# Build handoff: T508

Built **Multiple zeta values of length 5**, https://numberdb.org/T508, as an unpublished, unreviewed draft. It has not been offered for review. The separate critique and repair stages remain for the controller. Only this draft was written; no published tables were changed. The controller owns the proposal-queue update.

## Scope and conventions

Read family issue #199 first, both the live `/skill` and the local canonical skill, and `docs/design/guarding-generated-tables.md`. Screening with `already_here`, `already_asked`, and three numerical API lookups found no length-five table. T53, T54, T465 and T14 supply the existing neighbouring families. All four proposed tags exist. Search-result slugs and the destination documents were read before linking.

The draft holds all 462 integer tuples with s1 >= 2, the remaining four indices >= 1, and total weight <= 12. The definition uses strictly descending summation indices; Sage's arguments are reversed. Parameter order is s1, s2, s3, s4, s5. The full domain is in Parameters; the finite weight range is in Data properties. One named quantity is stored.

The family already settled the mathematical convention, weight limit, precision and rigour. Additional editorial choices were lexicographic enumeration, explicit symbols in the column headings, links to the lower-depth tables, and comments on zeta(2,1,1,1,1) = zeta(6) and zeta(2,2,2,2,2) = pi^10/11!. The first equality has a captioned entry link to T14#6. No new tag was needed and no convention was guessed.

## Computation and actual checks

- Sage 10.9, Python 3.12.3, PARI 2.17.1, numberdb 0.1.10. All Sage runs used `agents/sage.sh`.
- PARI's `zetamultall`, through Sage's `MultizetaValues`, was freshly recomputed at 150 and 200 decimal working digits, each with 16 guard bits. The minimum relative agreement was 155.05598 decimal digits. This explicitly rebuilds the singleton cache at each precision.
- The stored precision is 100 significant digits, with rigour `heuristic (agreement-checked)`, matching the family. No fixed-precision value was called a proven enclosure.
- An independent algorithm evaluates iterated integrals split at 1/2 using 650 terms of multiple-polylogarithm series in 550-bit Arb arithmetic. The omitted tail is bounded by sum(n^11 * 2^-n, n > 650), less than 1.938e-165. Every reference enclosure is finite and positive, with relative radius below 1e-125, and fits strictly within its written decimal interval.
- Seven known-value controls passed. Two deliberately wrong controls and a ten-last-place-unit displacement of each of the 462 decimals failed comparison as required.
- All seven weight-sum identities (weights 6 through 12) and both displayed special values passed against ordinary Arb zeta and pi.
- Ran the repository's unchanged `dry_run.py` and checks for exactness, prose, disguised exact values and named imports. No complaints. The longest serialized value is 107 characters. The actual named-parameter entries YAML is 87,120 bytes; the generic measurement helper estimates 69.29 KiB using a single synthetic key.
- Tested the displayed Sage program on all 462 indices.
- Sent the document and all generator-produced numbers in one fill. `verify(sample=None)` reported **462/462 matched, 0 differing, 0 missing, 0 extra**.
- Repeated all 462 independent enclosure comparisons, the seven sum identities, both special values and the failure controls on the values read back from the API.
- The authenticated site audit returned `findings: []`, `clean: true`.
- Downloaded seven attached source/evidence files and verified byte-for-byte equality with the local artifacts. Anonymous API access still hides the draft.
- Inspected a live preview of the definition, parameter labels, formulas, comments, metadata and both annotated rows. Chromium/MathJax reported no errors or warnings. The full stored document did not fit the deployed preview's 4094-byte request-line limit; the preview omitted the rigour-details paragraph, Similar tables, Programs and Keywords. The full document was audited, and Programs was executed separately.

## Reproducible artifacts

Attached to the website: `generate.py`, `checks.py`, unchanged shared `check.py`, `document.json`, `fill_once.py`, `versions.json`, `build-evidence.json`, `stored-evidence.json`, `audit.json`, and `program-checks.log`. The generator and independent checker were adapted from the published attachments of T465, with attribution in their docstrings. The mathematical source is Henrik Bachmann's *Multiple Zeta Values*, version 15 (2025), especially Sections 1.2 and 2.1, Propositions 1.8 and 2.5, and Theorem 4.3. The independent checker uses no PARI values for its references.

All source snapshots, logs, per-entry enclosures, preview evidence, and attachment hashes are retained in this work directory. No Git operations, deployment, publication or review actions were performed.

## Environment observations

The builder's installed client lacks the repository client's `provenance_headers` helper. The first fill wrapper stopped at import, before writing anything. Removing that optional import allowed the same checked values to be submitted; assistant provenance was set explicitly. Both attempt logs are retained. The live preview rejects request lines over 4094 bytes. These are deployment observations, recorded as artifacts rather than edits to environment documentation.