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        "x": "3"
      },
      "origin": "balanced expansion",
      "stored_interval_contains_ball": true,
      "accuracy_bits": 995,
      "mpmath_160_digits": true,
      "mpmath_210_digits": true,
      "structural_checks": [
        "bessel_wronskian",
        "elementary_half_order_recurrence"
      ]
    },
    {
      "params": {
        "nu": "3/2",
        "x": "5"
      },
      "origin": "balanced expansion",
      "stored_interval_contains_ball": true,
      "accuracy_bits": 995,
      "mpmath_160_digits": true,
      "mpmath_210_digits": true,
      "structural_checks": [
        "bessel_wronskian",
        "elementary_half_order_recurrence"
      ]
    },
    {
      "params": {
        "nu": "0",
        "x": "0"
      },
      "origin": "balanced expansion",
      "stored_interval_contains_ball": true,
      "accuracy_bits": null,
      "mpmath_160_digits": true,
      "mpmath_210_digits": true,
      "structural_checks": [
        "exact_or_continuous_origin"
      ]
    },
    {
      "params": {
        "nu": "1",
        "x": "0"
      },
      "origin": "balanced expansion",
      "stored_interval_contains_ball": true,
      "accuracy_bits": null,
      "mpmath_160_digits": true,
      "mpmath_210_digits": true,
      "structural_checks": [
        "exact_or_continuous_origin"
      ]
    }
  ],
  "limitations": "Retained values are fully Arb-recomputed; new values additionally have independent mpmath and family-identity checks. Existing manual numbers and annotations are not claimed to originate in this run."
}