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24374 bytes, as of the version from 2026-10-30 06:27 (current). Recorded here, not run.
{
"table": "T619",
"run": "20261030T061717Z",
"skill_policy": {
"manifest": "agents/runs/20261030T061717Z-repair-skills/manifest.json",
"manifest_sha256": "f3ffe644f05a2d8ba38978976adde3737ab5de3d1ebeb214066f311233b3080e",
"versions": [
{
"source": "local",
"file": "skill-local.md",
"sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199",
"verified_sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199"
},
{
"source": "live",
"file": "skill-live.md",
"sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199",
"verified_sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199"
}
],
"canonical_sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199",
"original_sidecar_sha256": "bb01cbf8b61fd1d8522daaa8841876431af61279cd457260b12550499690764f"
},
"source": "https://arxiv.org/html/1709.02469v1#S5.SS3",
"source_equations": [
28,
33
],
"derivation": "The spherical Bessel recurrence (2ell+1) j_ell(x)=x[j_(ell-1)(x)+j_(ell+1)(x)] simplifies equation (33) to j_(ell+1)(pi)/(2 j_(ell-1)(pi)); the common sqrt(pi/(2x)) factor cancels in the cylindrical Bessel ratio.",
"original_refusal": "Use selected indices and ell=2,3.",
"program_sha256": "7d060b9f99ffa8c90018d42547b7a6417154f509ae43e825b17baf962c31bc0d",
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"environment": {
"sage": "10.9",
"python": "3.12.3",
"mpmath": "1.4.1"
},
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"all_passed": true,
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"stored_analytic_entries_checked": 4,
"all_20_identities_match_generator": true,
"limits": "No nonlinear value or production generator was changed. This repair checks all four analytic stored entries and 31 degrees of each analytic family, not the 16 unchanged nonlinear values. The independent mpmath check uses two precisions, not a rigorous independent enclosure. Arb propagates pi uncertainty in the replacement program."
}