{
  "model": "Fixed isolated 3D point charges, k=q0=a=1; no softening",
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  "references": [
    {
      "title": "Fitzpatrick: Electric Field-Lines",
      "url": "https://farside.ph.utexas.edu/teaching/302l/lectures/node23.html",
      "used_for": "A field-line tangent follows E; near isolated positive/negative point charges the field points outward/inward."
    },
    {
      "title": "Feynman II, Chapter 4: Electrostatics",
      "url": "https://www.feynmanlectures.caltech.edu/II_04.html",
      "used_for": "Independent Coulomb superposition for scalar potential and vector field."
    },
    {
      "title": "Feynman II, Chapter 6, Section 1",
      "url": "https://www.feynmanlectures.caltech.edu/II_06.html",
      "used_for": "E=-grad(V); along dr/ds=E/|E|, potential must decrease as dV/ds=-|E|."
    }
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    "sampling": "symmetric",
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  "reference_implementation": "Independent Python scalar Coulomb sum using math.hypot and math.fsum, with 80-digit Decimal reevaluation for cancellation-dominated samples; never calls electrostatics.evaluate",
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    },
    "termination_counts": {
      "charge": 62,
      "null_limit": 2,
      "unresolved": 0,
      "failure": 0,
      "boundary": 0,
      "max_length": 0
    },
    "longest_curve_refinement": {
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      "seed_index": 17,
      "baseline_rtol": 1e-08,
      "baseline_atol": 1e-10,
      "baseline_max_step": 0.06,
      "reference_rtol": 1e-11,
      "reference_atol": 1e-13,
      "reference_max_step": 0.015,
      "common_arclength_samples": 500,
      "maximum_position_deviation": 2.809774433736555e-10,
      "baseline_maximum_radius_on_common_grid": 17.515649492714996,
      "reference_maximum_radius_on_common_grid": 17.515649492738575,
      "maximum_radius_difference_on_common_grid": 2.3579360686198925e-11,
      "baseline_path_length": 41.80046971959622,
      "reference_path_length": 41.80046971965535,
      "endpoint_position_difference": 6.096840534835776e-12,
      "baseline_endpoint_charge": 1,
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    },
    "null_limit_refinements": [
      {
        "source_index": 0,
        "seed_index": 0,
        "baseline_chart_radius": 0.001,
        "reference_chart_radius": 0.0005,
        "baseline_limit_point": [
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        "reference_limit_point": [
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        "limit_position_difference": 4.805933428997378e-12,
        "acceptance_limit": 1e-06,
        "passed": true
      },
      {
        "source_index": 2,
        "seed_index": 0,
        "baseline_chart_radius": 0.001,
        "reference_chart_radius": 0.0005,
        "baseline_limit_point": [
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        ],
        "reference_limit_point": [
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        ],
        "limit_position_difference": 1.4381829060994278e-12,
        "acceptance_limit": 1e-06,
        "passed": true
      }
    ],
    "passed": true
  },
  "original_tracer_termination_counts": {
    "charge": 24,
    "null_limit": 0,
    "unresolved": 0,
    "failure": 0,
    "boundary": 0,
    "max_length": 0
  },
  "passed": true,
  "scope": "Recomputed 24 default symmetric curves plus 64 explicit Fibonacci research curves; every displayed segment, independent sampled potential/field, complete reflection/charge-conjugation geometry, and actual default Plotly line/arrow arrays. Numerical validation is not an experimental measurement or a formal continuous-curve proof.",
  "interpretation": "No sampled/rendered curve connects positive charges if both audits pass. Perspective and occlusion can make distinct 3D paths appear joined in a 2D projection; the numerical audit does not identify which visual overlap a viewer noticed."
}