# Argument selection for T523

The sole free parameter is `n`, type `Z`, the positive integer order of the raw
moment E[A_ex^n]. Category: `discrete_index`. This is a sequence of moments of
one fixed distribution. Integer orders are the coefficients of its entire
Laplace transform, Janson (2007), equation (79); the mean and second moment
also determine its variance. The moments occur independently as factorial
multiples of Wright's graph-enumeration constants, equation (36).

The default enumeration is exactly n = 1, ..., 12, ascending. Twelve is an
editorial cutoff for an initial segment, not an intrinsically distinguished
order. It retains the low moments and a short sequence for moment identities
without an unneeded long listing. There are no skipped orders. The zeroth
moment 1 is a normalization control, not a stored row. The completeness note
states precisely this initial segment; the parameter domain remains n >= 1.

All continuous choices are fixed by the named standard process, not sampled.
Brownian motion has covariance min(s,t), variance t and generator (1/2)d²/dx².
The duration is 1. Each bridge is B(t)-tB(1); the excursion is the Euclidean
norm of three independent such bridges. These conventions are specified in
Janson, introduction p.83 and section 2, equations (1)-(3), and remove the
ambiguity of conditioning a process on a probability-zero event. Changing
duration to T scales the area by T^(3/2), so duration is not another parameter.
The Airy variable in Flajolet and Louchard's normalization is 2^(3/2) A_ex;
that invertible scaling is described in the table, not stored as another family.

Sources checked: S. Janson, Probability Surveys 4 (2007), 80–145,
https://doi.org/10.1214/07-PS104, https://arxiv.org/abs/0704.2289,
introduction p.83; equations (1)-(7), (36), (63)-(64), and (79); Table 1.
The Brownian excursion selection has no quantile, percentile, critical-value,
probability-grid, diffusion, drift, endpoint, or coupling parameter.

Instruction evidence: agents/runs/20261026T183502Z-build-skills/manifest.json.
Both archived versions and the canonical local skill and newly fetched live
https://numberdb.org/skill have SHA-256
b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18.
This is the builder's justification, not an independent argument review.