{
  "date": "2026-10-27",
  "method": "Official DLMF pages opened with the native web tool during this session; notes distinguish source-backed mathematics from our exploratory finite selections.",
  "research": [
    {
      "tables": [
        "T490",
        "T491",
        "T493",
        "T509"
      ],
      "urls": [
        "https://dlmf.nist.gov/10.61",
        "https://dlmf.nist.gov/10.63",
        "https://dlmf.nist.gov/10.73"
      ],
      "source_support": "Rotated Bessel definitions, including the order-dependent phase for ker/kei; integer-order derivative relations and elementary half-order cases.",
      "selection_judgment": "Order-zero sparse rational radii and x=sqrt(2),2sqrt(2),4sqrt(2) cover the common pair and equal-component complex Bessel inputs. Unit-argument adjacent orders and a half-order example add breadth without a full order/radius product. No universal physical scale is claimed."
    }
  ]
}