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# Argument selection for T529
The only free parameter is the positive integer moment order n, of type Z.
It is a discrete index of one quantity: the raw moment E[A^n] of the
positive-part Brownian bridge area. It is not an evaluation grid for a
continuous function or a selector between different statistics.
The model is the centered Gaussian bridge on [0,1] with covariance
min(s,t)-st. Its endpoints are zero, its duration is one, its underlying
Brownian motion has variance t and generator (1/2)d²/dx², and its barrier
is zero. Positive part means max(b(t),0) before integration. These are the
standard normalized process and area in Janson (2007), Section 24, equations
(236)–(240), and Appendix C.2, equations (364)–(371). Brownian scaling removes
duration and variance scale; they are fixed conventions, not sampled inputs.
There is no drift, endpoint, barrier or hidden coupling parameter.
The default selection is every n from 1 through 12 in ascending order.
The first moment is the mean; orders two through four give the information
needed for variance, skewness and kurtosis. The whole sequence supplies the
Taylor coefficients (-1)^n E[A^n]/n! of the Laplace transform at zero, and its
Gamma-weighted transform expansion in Janson equations (239)–(242). These
expansion coefficients justify the higher positive orders. Twelve is a short
initial editorial depth, not an intrinsic cutoff or a target count borrowed
from another table. The trivial zeroth moment is a formula and control.
The parameter domain stays n >= 1; the completeness note records 1 <= n <= 12.
No quantiles, percentiles or conventional critical values are included.
Source checked: Svante Janson, Brownian excursion area, Wright's constants
in graph enumeration, and other Brownian areas, Probability Surveys 4 (2007),
80–145, arXiv:0704.2289v3, DOI 10.1214/07-PS104. In particular, Section 24
and Table 6 identify the raw positive-part moments, rather than moments of
the absolute area or the positive part of the signed integral.
Instruction evidence: agents/runs/20261026T213949Z-build-skills/manifest.json,
archiving local and live skills at SHA-256
b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18.
The canonical file, both archived versions, and a fresh live fetch agree.
See skill-read-evidence.json for individual hashes and the manifest hash.
This is the builder's justification. The required independent argument review
belongs to the later critique session.