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6309 bytes, as of the version from 2026-10-26 19:23 (current). Recorded here, not run.
# Build handoff: T524
Built and filled **Moments of the absolute Brownian bridge area**,
https://numberdb.org/T524, slug `Moments_of_the_absolute_Brownian_bridge_area`.
It remains an unpublished draft, not offered for review. The separate critique
and repair stages, followed by the controller's offer, are still required.
Builder run: `20261026T191343Z`. Family: numberdb-data issue 214.
## Scope and decisions
The sole parameter is the positive integer raw moment order n. The entries
are n=1,...,12 in ascending order, with M_0=1 used only as a control. The
process is the zero-endpoint centered Gaussian bridge of covariance
min(s,t)-st on [0,1]; absolute value is inside the area integral. There are
no free continuous parameters. Twelve is an editorial initial cutoff of a
discrete sequence, not an intrinsic order. See attached argument-selection.md.
Six even moments are exact rationals. Six odd moments have 100-significant-
digit enclosures formed from exact rational multiples of sqrt(pi/2).
The first moments are sqrt(pi/2)/4, 7/60, 21 sqrt(pi/2)/512 and 19/720.
Working precision was 513 bits, with at least 509 bits of relative accuracy.
The longest serialized value is 104 characters; the measured entries block
is about 1.12 KiB. No ranges were enlarged to fill space.
No unsettled normalization was guessed. Brownian scaling follows directly:
sqrt(T)b(t/T) has covariance min(s,t)-st/T, and substituting t=Tu in the
area integral supplies T^(3/2). Thus each n-th raw moment scales by T^(3n/2).
## Checks actually completed
- Re-read issue 214, ran already_here and already_asked, searched the live
corpus and neighbours, and performed API lookups of the mean, 7/60 and
19/720. No duplicate bridge-area family was found. The title claim created
T524, and its twelve values were sent in one generator fill.
- Read Janson's paper, especially (135), (149), Table 2, the Airy coefficient
formulas (104)-(107), (137), and Appendix C.2. PDF and page images are
preserved locally with source-evidence.json.
- Ran the repository dry-run checker, including exactness, prose and size.
- Independently solved the polynomial coefficient equations of the
Feynman-Kac resolvent through order 12 with Python Fraction arithmetic;
independently divided the factorial Airy asymptotic series through order
12. Both agree exactly with every D coefficient, including order zero.
- Recovered the mean from the folded-normal marginal expectation and beta
integral. Checked the first four positive moments against Table 2.
- Ran controls first: P0=1, P1=-(1+x+x^2)/2, M0=1 and standard Gamma values.
Checked finiteness and narrowness before trusting ball comparisons.
- Checked all twelve serialized intervals against 768-bit independent
enclosures, and strict log-convexity at all eleven interior orders.
- Ran the displayed Programs snippet at every stored order.
- After filling, verify(sample=None) passed; all twelve values read from the
database were checked against the independent calculation. The D recurrence
was checked on intervals recovered from the stored values, with finite
residuals containing zero and radii below 10^(-90). Stored log-convexity and
the mean check passed.
- Final authenticated site audit: clean=true, findings=[].
The checks share Janson's moment/transform theory; the polynomial resolvent
algorithm and Airy-series quotient do not use the generator's recurrence.
The independent marginal mean check additionally tests the process scale.
This is build evidence, not an independent critique or review approval.
## Tags and links
Used existing `probability theory` and `integral`. The proposed `moments` tag
exists and lists T36, but the live draft audit calls it a singleton, so it was
removed for a clean audit. See environment-findings.md and both audit records.
The absent tag `Brownian motion` would fit all four family tables: excursion
area moments (T523), absolute bridge area moments (T524), absolute motion area
moments, and meander area moments. No new tag was created in this run.
T523 is an existing populated private draft, so it was read as family context
but no link to it was inserted in this draft's mathematical prose. Links to
T9's Gamma table and T201's Airy derivative table use slugs read from live
search results and checked by the site audit. No published table was edited.
No GitHub request provenance was added to mathematical prose.
## Instruction and selection evidence
Read the canonical local skill, both archived skill versions, and the freshly
fetched live /skill. All four byte streams agree with the archived manifest:
`agents/runs/20261026T191343Z-build-skills/manifest.json`.
SHA-256 for both versions:
`b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18`.
The manifest is also cited in numerical-evidence.json and stored-evidence.json;
full read/hash evidence is attached as skill-read-evidence.json.
Builder fingerprint: build-fingerprint.json. Selection SHA-256:
`c296cecb699ed8db81b22df88df332e913f6d02d38eafe38016908fc3c1f0299`.
The separate critic must inspect the live draft and attachment bytes, perform
its own argument and numerical checks, and obtain a fresh fingerprint:
python3 agents/argument_review.py fingerprint T524 --generator generate.py --generator checks.py --generator check.py --generator argument-selection.md
Only generate.py determines enumeration; it imports no local helper. The
additional files bind the supplied checks and selection justification. No
independent -arguments.json acceptance was created by this builder.
## Artifacts
Attached reproducible generator, checks.py, unchanged repository check.py,
argument-selection.md, numerical-evidence.json, stored-evidence.json,
skill-read-evidence.json, dry-run.txt, program-check.txt, source-evidence.json,
and this handoff. Build-working artifacts and failures are preserved in
`agents/runs/20261026T191343Z-build-work/`; nothing was deleted to make space.
Sage 10.9, Python 3.12.3, numberdb 0.1.10 were used for numerical work.
The required controller handoff is
`agents/runs/20261026T191343Z-build.table.json`, containing only `{"tid":"T524"}`.
The family checklist remains under controller ownership for the later stages.
No commit, push, deployment, publication, review or offer was performed.