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1664 bytes, as of the version from 2026-10-30 06:27 (current). Recorded here, not run.
# Sources checked for the T619 repair
The coordinated instructions are recorded in
`agents/runs/20261030T061717Z-repair-skills/manifest.json` (manifest SHA-256
`f3ffe644f05a2d8ba38978976adde3737ab5de3d1ebeb214066f311233b3080e`).
Both archived local and live skills, also matching the snapshot canonical file,
have SHA-256 `28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
Read Yip and Leung, [section 5.3, equations (28)–(33)](https://arxiv.org/html/1709.02469v1#S5.SS3)
through the web reader in this run. Equation (28) gives the incompressible
apsidal constant 3/[4(ell−1)]. Equation (33) gives the spherical-Bessel
expression for the n=1 model. The recurrence
(2ell+1) j_ell(x) = x (j_(ell−1)(x) + j_(ell+1)(x)) simplifies its denominator,
and the common factor sqrt(pi/(2x)) cancels when converting to cylindrical J.
These yield the program's J_(ell+3/2)(pi)/(2 J_(ell−1/2)(pi)).
This also substantiates the retained Bessel-family relationship.
Read the [Sage RealBall accuracy documentation](https://doc.sagemath.org/html/en/reference/rings_numerical/sage/rings/real_arb.html#sage.rings.real_arb.RealBall.accuracy):
accuracy() reports relative accuracy in bits. This was also executed with
Sage 10.9 in the repair checks. The current web documentation is version 10.10;
the actual computation, not an assumption of interface compatibility, establishes
that the methods used by the program work in the recorded environment.
A separate direct urllib download of the arXiv HTML returned HTTP 403.
The successful web-reader source inspection is the source check; no downloaded
copy or source hash is claimed for that failed request.