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5110 bytes, as of the version from 2026-10-26 20:13 (current). Recorded here, not run.
# T526 build handoff
Built **Moments of the Brownian meander area**, https://numberdb.org/T526.
The draft has twelve entries, n=1,...,12 in ascending order. Six even moments
are exact rationals; six odd moments are certified to 100 significant digits.
It remains unpublished and has not been offered, reviewed, or approved.
The controller must run the separate critique and repair stages before offering.
## Instructions and conventions
Family #214 was read before screening or computation; family-214.md preserves
it. The exact instructions are in
`agents/runs/20261026T200330Z-build-skills/manifest.json`. Both archived versions,
the canonical local file, and the freshly fetched https://numberdb.org/skill
have SHA-256 `b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18`.
The run's skill-read-sha256.json records each file, and the manifest is attached
to the draft as skill-manifest.json. Numerical evidence cites the original
manifest. No skill or pipeline source was changed.
The standard variance-t Brownian meander is constructed as the weak limit
from positive starting points, conditioned to avoid zero until time one, with
its endpoint free. The only parameter is positive integer raw moment order.
The first-twelve cutoff is editorial, not intrinsic. There are no continuous
arguments, quantiles, or critical values. This follows the family conventions;
no mathematical convention remained unresolved. See argument-selection.md.
This builder has not written an independent argument acceptance sidecar.
## Screening and sources
screening.json records `already_here`, `already_asked`, public text searches,
and initial numeric lookups. neighbors-and-tags.json adds the exact fourth
moment and symbolic third-moment lookups; neither had a hit. The first lookup
set included 1.5 as a generic numeric-search control, not an expected moment.
The family was absent. T523, T524, and T525 were read through the API as
companion tables, but were absent from public text searches and their public
pages were unavailable. They were not treated as published.
Janson's paper was downloaded as janson-0704.2289.pdf. The definition and
conditioning were checked in section 1 and Appendix C.3, the K recurrence in
(7), the moment formula in (194), and the Q recurrence in (199). Table 4
supplied the first four positive moments. The live T9 document and its search
result supplied the Gamma link's actual slug.
The table reuses `probability theory` and `integral`. The existing `moments`
tag currently reaches only T36; the companion drafts likewise omit it.
Propose the absent `Brownian motion` tag for T523 (excursion area), T524
(absolute bridge area), T525 (absolute motion area), and T526 (meander area),
when the four drafts are ready for a person's consideration. No other table
or tag was edited.
## Numerical evidence
- agents/table-build/dry_run.py passed for all twelve generated values;
the exactness and named-ring checks were clean.
- The killed-motion polynomial resolvent independently reconstructs Q_0,...,Q_12
using rational polynomial differential equations. Both ODE residuals and
boundary values were checked exactly at every order. The coefficients agree
exactly with the K/Q recurrence. See derivation.md and checks.py.
- Controls: M_0=1 and Janson Table 4's four positive moments, plus exact
interval-parser controls. Independent Gamma evaluations use Arb at 768 bits.
- All twelve final database values passed independent interval checks. Each
odd decimal's entire claimed interval contains the independent ball. All
even fractions agree exactly. Stored Q-recurrence intervals contain zero
with radius less than 10^-85. Strict log-convexity passes for n=1,...,11.
- Generator working precision: 513 bits; minimum odd relative accuracy: 509
bits. Written block: 1.118 KB; longest value: 102 characters. There are no
disguised exact values. The Programs snippet agrees at all twelve orders.
- verify(sample=None): 12/12 matched, 0 differing, 0 missing, 0 extra.
- Website audit: clean, no findings. audit.json records the response.
The attached generate.py reproduces the selection and values. checks.py is the
independent checker and imports the unchanged campaign check.py. Also attached:
argument-selection.md, derivation.md, skill-manifest.json, numerical-evidence.json,
and this handoff. The run used Sage 10.9 and numberdb 0.1.10. Numerical evidence
and source hashes are retained in this run's build-work directory.
## Next actor
Independently assess the argument selection and numerical claims. Inspect the
live draft and use agents/argument_review.py fingerprint with generate.py and
all relevant source dependencies. Here only generate.py controls selection;
checks.py and check.py support the numerical verification. The build's
fingerprint.json is a read-only hash record, not an acceptance. The critique
must make its own current fingerprint and required -arguments.json sidecar,
using its own NUMBERDB_RUN_ID. Any later changed source or selection needs a
fresh independent critique. The exact table handoff JSON names only T526.