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2264 bytes, as of the version from 2026-10-26 20:13 (current). Recorded here, not run.
# Argument selection for T526
The sole free parameter is the positive integer moment order n, declared Z with
n >= 1. It is a discrete_index, not a continuous argument sampled at integers.
The named object is the raw moment sequence of the area of the unit-duration
standard Brownian meander. Orders 1 and 2 give the mean and second moment;
all orders are coefficients (-1)^n M_n/n! of the Laplace transform. Janson,
section 22, equation (194), defines this entire sequence, and Table 4 gives
orders 0 through 4. Equations (199) and (201) give ways to compute higher orders.
The default enumeration is precisely n = 1,...,12 in ascending order. This is
an initial editorial truncation of an infinite discrete sequence, retaining its
low orders and their higher-order continuation. Twelve is not an intrinsic
mathematical cutoff. It follows family #214's scope while keeping the exact
fractions short. The domain in Parameters remains n >= 1; the completeness
note states the actual first-twelve selection and its Laplace-transform reason.
M_0=1 is a control and is not an entry. No further parameter or choice of a
quantity is encoded in a row.
The fixed normalization is standard drift-free Brownian motion with covariance
min(s,t), generator (1/2)d^2/dx^2 and unit duration, conditioned by the limit of
a positive starting point as it tends to zero, with no terminal constraint.
This is the standard meander of Janson, section 1, and Appendix C.3. Brownian
scaling removes duration: the area on [0,T] has the law T^(3/2) A_me. No drift,
diffusion, endpoint, duration, or probability grid is independently selected.
This is a moment table and contains no quantiles or conventional critical values.
Source: S. Janson, Probability Surveys 4 (2007), 80–145, sections 1 and 22,
Appendix C.3; https://arxiv.org/abs/0704.2289, DOI 10.1214/07-PS104.
Instructions read: agents/runs/20261026T200330Z-build-skills/manifest.json.
Both archived skill versions, the canonical local skill, and the freshly fetched
https://numberdb.org/skill have SHA-256
b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18.
This is the builder's justification. It is not an independent acceptance;
the separate critique must assess it and fingerprint the live attachments.