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# Arguments for T524: absolute Brownian bridge area moments
The quantity is the raw moment M_n = E[(integral_0^1 |b(t)| dt)^n],
where b is the centered Gaussian bridge with covariance min(s,t)-st.
Absolute value is inside the integral. This is one named quantity.
The sole free parameter is the positive integer moment order n (type Z,
category discrete_index). It is the degree in the Laplace expansion
E[exp(-s A)] = sum_n (-s)^n M_n/n!. Thus these are genuine moments of a
fixed stochastic process, not samples of a continuous exponent.
The first moments give its mean and higher raw-moment summaries; the
sequence also supplies coefficients of its transform and moment identities.
Janson, Probability Surveys 4 (2007), Section 20, equations (133), (135)
and (149), defines and computes this sequence; Table 2 gives orders 0 to 4.
Source: https://arxiv.org/abs/0704.2289, DOI 10.1214/07-PS104.
The default enumeration is precisely n = 1,...,12, ascending, in agreement
with family issue 214. Twelve is an initial editorial truncation of this
infinite discrete sequence, not a distinguished moment order or a resource
limit. It retains the usual small orders and a short extension useful for
transform-coefficient comparisons. The generator, Programs example,
completeness note, and stored entries all use this domain or this truncation.
M_0 = 1 is a check and is not a stored row. No quantiles are included.
There are no free continuous parameters. Standard Brownian motion starts
at zero, has zero mean, variance t and generator (1/2)d^2/dx^2. Subtracting
t B(1) pins the endpoint at zero. Unit duration is a scale normalization:
for duration T, the bridge absolute area is distributed as T^(3/2) A,
so M_n acquires the factor T^(3n/2). No duration, diffusion coefficient,
drift, endpoint height, or coupling is sampled. These conventions agree
with Janson's introduction and Section 20 and the family conventions.
All even moments are exactly rational; odd moments are positive rational
multiples of sqrt(pi/2). The rational factors are derived before conversion
to 100-digit enclosures. No digit pattern is used to decide exactness.
Instructions read: agents/runs/20261026T191343Z-build-skills/manifest.json.
Both archived versions and the fresh live /skill have SHA-256
b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18.
This is the builder's justification, not an independent acceptance.
The separate critique must assess it and fingerprint generate.py (the only
source controlling enumeration); checks.py tests it but does not define it.