, "maximum_scaled_magnitude_error": 6.774432708100706e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4187739472143914, "infinity_certificate": { "passed": true, "radius": 7.687439319873572, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2474361092153845, "actual_oriented_radial_cosine": 0.9922664147325053, "global_oriented_radial_lower_bound": 0.012691058965047476, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 41, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996988369, "maximum_tangent_angle_degrees": 0.001406172193538893, "maximum_scaled_magnitude_error": 6.774432708100706e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4187739472143914, "infinity_certificate": { "passed": true, "radius": 7.687439319873572, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2474361092153845, "actual_oriented_radial_cosine": 0.9922664147325053, "global_oriented_radial_lower_bound": 0.012691058965047476, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 42, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996988369, "maximum_tangent_angle_degrees": 0.001406172193538893, "maximum_scaled_magnitude_error": 6.774432708100706e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4187739472143914, "infinity_certificate": { "passed": true, "radius": 7.687439319873572, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2474361092153845, "actual_oriented_radial_cosine": 0.9922664147325053, "global_oriented_radial_lower_bound": 0.012691058965047476, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 43, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996988369, "maximum_tangent_angle_degrees": 0.001406172193538893, "maximum_scaled_magnitude_error": 6.774432708100706e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4187739472143914, "infinity_certificate": { "passed": true, "radius": 7.687439319873572, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2474361092153845, "actual_oriented_radial_cosine": 0.9922664147325053, "global_oriented_radial_lower_bound": 0.012691058965047476, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 44, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.999999999801056, "maximum_tangent_angle_degrees": 0.0011428862900009628, "maximum_scaled_magnitude_error": 8.87491519887831e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4231269765107386, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2916290063549297, "actual_oriented_radial_cosine": 0.9947013592208468, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 45, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.999999999801056, "maximum_tangent_angle_degrees": 0.0011428862900009628, "maximum_scaled_magnitude_error": 8.87491519887831e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4231269765107386, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2916290063549297, "actual_oriented_radial_cosine": 0.9947013592208468, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 46, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.999999999801056, "maximum_tangent_angle_degrees": 0.0011428862900009628, "maximum_scaled_magnitude_error": 8.87491519887831e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4231269765107386, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2916290063549297, "actual_oriented_radial_cosine": 0.9947013592208468, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 47, "source_index": null, "endpoint_charge": 1, "termination": "infinity", "minimum_tangent_cosine": 0.999999999801056, "maximum_tangent_angle_degrees": 0.0011428862900009628, "maximum_scaled_magnitude_error": 8.87491519887831e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4231269765107386, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.2916290063549297, "actual_oriented_radial_cosine": 0.9947013592208468, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 48, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.999999997848371, "maximum_tangent_angle_degrees": 0.0037585585803450155, "maximum_scaled_magnitude_error": 6.446205416490434e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4158726375354753, "infinity_certificate": { "passed": true, "radius": 7.687439319873575, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16851101783431047, "actual_oriented_radial_cosine": 0.9994908481177288, "global_oriented_radial_lower_bound": 0.012691058965047465, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 49, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.999999997848371, "maximum_tangent_angle_degrees": 0.0037585585803450155, "maximum_scaled_magnitude_error": 6.446205416490434e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4158726375354753, "infinity_certificate": { "passed": true, "radius": 7.687439319873575, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16851101783431047, "actual_oriented_radial_cosine": 0.9994908481177288, "global_oriented_radial_lower_bound": 0.012691058965047465, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 50, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.999999997848371, "maximum_tangent_angle_degrees": 0.0037585585803450155, "maximum_scaled_magnitude_error": 6.446205416490434e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4158726375354753, "infinity_certificate": { "passed": true, "radius": 7.687439319873575, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16851101783431047, "actual_oriented_radial_cosine": 0.9994908481177288, "global_oriented_radial_lower_bound": 0.012691058965047465, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 51, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.999999997848371, "maximum_tangent_angle_degrees": 0.0037585585803450155, "maximum_scaled_magnitude_error": 6.446205416490434e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.4158726375354753, "infinity_certificate": { "passed": true, "radius": 7.687439319873575, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16851101783431047, "actual_oriented_radial_cosine": 0.9994908481177288, "global_oriented_radial_lower_bound": 0.012691058965047465, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 52, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.9999999955692632, "maximum_tangent_angle_degrees": 0.005393561131396758, "maximum_scaled_magnitude_error": 9.01380933083514e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.2640096499360252, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16902065464387697, "actual_oriented_radial_cosine": 0.9978080106935753, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 53, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.9999999955692632, "maximum_tangent_angle_degrees": 0.005393561131396758, "maximum_scaled_magnitude_error": 9.01380933083514e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.2640096499360252, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16902065464387697, "actual_oriented_radial_cosine": 0.9978080106935753, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 54, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.9999999955692632, "maximum_tangent_angle_degrees": 0.005393561131396758, "maximum_scaled_magnitude_error": 9.01380933083514e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.2640096499360252, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16902065464387697, "actual_oriented_radial_cosine": 0.9978080106935753, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 55, "source_index": null, "endpoint_charge": 3, "termination": "infinity", "minimum_tangent_cosine": 0.9999999955692632, "maximum_tangent_angle_degrees": 0.005393561131396758, "maximum_scaled_magnitude_error": 9.01380933083514e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 1.2640096499360252, "infinity_certificate": { "passed": true, "radius": 7.687439319873573, "all_sources_radius": 1.0, "net_charge": -3.0, "bound": 0.75, "actual_relative_monopole_field_error": 0.16902065464387697, "actual_oriented_radial_cosine": 0.9978080106935753, "global_oriented_radial_lower_bound": 0.012691058965047472, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 56, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998879064281, "maximum_tangent_angle_degrees": 0.027128637872251622, "maximum_scaled_magnitude_error": 6.395910550517978e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 57, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998879064281, "maximum_tangent_angle_degrees": 0.027128637872251622, "maximum_scaled_magnitude_error": 6.395910550517978e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 58, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998879064281, "maximum_tangent_angle_degrees": 0.027128637872251622, "maximum_scaled_magnitude_error": 6.395910550517978e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 59, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998879064281, "maximum_tangent_angle_degrees": 0.027128637872251622, "maximum_scaled_magnitude_error": 6.395910550517978e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true } ], "line_density_interpretation": "Counts are proportional to both source/sink charge magnitudes; arbitrary displayed source directions do not calibrate local flux-tube cross-sectional area." }, "actual_source_symmetries": { "passed": true, "errors": [], "actual_group_order": 4, "transformations": [ { "matrix": [ [ -1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 2, 1, 0, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ -1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 2, 1, 0, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 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-37.69911184307752, "absolute_error": 7.105427357601002e-15 }, "far_field": { "leading_order": "monopole", "net_charge": -3.0, "dipole_moment": [ 0.0, -3.0, 0.0 ], "quadrupole_tensor": [ [ 9.0, 0.0, 0.0 ], [ 0.0, -12.0, 0.0 ], [ 0.0, 0.0, 3.0 ] ], "radii": [ 80.0, 160.0, 320.0 ], "potential_relative_errors": [ 0.006374641288746652, 0.0031881709779328178, 0.0015942593479771154 ], "field_relative_errors": [ 0.016439868406229984, 0.008280261262162348, 0.004155243516471399 ], "measured_last_doubling_slopes": [ -0.9976949592582984, -1.9953949317046822 ], "expected_slopes": [ -1, -2 ] } }, "representative_refinement": { "passed": true, "selected_curve_index": 20, "integration_orientation": -1.0, "reference_rtol": 1e-11, "reference_atol": 1e-13, "reference_max_step": 0.015, "common_arclength_samples": 500, "maximum_baseline_vs_strict_position_difference": 1.0734531419291076e-10, "maximum_actual_serialized_samples_vs_strict_difference": 1.0734531419291076e-10, "endpoint_assignments_agree": true }, "candidate_orbits_omitted_for_complexity": [] }, "positivesx2": { "passed": true, "charges": [ 2, -1, 2, -1 ], "positions": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ -1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ] ], "actual_serialized_viewer": { "passed": true, "separate_line_traces": 48, "arrow_count": 48, "arrow_points_on_correct_curves": true, "minimum_arrow_independent_field_cosine": 0.9999999999999999, "verified_actual_charge_markers": 4, "html_filename": "electric_field_3d_positivesx2.html", "html_sha256": "f8d0641c14c55bd1614f1daf95da1289b5de27b5a09c5e001c0fd315c2902b1e" }, "physical_curves": { "passed": true, "errors": [], "curve_count": 48, "actual_charge_endpoint_counts": [ 24, 12, 24, 12 ], "expected_charge_endpoint_counts": [ 24, 12, 24, 12 ], "actual_infinity_curve_count": 24, "expected_infinity_curve_count": 24, "source_to_sink_counts": { "0 -> 1": 6, "0 -> 3": 6, "0 -> infinity": 12, "2 -> 1": 6, "2 -> 3": 6, "2 -> infinity": 12 }, "worst_tangent_angle_degrees": 0.019691961227847662, "curves": [ { "curve_index": 0, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999519075083, "maximum_tangent_angle_degrees": 0.01776954350909054, "maximum_scaled_magnitude_error": 9.16984688012722e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": null, "passed": true }, { "curve_index": 1, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999519075083, "maximum_tangent_angle_degrees": 0.01776954350909054, "maximum_scaled_magnitude_error": 9.16984688012722e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": null, "passed": true }, { "curve_index": 2, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999519075083, "maximum_tangent_angle_degrees": 0.01776954350909054, "maximum_scaled_magnitude_error": 9.16984688012722e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": null, "passed": true }, { "curve_index": 3, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999519075083, "maximum_tangent_angle_degrees": 0.01776954350909054, "maximum_scaled_magnitude_error": 9.16984688012722e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": null, "passed": true }, { "curve_index": 4, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999519075083, "maximum_tangent_angle_degrees": 0.01776954350909054, "maximum_scaled_magnitude_error": 9.16984688012722e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": null, "passed": true }, { "curve_index": 5, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999519075083, "maximum_tangent_angle_degrees": 0.01776954350909054, "maximum_scaled_magnitude_error": 9.16984688012722e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": null, "passed": true }, { "curve_index": 6, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999519075083, "maximum_tangent_angle_degrees": 0.01776954350909054, "maximum_scaled_magnitude_error": 9.16984688012722e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": null, "passed": true }, { "curve_index": 7, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999519075083, "maximum_tangent_angle_degrees": 0.01776954350909054, "maximum_scaled_magnitude_error": 9.16984688012722e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": null, "passed": true }, { "curve_index": 8, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999409387439, "maximum_tangent_angle_degrees": 0.019691961227847662, "maximum_scaled_magnitude_error": 8.234363621580919e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 9, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999409387439, "maximum_tangent_angle_degrees": 0.019691961227847662, "maximum_scaled_magnitude_error": 8.234363621580919e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 10, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999409387439, "maximum_tangent_angle_degrees": 0.019691961227847662, "maximum_scaled_magnitude_error": 8.234363621580919e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 11, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999409387439, "maximum_tangent_angle_degrees": 0.019691961227847662, "maximum_scaled_magnitude_error": 8.234363621580919e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 12, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999409387439, "maximum_tangent_angle_degrees": 0.019691961227847662, "maximum_scaled_magnitude_error": 8.234363621580919e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 13, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999409387439, "maximum_tangent_angle_degrees": 0.019691961227847662, "maximum_scaled_magnitude_error": 8.234363621580919e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 14, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999409387439, "maximum_tangent_angle_degrees": 0.019691961227847662, "maximum_scaled_magnitude_error": 8.234363621580919e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 15, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999409387439, "maximum_tangent_angle_degrees": 0.019691961227847662, "maximum_scaled_magnitude_error": 8.234363621580919e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 16, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999500945819, "maximum_tangent_angle_degrees": 0.018101371489705854, "maximum_scaled_magnitude_error": 7.015801013556313e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 17, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999500945819, "maximum_tangent_angle_degrees": 0.018101371489705854, "maximum_scaled_magnitude_error": 7.015801013556313e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 18, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999500945819, "maximum_tangent_angle_degrees": 0.018101371489705854, "maximum_scaled_magnitude_error": 7.015801013556313e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 19, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999500945819, "maximum_tangent_angle_degrees": 0.018101371489705854, "maximum_scaled_magnitude_error": 7.015801013556313e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 20, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999500945819, "maximum_tangent_angle_degrees": 0.018101371489705854, "maximum_scaled_magnitude_error": 7.015801013556313e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 21, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999500945819, "maximum_tangent_angle_degrees": 0.018101371489705854, "maximum_scaled_magnitude_error": 7.015801013556313e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 22, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999500945819, "maximum_tangent_angle_degrees": 0.018101371489705854, "maximum_scaled_magnitude_error": 7.015801013556313e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 23, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999500945819, "maximum_tangent_angle_degrees": 0.018101371489705854, "maximum_scaled_magnitude_error": 7.015801013556313e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 24, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999920607027, "maximum_tangent_angle_degrees": 0.007219858132435846, "maximum_scaled_magnitude_error": 7.232254198105314e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": { "passed": true, "radius": 9.472135954999576, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.06339455453075457, "actual_oriented_radial_cosine": 0.9999188232585313, "global_oriented_radial_lower_bound": 0.005572809000084111, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 25, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999920607027, "maximum_tangent_angle_degrees": 0.007219858132435846, "maximum_scaled_magnitude_error": 7.232254198105314e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": { "passed": true, "radius": 9.472135954999576, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.06339455453075457, "actual_oriented_radial_cosine": 0.9999188232585313, "global_oriented_radial_lower_bound": 0.005572809000084111, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 26, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999920607027, "maximum_tangent_angle_degrees": 0.007219858132435846, "maximum_scaled_magnitude_error": 7.232254198105314e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": { "passed": true, "radius": 9.472135954999576, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.06339455453075457, "actual_oriented_radial_cosine": 0.9999188232585313, "global_oriented_radial_lower_bound": 0.005572809000084111, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 27, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999920607027, "maximum_tangent_angle_degrees": 0.007219858132435846, "maximum_scaled_magnitude_error": 7.232254198105314e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": { "passed": true, "radius": 9.472135954999576, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.06339455453075457, "actual_oriented_radial_cosine": 0.9999188232585313, "global_oriented_radial_lower_bound": 0.005572809000084111, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 28, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999920607027, "maximum_tangent_angle_degrees": 0.007219858132435846, "maximum_scaled_magnitude_error": 7.232254198105314e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": { "passed": true, "radius": 9.472135954999576, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.06339455453075457, "actual_oriented_radial_cosine": 0.9999188232585313, "global_oriented_radial_lower_bound": 0.005572809000084111, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 29, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999920607027, "maximum_tangent_angle_degrees": 0.007219858132435846, "maximum_scaled_magnitude_error": 7.232254198105314e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": { "passed": true, "radius": 9.472135954999576, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.06339455453075457, "actual_oriented_radial_cosine": 0.9999188232585313, "global_oriented_radial_lower_bound": 0.005572809000084111, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 30, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999920607027, "maximum_tangent_angle_degrees": 0.007219858132435846, "maximum_scaled_magnitude_error": 7.232254198105314e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": { "passed": true, "radius": 9.472135954999576, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.06339455453075457, "actual_oriented_radial_cosine": 0.9999188232585313, "global_oriented_radial_lower_bound": 0.005572809000084111, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 31, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999920607027, "maximum_tangent_angle_degrees": 0.007219858132435846, "maximum_scaled_magnitude_error": 7.232254198105314e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": { "passed": true, "radius": 9.472135954999576, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.06339455453075457, "actual_oriented_radial_cosine": 0.9999188232585313, "global_oriented_radial_lower_bound": 0.005572809000084111, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 32, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999990939235, "maximum_tangent_angle_degrees": 0.0024390464706302356, "maximum_scaled_magnitude_error": 7.83414835669963e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 9.47213595499958, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.04444429375737752, "actual_oriented_radial_cosine": 0.9991219842329085, "global_oriented_radial_lower_bound": 0.005572809000084107, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 33, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999990939235, "maximum_tangent_angle_degrees": 0.0024390464706302356, "maximum_scaled_magnitude_error": 7.83414835669963e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 9.47213595499958, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.04444429375737752, "actual_oriented_radial_cosine": 0.9991219842329085, "global_oriented_radial_lower_bound": 0.005572809000084107, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 34, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999990939235, "maximum_tangent_angle_degrees": 0.0024390464706302356, "maximum_scaled_magnitude_error": 7.83414835669963e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 9.47213595499958, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.04444429375737752, "actual_oriented_radial_cosine": 0.9991219842329085, "global_oriented_radial_lower_bound": 0.005572809000084107, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 35, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999990939235, "maximum_tangent_angle_degrees": 0.0024390464706302356, "maximum_scaled_magnitude_error": 7.83414835669963e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 9.47213595499958, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.04444429375737752, "actual_oriented_radial_cosine": 0.9991219842329085, "global_oriented_radial_lower_bound": 0.005572809000084107, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 36, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999990939235, "maximum_tangent_angle_degrees": 0.0024390464706302356, "maximum_scaled_magnitude_error": 7.83414835669963e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 9.47213595499958, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.04444429375737752, "actual_oriented_radial_cosine": 0.9991219842329085, "global_oriented_radial_lower_bound": 0.005572809000084107, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 37, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999990939235, "maximum_tangent_angle_degrees": 0.0024390464706302356, "maximum_scaled_magnitude_error": 7.83414835669963e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 9.47213595499958, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.04444429375737752, "actual_oriented_radial_cosine": 0.9991219842329085, "global_oriented_radial_lower_bound": 0.005572809000084107, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 38, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999990939235, "maximum_tangent_angle_degrees": 0.0024390464706302356, "maximum_scaled_magnitude_error": 7.83414835669963e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 9.47213595499958, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.04444429375737752, "actual_oriented_radial_cosine": 0.9991219842329085, "global_oriented_radial_lower_bound": 0.005572809000084107, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 39, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999990939235, "maximum_tangent_angle_degrees": 0.0024390464706302356, "maximum_scaled_magnitude_error": 7.83414835669963e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": { "passed": true, "radius": 9.47213595499958, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.04444429375737752, "actual_oriented_radial_cosine": 0.9991219842329085, "global_oriented_radial_lower_bound": 0.005572809000084107, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 40, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996163531, "maximum_tangent_angle_degrees": 0.0015870970061136883, "maximum_scaled_magnitude_error": 8.414523405723587e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 9.472135954999578, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.05101177724606864, "actual_oriented_radial_cosine": 0.9990271686123404, "global_oriented_radial_lower_bound": 0.005572809000084109, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 41, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996163531, "maximum_tangent_angle_degrees": 0.0015870970061136883, "maximum_scaled_magnitude_error": 8.414523405723587e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 9.472135954999578, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.05101177724606864, "actual_oriented_radial_cosine": 0.9990271686123404, "global_oriented_radial_lower_bound": 0.005572809000084109, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 42, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996163531, "maximum_tangent_angle_degrees": 0.0015870970061136883, "maximum_scaled_magnitude_error": 8.414523405723587e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 9.472135954999578, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.05101177724606864, "actual_oriented_radial_cosine": 0.9990271686123404, "global_oriented_radial_lower_bound": 0.005572809000084109, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 43, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996163531, "maximum_tangent_angle_degrees": 0.0015870970061136883, "maximum_scaled_magnitude_error": 8.414523405723587e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 9.472135954999578, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.05101177724606864, "actual_oriented_radial_cosine": 0.9990271686123404, "global_oriented_radial_lower_bound": 0.005572809000084109, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 44, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996163531, "maximum_tangent_angle_degrees": 0.0015870970061136883, "maximum_scaled_magnitude_error": 8.414523405723587e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 9.472135954999578, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.05101177724606864, "actual_oriented_radial_cosine": 0.9990271686123404, "global_oriented_radial_lower_bound": 0.005572809000084109, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 45, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996163531, "maximum_tangent_angle_degrees": 0.0015870970061136883, "maximum_scaled_magnitude_error": 8.414523405723587e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 9.472135954999578, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.05101177724606864, "actual_oriented_radial_cosine": 0.9990271686123404, "global_oriented_radial_lower_bound": 0.005572809000084109, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 46, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996163531, "maximum_tangent_angle_degrees": 0.0015870970061136883, "maximum_scaled_magnitude_error": 8.414523405723587e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 9.472135954999578, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.05101177724606864, "actual_oriented_radial_cosine": 0.9990271686123404, "global_oriented_radial_lower_bound": 0.005572809000084109, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 47, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999996163531, "maximum_tangent_angle_degrees": 0.0015870970061136883, "maximum_scaled_magnitude_error": 8.414523405723587e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999957, "infinity_certificate": { "passed": true, "radius": 9.472135954999578, "all_sources_radius": 1.0, "net_charge": 2.0, "bound": 0.7500000000000007, "actual_relative_monopole_field_error": 0.05101177724606864, "actual_oriented_radial_cosine": 0.9990271686123404, "global_oriented_radial_lower_bound": 0.005572809000084109, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true } ], "line_density_interpretation": "Counts are proportional to both source/sink charge magnitudes; arbitrary displayed source directions do not calibrate local flux-tube cross-sectional area." }, "actual_source_symmetries": { "passed": true, "errors": [], "actual_group_order": 8, "transformations": [ { "matrix": [ [ -1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 2, 3, 0, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ -1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 2, 3, 0, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ -1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 2, 1, 0, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ -1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 2, 1, 0, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 3, 2, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 3, 2, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 } ] }, "gauss_multipoles_kernel_checks": { "passed": true, "cpu_independent_reference_maximum_scaled_error": 9.305364597889227e-16, "gpu": { "requested": true, "passed": true, "maximum_scaled_error": 9.305364597889227e-16 }, "individual_source_gauss_fluxes": [ { "source_index": 0, "charge": 2.0, "expected": 25.132741228718345, "measured": 25.13274122871834, "absolute_error": 3.552713678800501e-15 }, { "source_index": 1, "charge": -1.0, "expected": -12.566370614359172, "measured": -12.56637061435917, "absolute_error": 1.7763568394002505e-15 }, { "source_index": 2, "charge": 2.0, "expected": 25.132741228718345, "measured": 25.13274122871834, "absolute_error": 3.552713678800501e-15 }, { "source_index": 3, "charge": -1.0, "expected": -12.566370614359172, "measured": -12.56637061435917, "absolute_error": 1.7763568394002505e-15 } ], "enclosing_gauss_flux": { "measured": 25.132741228718338, "expected": 25.132741228718345, "absolute_error": 7.105427357601002e-15 }, "far_field": { "leading_order": "monopole", "net_charge": 2.0, "dipole_moment": [ 0.0, 0.0, 0.0 ], "quadrupole_tensor": [ [ 10.0, 0.0, 0.0 ], [ 0.0, -8.0, 0.0 ], [ 0.0, 0.0, -2.0 ] ], "radii": [ 80.0, 160.0, 320.0 ], "potential_relative_errors": [ 7.490674149845944e-05, 1.8727561597875475e-05, 4.6819451554602765e-06 ], "field_relative_errors": [ 0.00047748491152256394, 0.00011938925662088385, 2.984844100787315e-05 ], "measured_last_doubling_slopes": [ -0.9999797362216294, -1.9999392155373528 ], "expected_slopes": [ -1, -2 ] } }, "representative_refinement": { "passed": true, "selected_curve_index": 24, "integration_orientation": 1.0, "reference_rtol": 1e-11, "reference_atol": 1e-13, "reference_max_step": 0.015, "common_arclength_samples": 500, "maximum_baseline_vs_strict_position_difference": 7.680489516991292e-10, "maximum_actual_serialized_samples_vs_strict_difference": 7.680489516991292e-10, "endpoint_assignments_agree": true }, "candidate_orbits_omitted_for_complexity": [] }, "positivesx4": { "passed": true, "charges": [ 4, -1, 4, -1 ], "positions": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ -1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ] ], "actual_serialized_viewer": { "passed": true, "separate_line_traces": 96, "arrow_count": 96, "arrow_points_on_correct_curves": true, "minimum_arrow_independent_field_cosine": 0.9999999999999998, "verified_actual_charge_markers": 4, "html_filename": "electric_field_3d_positivesx4.html", "html_sha256": "71a01673f516f9faa628b64c96bdb5513736d92ac985e51d4df6e2d8ef4bfacd" }, "physical_curves": { "passed": true, "errors": [], "curve_count": 96, "actual_charge_endpoint_counts": [ 48, 12, 48, 12 ], "expected_charge_endpoint_counts": [ 48, 12, 48, 12 ], "actual_infinity_curve_count": 72, "expected_infinity_curve_count": 72, "source_to_sink_counts": { "0 -> 1": 6, "0 -> 3": 6, "0 -> infinity": 36, "2 -> 1": 6, "2 -> 3": 6, "2 -> infinity": 36 }, "worst_tangent_angle_degrees": 0.04474077546631969, "curves": [ { "curve_index": 0, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999997183243428, "maximum_tangent_angle_degrees": 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0.04300434116812238, "maximum_scaled_magnitude_error": 7.806181951218969e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": null, "passed": true }, { "curve_index": 6, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999997183243428, "maximum_tangent_angle_degrees": 0.04300434116812238, "maximum_scaled_magnitude_error": 7.806181951218969e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": null, "passed": true }, { "curve_index": 7, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999997183243428, "maximum_tangent_angle_degrees": 0.04300434116812238, "maximum_scaled_magnitude_error": 7.806181951218969e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": null, "passed": true }, { "curve_index": 8, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999996951180371, "maximum_tangent_angle_degrees": 0.04474077546631969, "maximum_scaled_magnitude_error": 6.990108659623598e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 9, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999996951180371, "maximum_tangent_angle_degrees": 0.04474077546631969, "maximum_scaled_magnitude_error": 6.990108659623598e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 10, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999996951180371, "maximum_tangent_angle_degrees": 0.04474077546631969, "maximum_scaled_magnitude_error": 6.990108659623598e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 11, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999996951180371, "maximum_tangent_angle_degrees": 0.04474077546631969, "maximum_scaled_magnitude_error": 6.990108659623598e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 12, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999996951180371, "maximum_tangent_angle_degrees": 0.04474077546631969, "maximum_scaled_magnitude_error": 6.990108659623598e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 13, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999996951180371, "maximum_tangent_angle_degrees": 0.04474077546631969, "maximum_scaled_magnitude_error": 6.990108659623598e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 14, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999996951180371, "maximum_tangent_angle_degrees": 0.04474077546631969, "maximum_scaled_magnitude_error": 6.990108659623598e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 15, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999996951180371, "maximum_tangent_angle_degrees": 0.04474077546631969, "maximum_scaled_magnitude_error": 6.990108659623598e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": null, "passed": true }, { "curve_index": 16, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998283670677, "maximum_tangent_angle_degrees": 0.03356896471977831, "maximum_scaled_magnitude_error": 8.271609893860402e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 17, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998283670677, "maximum_tangent_angle_degrees": 0.03356896471977831, "maximum_scaled_magnitude_error": 8.271609893860402e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 18, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998283670677, "maximum_tangent_angle_degrees": 0.03356896471977831, "maximum_scaled_magnitude_error": 8.271609893860402e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 19, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998283670677, "maximum_tangent_angle_degrees": 0.03356896471977831, "maximum_scaled_magnitude_error": 8.271609893860402e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 20, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998283670677, "maximum_tangent_angle_degrees": 0.03356896471977831, "maximum_scaled_magnitude_error": 8.271609893860402e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 21, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999998283670677, "maximum_tangent_angle_degrees": 0.03356896471977831, "maximum_scaled_magnitude_error": 8.271609893860402e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 22, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998283670677, "maximum_tangent_angle_degrees": 0.03356896471977831, "maximum_scaled_magnitude_error": 8.271609893860402e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 23, "source_index": 2, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999998283670677, "maximum_tangent_angle_degrees": 0.03356896471977831, "maximum_scaled_magnitude_error": 8.271609893860402e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000023, "infinity_certificate": null, "passed": true }, { "curve_index": 24, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999895947715, "maximum_tangent_angle_degrees": 0.008265391716064918, "maximum_scaled_magnitude_error": 1.0744431986112196e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07824733591271395, "actual_oriented_radial_cosine": 0.999833267495399, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 25, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999895947715, "maximum_tangent_angle_degrees": 0.008265391716064918, "maximum_scaled_magnitude_error": 1.0744431986112196e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07824733591271395, "actual_oriented_radial_cosine": 0.999833267495399, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 26, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999895947715, "maximum_tangent_angle_degrees": 0.008265391716064918, "maximum_scaled_magnitude_error": 1.0744431986112196e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07824733591271395, "actual_oriented_radial_cosine": 0.999833267495399, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 27, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999895947715, "maximum_tangent_angle_degrees": 0.008265391716064918, "maximum_scaled_magnitude_error": 1.0744431986112196e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07824733591271395, "actual_oriented_radial_cosine": 0.999833267495399, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 28, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999895947715, "maximum_tangent_angle_degrees": 0.008265391716064918, "maximum_scaled_magnitude_error": 1.0744431986112196e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07824733591271395, "actual_oriented_radial_cosine": 0.999833267495399, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 29, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999895947715, "maximum_tangent_angle_degrees": 0.008265391716064918, "maximum_scaled_magnitude_error": 1.0744431986112196e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07824733591271395, "actual_oriented_radial_cosine": 0.999833267495399, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 30, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999895947715, "maximum_tangent_angle_degrees": 0.008265391716064918, "maximum_scaled_magnitude_error": 1.0744431986112196e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07824733591271395, "actual_oriented_radial_cosine": 0.999833267495399, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 31, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999895947715, "maximum_tangent_angle_degrees": 0.008265391716064918, "maximum_scaled_magnitude_error": 1.0744431986112196e-15, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07824733591271395, "actual_oriented_radial_cosine": 0.999833267495399, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 32, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999992720809, "maximum_tangent_angle_degrees": 0.002186146064369399, "maximum_scaled_magnitude_error": 7.605042507984384e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06576394810757898, "actual_oriented_radial_cosine": 0.9991577284866467, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 33, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999992720809, "maximum_tangent_angle_degrees": 0.002186146064369399, "maximum_scaled_magnitude_error": 7.605042507984384e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06576394810757898, "actual_oriented_radial_cosine": 0.9991577284866467, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 34, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999992720809, "maximum_tangent_angle_degrees": 0.002186146064369399, "maximum_scaled_magnitude_error": 7.605042507984384e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06576394810757898, "actual_oriented_radial_cosine": 0.9991577284866467, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 35, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999992720809, "maximum_tangent_angle_degrees": 0.002186146064369399, "maximum_scaled_magnitude_error": 7.605042507984384e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06576394810757898, "actual_oriented_radial_cosine": 0.9991577284866467, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 36, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999992720809, "maximum_tangent_angle_degrees": 0.002186146064369399, "maximum_scaled_magnitude_error": 7.605042507984384e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06576394810757898, "actual_oriented_radial_cosine": 0.9991577284866467, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 37, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999992720809, "maximum_tangent_angle_degrees": 0.002186146064369399, "maximum_scaled_magnitude_error": 7.605042507984384e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06576394810757898, "actual_oriented_radial_cosine": 0.9991577284866467, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 38, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999992720809, "maximum_tangent_angle_degrees": 0.002186146064369399, "maximum_scaled_magnitude_error": 7.605042507984384e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06576394810757898, "actual_oriented_radial_cosine": 0.9991577284866467, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 39, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999992720809, "maximum_tangent_angle_degrees": 0.002186146064369399, "maximum_scaled_magnitude_error": 7.605042507984384e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06576394810757898, "actual_oriented_radial_cosine": 0.9991577284866467, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 40, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997055006, "maximum_tangent_angle_degrees": 0.0013905283758404196, "maximum_scaled_magnitude_error": 7.692294309691436e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.061445878963153296, "actual_oriented_radial_cosine": 0.9986626506406224, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 41, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997055006, "maximum_tangent_angle_degrees": 0.0013905283758404196, "maximum_scaled_magnitude_error": 7.692294309691436e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.061445878963153296, "actual_oriented_radial_cosine": 0.9986626506406224, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 42, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997055006, "maximum_tangent_angle_degrees": 0.0013905283758404196, "maximum_scaled_magnitude_error": 7.692294309691436e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.061445878963153296, "actual_oriented_radial_cosine": 0.9986626506406224, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 43, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997055006, "maximum_tangent_angle_degrees": 0.0013905283758404196, "maximum_scaled_magnitude_error": 7.692294309691436e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.061445878963153296, "actual_oriented_radial_cosine": 0.9986626506406224, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 44, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997055006, "maximum_tangent_angle_degrees": 0.0013905283758404196, "maximum_scaled_magnitude_error": 7.692294309691436e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.061445878963153296, "actual_oriented_radial_cosine": 0.9986626506406224, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 45, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997055006, "maximum_tangent_angle_degrees": 0.0013905283758404196, "maximum_scaled_magnitude_error": 7.692294309691436e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.061445878963153296, "actual_oriented_radial_cosine": 0.9986626506406224, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 46, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997055006, "maximum_tangent_angle_degrees": 0.0013905283758404196, "maximum_scaled_magnitude_error": 7.692294309691436e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.061445878963153296, "actual_oriented_radial_cosine": 0.9986626506406224, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 47, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997055006, "maximum_tangent_angle_degrees": 0.0013905283758404196, "maximum_scaled_magnitude_error": 7.692294309691436e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000001, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.061445878963153296, "actual_oriented_radial_cosine": 0.9986626506406224, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 48, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997821326, "maximum_tangent_angle_degrees": 0.0011960070685308594, "maximum_scaled_magnitude_error": 7.698729802836938e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 5.89813212862051, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06076316935282578, "actual_oriented_radial_cosine": 0.9982135270563866, "global_oriented_radial_lower_bound": 0.043118363008490534, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 49, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997821326, "maximum_tangent_angle_degrees": 0.0011960070685308594, "maximum_scaled_magnitude_error": 7.698729802836938e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 5.89813212862051, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06076316935282578, "actual_oriented_radial_cosine": 0.9982135270563866, "global_oriented_radial_lower_bound": 0.043118363008490534, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 50, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997821326, "maximum_tangent_angle_degrees": 0.0011960070685308594, "maximum_scaled_magnitude_error": 7.698729802836938e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 5.89813212862051, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06076316935282578, "actual_oriented_radial_cosine": 0.9982135270563866, "global_oriented_radial_lower_bound": 0.043118363008490534, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 51, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997821326, "maximum_tangent_angle_degrees": 0.0011960070685308594, "maximum_scaled_magnitude_error": 7.698729802836938e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 5.89813212862051, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06076316935282578, "actual_oriented_radial_cosine": 0.9982135270563866, "global_oriented_radial_lower_bound": 0.043118363008490534, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 52, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997821326, "maximum_tangent_angle_degrees": 0.0011960070685308594, "maximum_scaled_magnitude_error": 7.698729802836938e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 5.89813212862051, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06076316935282578, "actual_oriented_radial_cosine": 0.9982135270563866, "global_oriented_radial_lower_bound": 0.043118363008490534, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 53, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997821326, "maximum_tangent_angle_degrees": 0.0011960070685308594, "maximum_scaled_magnitude_error": 7.698729802836938e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 5.89813212862051, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06076316935282578, "actual_oriented_radial_cosine": 0.9982135270563866, "global_oriented_radial_lower_bound": 0.043118363008490534, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 54, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997821326, "maximum_tangent_angle_degrees": 0.0011960070685308594, "maximum_scaled_magnitude_error": 7.698729802836938e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 5.89813212862051, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06076316935282578, "actual_oriented_radial_cosine": 0.9982135270563866, "global_oriented_radial_lower_bound": 0.043118363008490534, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 55, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999997821326, "maximum_tangent_angle_degrees": 0.0011960070685308594, "maximum_scaled_magnitude_error": 7.698729802836938e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000016, "infinity_certificate": { "passed": true, "radius": 5.89813212862051, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06076316935282578, "actual_oriented_radial_cosine": 0.9982135270563866, "global_oriented_radial_lower_bound": 0.043118363008490534, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 56, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998010288, "maximum_tangent_angle_degrees": 0.0011429644174622148, "maximum_scaled_magnitude_error": 8.316477229192366e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06346962273394936, "actual_oriented_radial_cosine": 0.9980017501018059, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 57, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998010288, "maximum_tangent_angle_degrees": 0.0011429644174622148, "maximum_scaled_magnitude_error": 8.316477229192366e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06346962273394936, "actual_oriented_radial_cosine": 0.9980017501018059, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 58, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998010288, "maximum_tangent_angle_degrees": 0.0011429644174622148, "maximum_scaled_magnitude_error": 8.316477229192366e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06346962273394936, "actual_oriented_radial_cosine": 0.9980017501018059, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 59, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998010288, "maximum_tangent_angle_degrees": 0.0011429644174622148, "maximum_scaled_magnitude_error": 8.316477229192366e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06346962273394936, "actual_oriented_radial_cosine": 0.9980017501018059, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 60, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998010288, "maximum_tangent_angle_degrees": 0.0011429644174622148, "maximum_scaled_magnitude_error": 8.316477229192366e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06346962273394936, "actual_oriented_radial_cosine": 0.9980017501018059, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 61, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998010288, "maximum_tangent_angle_degrees": 0.0011429644174622148, "maximum_scaled_magnitude_error": 8.316477229192366e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06346962273394936, "actual_oriented_radial_cosine": 0.9980017501018059, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 62, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998010288, "maximum_tangent_angle_degrees": 0.0011429644174622148, "maximum_scaled_magnitude_error": 8.316477229192366e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06346962273394936, "actual_oriented_radial_cosine": 0.9980017501018059, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 63, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998010288, "maximum_tangent_angle_degrees": 0.0011429644174622148, "maximum_scaled_magnitude_error": 8.316477229192366e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999999, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.06346962273394936, "actual_oriented_radial_cosine": 0.9980017501018059, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 64, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998409125, "maximum_tangent_angle_degrees": 0.0010220112758138392, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07342909157038703, "actual_oriented_radial_cosine": 0.9979130835129472, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 65, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998409125, "maximum_tangent_angle_degrees": 0.0010220112758138392, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07342909157038703, "actual_oriented_radial_cosine": 0.9979130835129472, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 66, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998409125, "maximum_tangent_angle_degrees": 0.0010220112758138392, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07342909157038703, "actual_oriented_radial_cosine": 0.9979130835129472, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 67, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998409125, "maximum_tangent_angle_degrees": 0.0010220112758138392, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07342909157038703, "actual_oriented_radial_cosine": 0.9979130835129472, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 68, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998409125, "maximum_tangent_angle_degrees": 0.0010220112758138392, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07342909157038703, "actual_oriented_radial_cosine": 0.9979130835129472, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 69, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998409125, "maximum_tangent_angle_degrees": 0.0010220112758138392, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07342909157038703, "actual_oriented_radial_cosine": 0.9979130835129472, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 70, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998409125, "maximum_tangent_angle_degrees": 0.0010220112758138392, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07342909157038703, "actual_oriented_radial_cosine": 0.9979130835129472, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 71, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998409125, "maximum_tangent_angle_degrees": 0.0010220112758138392, "maximum_scaled_magnitude_error": 7.771561172376096e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999968, "infinity_certificate": { "passed": true, "radius": 5.898132128620509, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.07342909157038703, "actual_oriented_radial_cosine": 0.9979130835129472, "global_oriented_radial_lower_bound": 0.04311836300849054, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 72, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998752485, "maximum_tangent_angle_degrees": 0.0009050250335435824, "maximum_scaled_magnitude_error": 8.287202974486074e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.08403464195549577, "actual_oriented_radial_cosine": 0.9980613534154741, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 73, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998752485, "maximum_tangent_angle_degrees": 0.0009050250335435824, "maximum_scaled_magnitude_error": 8.287202974486074e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.08403464195549577, "actual_oriented_radial_cosine": 0.9980613534154741, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 74, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998752485, "maximum_tangent_angle_degrees": 0.0009050250335435824, "maximum_scaled_magnitude_error": 8.287202974486074e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.08403464195549577, "actual_oriented_radial_cosine": 0.9980613534154741, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 75, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998752485, "maximum_tangent_angle_degrees": 0.0009050250335435824, "maximum_scaled_magnitude_error": 8.287202974486074e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.08403464195549577, "actual_oriented_radial_cosine": 0.9980613534154741, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 76, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998752485, "maximum_tangent_angle_degrees": 0.0009050250335435824, "maximum_scaled_magnitude_error": 8.287202974486074e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.08403464195549577, "actual_oriented_radial_cosine": 0.9980613534154741, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 77, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998752485, "maximum_tangent_angle_degrees": 0.0009050250335435824, "maximum_scaled_magnitude_error": 8.287202974486074e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.08403464195549577, "actual_oriented_radial_cosine": 0.9980613534154741, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 78, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998752485, "maximum_tangent_angle_degrees": 0.0009050250335435824, "maximum_scaled_magnitude_error": 8.287202974486074e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.08403464195549577, "actual_oriented_radial_cosine": 0.9980613534154741, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 79, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999998752485, "maximum_tangent_angle_degrees": 0.0009050250335435824, "maximum_scaled_magnitude_error": 8.287202974486074e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.08403464195549577, "actual_oriented_radial_cosine": 0.9980613534154741, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 80, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999893525, "maximum_tangent_angle_degrees": 0.0008361064209071734, "maximum_scaled_magnitude_error": 9.105775635612928e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.09043754934677965, "actual_oriented_radial_cosine": 0.9982107681063563, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 81, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999893525, "maximum_tangent_angle_degrees": 0.0008361064209071734, "maximum_scaled_magnitude_error": 9.105775635612928e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.09043754934677965, "actual_oriented_radial_cosine": 0.9982107681063563, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 82, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999893525, "maximum_tangent_angle_degrees": 0.0008361064209071734, "maximum_scaled_magnitude_error": 9.105775635612928e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.09043754934677965, "actual_oriented_radial_cosine": 0.9982107681063563, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 83, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999893525, "maximum_tangent_angle_degrees": 0.0008361064209071734, "maximum_scaled_magnitude_error": 9.105775635612928e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.09043754934677965, "actual_oriented_radial_cosine": 0.9982107681063563, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 84, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999893525, "maximum_tangent_angle_degrees": 0.0008361064209071734, "maximum_scaled_magnitude_error": 9.105775635612928e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.09043754934677965, "actual_oriented_radial_cosine": 0.9982107681063563, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 85, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999893525, "maximum_tangent_angle_degrees": 0.0008361064209071734, "maximum_scaled_magnitude_error": 9.105775635612928e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.09043754934677965, "actual_oriented_radial_cosine": 0.9982107681063563, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 86, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999893525, "maximum_tangent_angle_degrees": 0.0008361064209071734, "maximum_scaled_magnitude_error": 9.105775635612928e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.09043754934677965, "actual_oriented_radial_cosine": 0.9982107681063563, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 87, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.999999999893525, "maximum_tangent_angle_degrees": 0.0008361064209071734, "maximum_scaled_magnitude_error": 9.105775635612928e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999936, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.09043754934677965, "actual_oriented_radial_cosine": 0.9982107681063563, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 88, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999999301575, "maximum_tangent_angle_degrees": 0.0006771695328053967, "maximum_scaled_magnitude_error": 9.17699019510761e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.1052399959525861, "actual_oriented_radial_cosine": 0.99867971240364, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 89, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999999301575, "maximum_tangent_angle_degrees": 0.0006771695328053967, "maximum_scaled_magnitude_error": 9.17699019510761e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.1052399959525861, "actual_oriented_radial_cosine": 0.99867971240364, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 90, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999999301575, "maximum_tangent_angle_degrees": 0.0006771695328053967, "maximum_scaled_magnitude_error": 9.17699019510761e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.1052399959525861, "actual_oriented_radial_cosine": 0.99867971240364, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 91, "source_index": 0, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999999301575, "maximum_tangent_angle_degrees": 0.0006771695328053967, "maximum_scaled_magnitude_error": 9.17699019510761e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.1052399959525861, "actual_oriented_radial_cosine": 0.99867971240364, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 92, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999999301575, "maximum_tangent_angle_degrees": 0.0006771695328053967, "maximum_scaled_magnitude_error": 9.17699019510761e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.1052399959525861, "actual_oriented_radial_cosine": 0.99867971240364, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 93, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999999301575, "maximum_tangent_angle_degrees": 0.0006771695328053967, "maximum_scaled_magnitude_error": 9.17699019510761e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.1052399959525861, "actual_oriented_radial_cosine": 0.99867971240364, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 94, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999999301575, "maximum_tangent_angle_degrees": 0.0006771695328053967, "maximum_scaled_magnitude_error": 9.17699019510761e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.1052399959525861, "actual_oriented_radial_cosine": 0.99867971240364, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true }, { "curve_index": 95, "source_index": 2, "endpoint_charge": null, "termination": "infinity", "minimum_tangent_cosine": 0.9999999999301575, "maximum_tangent_angle_degrees": 0.0006771695328053967, "maximum_scaled_magnitude_error": 9.17699019510761e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000034, "infinity_certificate": { "passed": true, "radius": 5.898132128620508, "all_sources_radius": 1.0, "net_charge": 6.0, "bound": 0.7500000000000003, "actual_relative_monopole_field_error": 0.1052399959525861, "actual_oriented_radial_cosine": 0.99867971240364, "global_oriented_radial_lower_bound": 0.04311836300849056, "display_limit_is_finite": true, "interpretation": "Global outward/inward escape is certified; the remaining field line is neither drawn to literal infinity nor assumed exactly radial." }, "passed": true } ], "line_density_interpretation": "Counts are proportional to both source/sink charge magnitudes; arbitrary displayed source directions do not calibrate local flux-tube cross-sectional area." }, "actual_source_symmetries": { "passed": true, "errors": [], "actual_group_order": 8, "transformations": [ { "matrix": [ [ -1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 2, 3, 0, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ -1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 2, 3, 0, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ -1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 2, 1, 0, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ -1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 2, 1, 0, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 3, 2, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 3, 2, 1 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 } ] }, "gauss_multipoles_kernel_checks": { "passed": true, "cpu_independent_reference_maximum_scaled_error": 1.137640067256873e-15, "gpu": { "requested": true, "passed": true, "maximum_scaled_error": 1.137640067256873e-15 }, "individual_source_gauss_fluxes": [ { "source_index": 0, "charge": 4.0, "expected": 50.26548245743669, "measured": 50.26548245743668, "absolute_error": 7.105427357601002e-15 }, { "source_index": 1, "charge": -1.0, "expected": -12.566370614359172, "measured": -12.56637061435917, "absolute_error": 1.7763568394002505e-15 }, { "source_index": 2, "charge": 4.0, "expected": 50.26548245743669, "measured": 50.26548245743668, "absolute_error": 7.105427357601002e-15 }, { "source_index": 3, "charge": -1.0, "expected": -12.566370614359172, "measured": -12.56637061435917, "absolute_error": 1.7763568394002505e-15 } ], "enclosing_gauss_flux": { "measured": 75.39822368615502, "expected": 75.39822368615503, "absolute_error": 1.4210854715202004e-14 }, "far_field": { "leading_order": "monopole", "net_charge": 6.0, "dipole_moment": [ 0.0, 0.0, 0.0 ], "quadrupole_tensor": [ [ 18.0, 0.0, 0.0 ], [ 0.0, -12.0, 0.0 ], [ 0.0, 0.0, -6.0 ] ], "radii": [ 80.0, 160.0, 320.0 ], "potential_relative_errors": [ 5.564490344852254e-05, 1.3911345149349627e-05, 3.477843733001862e-06 ], "field_relative_errors": [ 0.00029273292059241683, 7.319282571175465e-05, 1.829880618757754e-05 ], "measured_last_doubling_slopes": [ -0.999984947508372, -1.9999548442925021 ], "expected_slopes": [ -1, -2 ] } }, "representative_refinement": { "passed": true, "selected_curve_index": 24, "integration_orientation": 1.0, "reference_rtol": 1e-11, "reference_atol": 1e-13, "reference_max_step": 0.015, "common_arclength_samples": 500, "maximum_baseline_vs_strict_position_difference": 2.0066174350131954e-10, "maximum_actual_serialized_samples_vs_strict_difference": 2.0066174350131954e-10, "endpoint_assignments_agree": true }, "candidate_orbits_omitted_for_complexity": [] }, "p1n1x2": { "passed": true, "charges": [ 2, -2, 1, -1 ], "positions": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ -1.0, 0.0, 0.0 ], [ 0.0, -1.0, 0.0 ] ], "actual_serialized_viewer": { "passed": true, "separate_line_traces": 36, "arrow_count": 36, "arrow_points_on_correct_curves": true, "minimum_arrow_independent_field_cosine": 0.9999999999999998, "verified_actual_charge_markers": 4, "html_filename": "electric_field_3d_p1n1x2.html", "html_sha256": "9f682894e8359eeeff4c30a836412f3009b35c805e093c865d2fd74167da44d0" }, "physical_curves": { "passed": true, "errors": [], "curve_count": 36, "actual_charge_endpoint_counts": [ 24, 24, 12, 12 ], "expected_charge_endpoint_counts": [ 24, 24, 12, 12 ], "actual_infinity_curve_count": 0, "expected_infinity_curve_count": 0, "source_to_sink_counts": { "0 -> 1": 12, "0 -> 3": 12, "2 -> 1": 12 }, "worst_tangent_angle_degrees": 0.014312925405516628, "curves": [ { "curve_index": 0, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999982770444, "maximum_tangent_angle_degrees": 0.003363370167455675, "maximum_scaled_magnitude_error": 9.688831796780658e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999964, "infinity_certificate": null, "passed": true }, { "curve_index": 1, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999982770444, "maximum_tangent_angle_degrees": 0.003363370167455675, "maximum_scaled_magnitude_error": 9.688831796780658e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999964, "infinity_certificate": null, "passed": true }, { "curve_index": 2, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999882842417, "maximum_tangent_angle_degrees": 0.008770469276084835, "maximum_scaled_magnitude_error": 6.666141910743181e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999964, "infinity_certificate": null, "passed": true }, { "curve_index": 3, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999882842417, "maximum_tangent_angle_degrees": 0.008770469276084835, "maximum_scaled_magnitude_error": 6.666141910743181e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999964, "infinity_certificate": null, "passed": true }, { "curve_index": 4, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999882842417, "maximum_tangent_angle_degrees": 0.008770469276084835, "maximum_scaled_magnitude_error": 6.666141910743181e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000134, "infinity_certificate": null, "passed": true }, { "curve_index": 5, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999882842417, "maximum_tangent_angle_degrees": 0.008770469276084835, "maximum_scaled_magnitude_error": 6.666141910743181e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000134, "infinity_certificate": null, "passed": true }, { "curve_index": 6, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999946095937, "maximum_tangent_angle_degrees": 0.00594906046187308, "maximum_scaled_magnitude_error": 8.183113463451126e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 7, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999946095937, "maximum_tangent_angle_degrees": 0.00594906046187308, "maximum_scaled_magnitude_error": 8.183113463451126e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 8, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999801642988, "maximum_tangent_angle_degrees": 0.011411990715694464, "maximum_scaled_magnitude_error": 7.657012013028942e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 9, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999801642988, "maximum_tangent_angle_degrees": 0.011411990715694464, "maximum_scaled_magnitude_error": 7.657012013028942e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000006, "infinity_certificate": null, "passed": true }, { "curve_index": 10, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999801642988, "maximum_tangent_angle_degrees": 0.011411990715694464, "maximum_scaled_magnitude_error": 7.657012013028942e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000054, "infinity_certificate": null, "passed": true }, { "curve_index": 11, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999801642988, "maximum_tangent_angle_degrees": 0.011411990715694464, "maximum_scaled_magnitude_error": 7.657012013028942e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000054, "infinity_certificate": null, "passed": true }, { "curve_index": 12, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999933906787, "maximum_tangent_angle_degrees": 0.0065874307583057646, "maximum_scaled_magnitude_error": 6.137556074252399e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": null, "passed": true }, { "curve_index": 13, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999933906787, "maximum_tangent_angle_degrees": 0.0065874307583057646, "maximum_scaled_magnitude_error": 6.137556074252399e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": null, "passed": true }, { "curve_index": 14, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999758987662, "maximum_tangent_angle_degrees": 0.012579323005250845, "maximum_scaled_magnitude_error": 7.614084469663957e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": null, "passed": true }, { "curve_index": 15, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999758987662, "maximum_tangent_angle_degrees": 0.012579323005250845, "maximum_scaled_magnitude_error": 7.614084469663957e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": null, "passed": true }, { "curve_index": 16, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999758987662, "maximum_tangent_angle_degrees": 0.012579323005250845, "maximum_scaled_magnitude_error": 7.614084469663957e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999996, "infinity_certificate": null, "passed": true }, { "curve_index": 17, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999758987662, "maximum_tangent_angle_degrees": 0.012579323005250845, "maximum_scaled_magnitude_error": 7.614084469663957e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999996, "infinity_certificate": null, "passed": true }, { "curve_index": 18, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999872548502, "maximum_tangent_angle_degrees": 0.009147661872227729, "maximum_scaled_magnitude_error": 5.64283192774782e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 19, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999872548502, "maximum_tangent_angle_degrees": 0.009147661872227729, "maximum_scaled_magnitude_error": 5.64283192774782e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 20, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999861729345, "maximum_tangent_angle_degrees": 0.009528019574462202, "maximum_scaled_magnitude_error": 7.5893630488521e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": null, "passed": true }, { "curve_index": 21, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999861729345, "maximum_tangent_angle_degrees": 0.009528019574462202, "maximum_scaled_magnitude_error": 7.5893630488521e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": null, "passed": true }, { "curve_index": 22, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999865542258, "maximum_tangent_angle_degrees": 0.009395730189251378, "maximum_scaled_magnitude_error": 6.472211887927421e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": null, "passed": true }, { "curve_index": 23, "source_index": 0, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999865542258, "maximum_tangent_angle_degrees": 0.009395730189251378, "maximum_scaled_magnitude_error": 6.472211887927421e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.030000000000000002, "infinity_certificate": null, "passed": true }, { "curve_index": 24, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999687980632, "maximum_tangent_angle_degrees": 0.014312925405516628, "maximum_scaled_magnitude_error": 6.856639241590214e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 25, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999687980632, "maximum_tangent_angle_degrees": 0.014312925405516628, "maximum_scaled_magnitude_error": 6.856639241590214e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 26, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999687980632, "maximum_tangent_angle_degrees": 0.014312925405516628, "maximum_scaled_magnitude_error": 6.856639241590214e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999985, "infinity_certificate": null, "passed": true }, { "curve_index": 27, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999687980632, "maximum_tangent_angle_degrees": 0.014312925405516628, "maximum_scaled_magnitude_error": 6.856639241590214e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999985, "infinity_certificate": null, "passed": true }, { "curve_index": 28, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999776509169, "maximum_tangent_angle_degrees": 0.012113439835258418, "maximum_scaled_magnitude_error": 6.572180242965823e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 29, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999776509169, "maximum_tangent_angle_degrees": 0.012113439835258418, "maximum_scaled_magnitude_error": 6.572180242965823e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.029999999999999992, "infinity_certificate": null, "passed": true }, { "curve_index": 30, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999776509169, "maximum_tangent_angle_degrees": 0.012113439835258418, "maximum_scaled_magnitude_error": 6.572180242965823e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 31, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999776509169, "maximum_tangent_angle_degrees": 0.012113439835258418, "maximum_scaled_magnitude_error": 6.572180242965823e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999995, "infinity_certificate": null, "passed": true }, { "curve_index": 32, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999925325469, "maximum_tangent_angle_degrees": 0.007002028632710589, "maximum_scaled_magnitude_error": 5.919868404408772e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": null, "passed": true }, { "curve_index": 33, "source_index": 2, "endpoint_charge": 1, "termination": "charge", "minimum_tangent_cosine": 0.9999999925325469, "maximum_tangent_angle_degrees": 0.007002028632710589, "maximum_scaled_magnitude_error": 5.919868404408772e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.03000000000000004, "infinity_certificate": null, "passed": true }, { "curve_index": 34, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999925325469, "maximum_tangent_angle_degrees": 0.007002028632710589, "maximum_scaled_magnitude_error": 5.919868404408772e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999988, "infinity_certificate": null, "passed": true }, { "curve_index": 35, "source_index": 0, "endpoint_charge": 3, "termination": "charge", "minimum_tangent_cosine": 0.9999999925325469, "maximum_tangent_angle_degrees": 0.007002028632710589, "maximum_scaled_magnitude_error": 5.919868404408772e-16, "maximum_independent_potential_increase": 0.0, "minimum_positive_source_distance": 0.02999999999999988, "infinity_certificate": null, "passed": true } ], "line_density_interpretation": "Counts are proportional to both source/sink charge magnitudes; arbitrary displayed source directions do not calibrate local flux-tube cross-sectional area." }, "actual_source_symmetries": { "passed": true, "errors": [], "actual_group_order": 4, "transformations": [ { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 1.0, 0.0, 0.0 ], [ 0.0, 1.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": 1, "source_mapping": [ 0, 1, 2, 3 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 0.0, 1.0, 0.0 ], [ 1.0, 0.0, 0.0 ], [ 0.0, 0.0, -1.0 ] ], "charge_sign": -1, "source_mapping": [ 1, 0, 3, 2 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 }, { "matrix": [ [ 0.0, 1.0, 0.0 ], [ 1.0, 0.0, 0.0 ], [ 0.0, 0.0, 1.0 ] ], "charge_sign": -1, "source_mapping": [ 1, 0, 3, 2 ], "maximum_full_path_error": 0.0, "maximum_independent_field_scaled_error": 0.0 } ] }, "gauss_multipoles_kernel_checks": { "passed": true, "cpu_independent_reference_maximum_scaled_error": 6.534607532772306e-16, "gpu": { "requested": true, "passed": true, "maximum_scaled_error": 6.534607532772306e-16 }, "individual_source_gauss_fluxes": [ { "source_index": 0, "charge": 2.0, "expected": 25.132741228718345, "measured": 25.13274122871834, "absolute_error": 3.552713678800501e-15 }, { "source_index": 1, "charge": -2.0, "expected": -25.132741228718345, "measured": -25.132741228718338, "absolute_error": 7.105427357601002e-15 }, { "source_index": 2, "charge": 1.0, "expected": 12.566370614359172, "measured": 12.56637061435917, "absolute_error": 1.7763568394002505e-15 }, { "source_index": 3, "charge": -1.0, "expected": -12.566370614359172, "measured": -12.56637061435917, "absolute_error": 1.7763568394002505e-15 } ], "enclosing_gauss_flux": { "measured": -9.656354679545382e-16, "expected": 0.0, "absolute_error": 9.656354679545382e-16 }, "far_field": { "leading_order": "dipole", "net_charge": 0.0, "dipole_moment": [ 1.0, -1.0, 0.0 ], "quadrupole_tensor": [ [ 9.0, 0.0, 0.0 ], [ 0.0, -9.0, 0.0 ], [ 0.0, 0.0, 0.0 ] ], "radii": [ 80.0, 160.0, 320.0 ], "potential_relative_errors": [ 0.008029526074255182, 0.0039771514264221736, 0.0019790945855603314 ], "field_relative_errors": [ 0.034925257388516706, 0.01745807483806866, 0.00872759926111751 ], "measured_last_doubling_slopes": [ -1.9971088019962504, -2.9967322656377493 ], "expected_slopes": [ -2, -3 ] } }, "representative_refinement": { "passed": true, "selected_curve_index": 22, "integration_orientation": 1.0, "reference_rtol": 1e-11, "reference_atol": 1e-13, "reference_max_step": 0.015, "common_arclength_samples": 500, "maximum_baseline_vs_strict_position_difference": 9.427792512844545e-11, "maximum_actual_serialized_samples_vs_strict_difference": 2.804698938761816e-11, "endpoint_assignments_agree": true }, "candidate_orbits_omitted_for_complexity": [] } }, "independent_reference": "Scalar Coulomb superposition using math.hypot/math.fsum and 80-digit Decimal near cancellations; actual serialized line/arrow arrays, source values, field magnitudes and endpoint counts are verified.", "infinity_scope": "Each infinity curve is displayed only to a finite computed radius. A conservative global Coulomb bound below one certifies its continuation; this does not make its tail exactly radial or bound the complete omitted-tail positional error.", "line_count_scope": "Exactly twelve drawn lines per unit charge at every source AND sink, plus twelve per unit absolute net charge for infinity. Local line positions are illustrative rather than calibrated flux-tube areas." }