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# Argument selection for T527
The sole parameter is the positive integer moment order n, with mathematical domain n >= 1. The generator enumerates every order 1 through 12 in increasing order. This is a discrete index, not a discretized continuous input. It indexes raw moments of one fixed random variable.
The area is the integral over [0,1] of standard Brownian motion minus its minimum over the whole interval. Brownian motion starts at zero, has zero drift and covariance min(s,t), and has generator (1/2)d²/dx². Janson, section 23, equations (215)–(216), fixes this convention. The global minimum is not replaced by a running minimum, and the process is not conditioned to return to zero. Unit duration and unit variance rate remove Brownian scaling; they do not specify sampled parameters. The two meanders' random joining time is integrated with the arcsine law, not enumerated.
Positive integer orders arise as the coefficients (-1)^n E[A^n]/n! in the Laplace transform expansion. Janson's equations (221), (229), and (231)–(233) and Majumdar–Comtet's equations (72)–(74) explicitly use these coefficients. Orders 1–4 determine location, variance, skewness and kurtosis; higher orders supply subsequent expansion coefficients. Twelve is an editorial truncation of the initial sequence, not a distinguished endpoint and not a consequence of the ranges of neighboring tables. There are no gaps within the selected initial segment. The zeroth moment equals one identically and is a normalization control, not a stored row.
No quantiles, probability levels, continuous-parameter grids, recurrence coefficients, central moments or cumulants are stored. The completeness note states the selected finite range and its purpose while the parameter constraint remains n >= 1.
Sources read:
- S. Janson, Brownian excursion area, Wright's constants in graph enumeration, and other Brownian areas, Probability Surveys 4 (2007), 80–145; arXiv:0704.2289v3, section 23, equations (215)–(233), Table 5. https://arxiv.org/pdf/0704.2289
- S. N. Majumdar and A. Comtet, Airy distribution function: from the area under a Brownian excursion to the maximal height of fluctuating interfaces, J. Stat. Phys. 119 (2005), 777–826; arXiv:cond-mat/0409566, section IV, equations (72)–(75). These identify the free-boundary F-Airy law and its moment expansion. https://arxiv.org/pdf/cond-mat/0409566
Instructions: agents/runs/20261026T204019Z-build-skills/manifest.json records both archived skill versions, each SHA-256 b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18. The current canonical file and live /skill were read and have the same hash. See skill-read-evidence.json. This build supplies a justification, not the separate critique's independent acceptance sidecar.