{
  "table": "T618",
  "checks_passed": true,
  "sage_version": "10.9",
  "skill_manifest": "agents/runs/20261030T052522Z-repair-skills/manifest.json",
  "skill_versions": [
    {
      "source": "local",
      "file": "skill-local.md",
      "sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199",
      "verified_sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199",
      "bytes": 58218
    },
    {
      "source": "live",
      "file": "skill-live.md",
      "sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199",
      "verified_sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199",
      "bytes": 58218
    }
  ],
  "scope": "Index-one analytic claim and comment only; no other ODE integrations rerun.",
  "profile": "sin(xi)/xi",
  "lane_emden_residual": "0",
  "central_value": "1",
  "central_derivative": "0",
  "second_derivative_at_pi": "2/pi^2",
  "mass_at_pi": "pi",
  "coefficient": "2/pi",
  "independent_ball_bits": 500,
  "independent_ball": "[0.636619772367581343075535053490057448137838582961825794990669376235587190536906140360455211065012343824291370907031832147571647384458314611511869642927 +/- 7.17e-151]",
  "stored_ulp": "1/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
  "difference_in_stored_ulps": "[0.24291370907031832147571647384458314611511869642927 +/- 8.71e-51]",
  "stored_interval_contains_independent_ball": true,
  "stored_interval_contains_generator_ball": true,
  "ordered_enumeration": [
    {
      "n": "1/2"
    },
    {
      "n": "1"
    },
    {
      "n": "3/2"
    },
    {
      "n": "2"
    },
    {
      "n": "5/2"
    },
    {
      "n": "3"
    },
    {
      "n": "7/2"
    },
    {
      "n": "4"
    },
    {
      "n": "9/2"
    }
  ],
  "numbers_and_parameters_unchanged": true,
  "generator_changed_only_returned_comment": true,
  "revised_comment": "The index-one profile $\\theta_1(\\xi)=\\sin(\\xi)/\\xi$ gives $N_1=2/\\pi$.",
  "source": "https://www.astro.princeton.edu/~gk/A403/polytrop.pdf (poly.6), (poly.9), (poly.11b)"
}