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3015 bytes, as of the version from 2026-10-28 01:47 (current). Recorded here, not run.
# Argument selection for T568
This build follows the archived canonical skill recorded in
`agents/runs/20261028T013533Z-build-skills/manifest.json`. Both the local and
live copies have SHA-256
`e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
The same manifest is attached as `skill-manifest.json`. This document is the
builder's justification, not an independent critique or acceptance sidecar.
The only free table parameter is the nonnegative integer `k`, the order of an
asymptotic correction. Its category is `discrete_index`. DLMF 10.41.5–10.41.9
identifies this index in the large-order expansions of the derivatives of the
modified Bessel functions. The polynomial indeterminate `p` is retained
symbolically, with every exact rational coefficient, and is not sampled.
There is no hidden choice of z, nu, evaluation points, branch or probability.
For interpreting the expansion we use positive real z and positive roots,
p=(1+z^2)^(-1/2), as DLMF 10.41(ii) specifies. Prime on the Bessel function
means differentiation with respect to its full argument.
The default enumeration is every k=0,1,...,12 in increasing order. It gives
successive corrections without holes and contains the complete polynomial at
each order, through degree 36. The bound 12 is a noncanonical editorial
choice: it covers an initial sequence of small and intermediate corrections
while retaining readable expanded coefficients. The largest polynomial is
702 characters; the measured flat block is about 3.8 KiB. Storage is not the
reason to extend the prefix further. The companion U_k family, these
V_k derivative coefficients, and the separate fixed-order a_k and b_k
families cover different asymptotic uses; covering those distinct objects
has priority over deeper orders in just one. This is not a famous-points
selection, an exploratory numerical grid, or a Cartesian product.
The family domain in Parameters remains k >= 0. The finite selection and its
rationale are stated in complete-note with complete: no. The generator and
Programs snippet both enumerate exactly range(13). V_k is one named
quantity; it is not pooled with U_k under a form selector. Differentiation
is a relation between the two families, not an invertible normalization.
Sources actually checked: NIST DLMF 10.41(ii), especially equations
10.41.5–10.41.9 and the explicit V_1,V_2,V_3 in 10.41.11;
https://dlmf.nist.gov/10.41#ii. The independent coefficient computation uses
the differentiated integral in DLMF 10.32.9,
https://dlmf.nist.gov/10.32#E9. The proposal's cutoff was reassessed against
the current skill and retained after the exactness and size measurements.
All selection-controlling generator code is in generate.py; it has no
imported local source or input-data dependencies. checks.py and check.py
provide validation rather than selection. Independent critique must inspect
the live enumeration, all source dependencies and this justification and
create its own fingerprinted sidecar under its own reviewer_run.