balanced-selection.json

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11923 bytes, as of the version from 2026-10-27 01:14 (current). Recorded here, not run.

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      "role": "order-one companion for radial derivative relations",
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  "baseline_captured_utc": "2026-10-27T00:49:03.570188+00:00",
  "rationale": "it preserves the existing order-zero extremal heights and finite initial value where present. Order zero gains the sparse references $x=1/2,1,2,3,5,8$ and $x=\\sqrt2,2\\sqrt2,4\\sqrt2$. The latter give equal integer-sized real and imaginary components in the rotated Bessel argument; this is a normalization-based reference, not a universal physical scale. Orders $1,2,3,1/2$ are sampled only at $x=1$, with order $1$ also at $x=2$, to cover adjacent integer-order relations and the elementary half-order reduction. These finite exploratory slices avoid a Cartesian grid and make no demand claim for each radius",
  "sources": [
    "https://dlmf.nist.gov/10.61",
    "https://dlmf.nist.gov/10.63",
    "https://dlmf.nist.gov/10.73"
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