# Build handoff: T469

The build succeeded. The draft is **T469**, “Mean distance from a uniform random point of a region to its centroid”, at https://numberdb.org/T469. It remains unpublished and was not offered for review. The separate critique and repair stages, followed by the controller's offer action, remain outstanding. This file reports build verification and does not stand in for the independent critique.

## Scope and convention

One symbolic parameter, region, names thirteen standard geometric regions. Each row stores M(K)=E||X-E[X]|| for the explicitly specified uniform measure. There are eight certified 100-significant-digit decimal entries and five exact rational entries. The latter are 1/4 for the unit interval, 2/3 for the unit disk, 3/4 for the unit solid ball in R^3, and 1 for each unit circle and unit sphere.

The family issue #200 was read before corpus screening. The title was successfully claimed before computation; claim-response.json records T469 as unpublished with ready_for_review=false. There was no collision. already_here and already_asked were run; square and cube sample-value lookups were empty, and the rational disk value matched unrelated tables only. T467 is the related two-point-distance draft, with a different defining quantity. No published table was edited, and no batch-exhausted marker was made.

Choices left to the builder:

* A short set of classical low-dimensional sampling benchmarks, rather than a grid of dimensions or aspect ratios. The regular polygons cover three through eight sides, including the square and triangle.
* The triangle and square have side 1, as specified by the family. The regular pentagon through octagon have circumradius 1, matching T390's normalization and region keys. The rectangle has sides 1 and 2. The cube has side 1; all round regions have radius 1.
* Uniform measure is length/area/volume on filled regions, arc length on the circle, and surface area on the sphere. The circle and sphere use ambient Euclidean distance to their centroids, which is constant 1.
* Exact rational spelling takes precedence over the family's older suggestion to write every row as a decimal. The local/live skill and artifact policy require this.
* The proposed geometric probability tag does not exist. Existing probability theory, elementary geometry and integral tags are used. A new shared tag would apply to T467, T468, T469, T19 and T283; this run did not create or retrofit it.
* HREF{T467} uses the authoritative T-number read from the family and table API. The authenticated table API supplies its document but no slug, and the website page returns 404 for this draft. The local audit implementation explicitly supports T-number HREFs. This avoids inventing a slug. T469 and T467 are both drafts; eventual publication should account for their link dependency.

## Verification performed

* dry_run.py: 13 entries, no exactness or prose complaints; longest working-precision entry 142 characters, block about 3 KB. Actual stored number strings are at most 102 characters.
* Every irrational value was evaluated throughout in Arb at 413 bits (100 decimal digits plus 80 guard bits). Largest radius: 4.298304014e-124. All balls are finite, with relative radius below 1e-120.
* Independent geometric quadratures at 130 and 170 decimal digits, for every region. Normalization and second-moment controls precede the mean comparisons. Scaling by 3/2 is checked throughout. All comparisons pass at absolute tolerance 1e-120.
* Direct uniform sampling, 300000 points per region with seed 46920261024. Centroid and second-moment controls pass, as do mean comparisons, under a predetermined six-standard-error limit. The largest mean discrepancy is 2.680 standard errors. These are low-precision independent checks of the geometry, not a source of stored digits.
* The displayed program was executed and checked for all six regular-polygon cases with their actual normalizations. The general rectangle formula was checked for both stored rectangles. Simplified triangle and hexagon comments agree with the independent quadratures.
* After the full document was sent once, every database entry was read back. Exact decimal parsing verified that each whole Arb ball lies inside the stored decimal interval; every independent quadrature value also lies inside its stored interval.
* Generator.verify(sample=None): 13/13 matched, 0 differing, 0 missing, 0 extra.
* The authenticated site audit returned findings=[] and clean=true. The audit API does not perform the database command's optional outward-link checks. Sources were read independently as documented in sources-and-derivations.md.
* The unauthenticated table API still conceals T469. No offer, review, publication or queue-completion action was taken.

## Authoritative and local artifacts

The website database holds the final mathematical document, entries, generator and checks. The document and numbers were assembled locally, using the numberdb client's number serializer on the checked generator values, then submitted in one complete-document write. The package's whole-document endpoint requires entries, so the initial empty title claim was not repeatedly edited during development. Attachment uploads share a run identifier. All source and numerical work was done privately before that write.

Main local files: generate.py, checks.py, final-document.yaml, numbers.json, stored-document.json, dry-run.log, checks-local.log, checks-stored.log, program.py, check_program.py, program-check.log, audit.json, convention.md and sources-and-derivations.md. The copied check.py and dry_run.py are the unchanged repository helpers. The source PDFs, screening evidence and response receipts are retained here too. lessons.md records the explicit attachment-manifest trap, with a reproducible control.

A harmless post-upload scripting error omitted the empty parameter dictionary in Client.request for the audit endpoint. Uploads had already succeeded. audit_readback.py corrected that call and completed the audit; no numbers or prose were resubmitted to address it. This is recorded in fill.log.

No source snapshot files, pipeline files, prompts or skills were edited. No commit, push or deployment was attempted. The controller marker 20261024T214148Z-build.table.json names only T469, the draft filled by this build.