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2143 bytes, as of the version from 2026-10-30 05:29 (current). Recorded here, not run.
{
"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)"
}