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3073 bytes, as of the version from 2026-10-26 19:01 (current). Recorded here, not run.
# Build validation for T523
The table contains raw moments of the unit-duration standard Brownian excursion
area, n = 1,...,12. It stores six exact rational moments and six 100-significant-
digit decimal enclosures of rational multiples of sqrt(pi/2). It remains an
unoffered, unpublished draft.
Instruction manifest: agents/runs/20261026T183502Z-build-skills/manifest.json,
also attached as skills-manifest.json. All four reads (canonical local file,
archived local, archived live, fresh live) agree with SHA-256
b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18.
The named-ring generator uses an exact rational Takács recurrence. The measured
working precision is 513 bits, minimum odd-row accuracy 510 bits. The decimal
writer's 100-digit intervals strictly contain the independently recomputed
768-bit enclosures. The longest stored number is 102 characters, and the
serialized twelve-value block is about 1.1 KiB. The longest exact rational
is the twelfth moment, 89585870372335/739346190815232 (30 characters).
Checks run with agents/sage.sh, in the isolated Sage builder:
- Repository dry_run.py and check.py: no float contamination, nonfinite
values, disguised exact decimals, or naming/prose complaints.
- Formal logarithm of the factorial series for graph enumeration, followed by
Spencer's relation, agrees exactly for moments 2 through 12 after removing
sqrt(pi/2) at odd orders. This independent computation uses no generator
helper. Sources: Janson (2007), equations (34), (36), (63), (64).
- Controls first: log(1+z), log(exp(z)), c1=5/24, c2=5/16, c3=1105/1152,
Gamma(1)=Gamma(2)=1, and M0=1.
- The mean follows from the Maxwell radial mean 2 sqrt(2/pi) times the beta
integral B(3/2,3/2)=pi/8, fixing the process normalization independently.
- Table 1 of Janson (visually inspected on PDF page 12) gives the first four
moments: sqrt(2*pi)/4, 5/12, 15*sqrt(2*pi)/128, 221/1008; all agree.
- Direct Arb evaluation of the uncancelled Gamma moment formula agrees at all
12 orders. Every comparison is preceded by finiteness and width checks.
- The standalone Programs snippet agrees for every included order.
- Read-back of the actual stored document: six exact rational equalities;
six 100-digit intervals containing independent values; twelve recurrence
residuals containing zero; eleven strictly positive log-convexity margins.
- Generator.verify(sample=None): 12/12 matched, zero differing, missing or extra.
Brownian scaling is an analytic normalization statement: if e_T(t) has the
standard excursion law on [0,T], then e_T(t) has the law of sqrt(T)e(t/T).
Changing variables in its area integral gives T^(3/2), and raising to order n
gives T^(3n/2). The Airy-variable factor 2^(3/2) is a definition checked against
Janson equation (2). Neither relation relies on a fitted numerical observation.
There is no independent critique verdict in this build. The next actor must
read argument-selection.md and bind its own review to the live selection and
attached sources using agents/argument_review.py fingerprint.