# Build handoff: T625

Built **Volumes of real and complex Grassmann manifolds**,
https://numberdb.org/T625, in family numberdb-data#249. The draft is populated
and remains unpublished and not offered. Only the controller may advance it
through separate critique and repair. No independent acceptance sidecar was
created, and no published table was edited.

## Policy and selection

Read the family first. The coordinated skill manifest is
`agents/runs/20261030T115517Z-build-skills/manifest.json`; both archived versions
have SHA-256 `28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
Its copy and per-source hash evidence are attached to the draft.

Parameters are (field,n,k), with field real or complex. Stored coverage is both
fields, every 2 <= n <= 16 and 1 <= k <= floor(n/2): 128 entries. The intrinsic
domain is 1 <= k < n. Complementation is an isometry. The definition fixes the
half-projector Frobenius metric and unoriented real spaces, matching T624.
`argument-selection.md` justifies every parameter as a discrete geometric
index and the noncanonical practical bound, with breadth across ranks before
depth in dimension. There are no extra sampled continuous arguments.

The family settled the metric, indexing and extent. This build retained them,
chose exact rational-times-pi-power reduction, 397 working bits with a 64-bit
guard, and used the Plücker degree/tableau identity as an additional independent
check for the complex coefficients. It chose no alternate orientation or scale.

## Evidence and outcomes

* `preflight.json`: already_here, already_asked, and live corpus searches.
  The requested family was absent; related hits do not store this volume family.
* `lookup-tags-urls.json`, `verified-slugs.json`: three sample numerical lookups,
  existing tags, and slugs read from live pages. T9, T27, T28, T549, T550, T552,
  T571, T572 and T624 were read. Draft T624 is linked with an explicit quotient
  relation. No unbuilt companion was assigned an identifier.
* `dry-run.log`: all 128 entries passed exactness, prose and size checks.
* `local-checks.json`, `stored-checks.json`: all 128 generating balls are
  contained by the 100-significant-digit serialized intervals, with at least
  390 bits of relative accuracy. Independent 600-bit Gamma and sphere-recurrence
  group quotients also fit inside all written intervals. All complementary
  checks passed. All 64 complex rational coefficients agree exactly with
  recursive standard-tableau counts. All 112 available ambient-dimension
  recurrence comparisons passed. Metric checks covered 4896 tangent coordinates
  and their pairwise Gram entries, plus real skew-block determinant factors.
* Stored-value comparisons: 128 T624 frame/fibre quotients, 30 T572 pure-state
  volumes, 30 rescaled T571 pure-state volumes and 30 T27/T28 controls passed.
  Finite-width and positivity gates, known-answer controls and a deliberately
  corrupted value were checked first.
* `program-check.log`: the page's Programs snippet agrees for all 128 rows.
* `verify.log`: **128/128 matched, 0 differing, 0 missing, 0 extra**.
  Sage 10.9, numberdb 0.1.10, Python 3.12.3.
* The longest serialized value is 107 characters; the exact flat Numbers block
  is 21,208 bytes of YAML. The helper's generic-key estimate is 19.46 KiB.
* `mathematical-checks.md`: source locators, metric derivations, independent
  methods and limitations. `check-development-notes.md` records two corrected
  checker mistakes; neither required changing values or enumeration.

## Audit and outstanding independent judgment

The site audit found only its structural question about `field=real|complex`.
`audit.json` honestly retains **clean=false**. `audit-disposition.md` explains
why field is an argument specifying the manifold and every row stores one
quantity G_F(n,k), consistent with the family and the value-column heading.
The critic should independently assess this rationale; no source-code bypass
or artificial parameter encoding was used to silence it.

The absent Riemannian geometry tag is recommended for T624, T625, T571 and
T572. This draft uses existing volume, groups and integral tags. No existing
tables were changed to add a tag or backfill links.

## Reproduction and critique

The draft carries generate.py, check_values.py, the unmodified campaign check.py,
argument-selection.md, mathematical-checks.md and numerical/policy evidence.
The generator has no selection or numerical source dependencies outside itself
and the named installed numberdb/Sage libraries. It has no data-file inputs.
The checker imports generate.py and check.py; keep those beside it.

Run through agents/sage.sh on this machine. Ordinary contributors can use
`sage -python generate.py` for verification and `sage -python check_values.py
--stored` for independent stored checks, with an API key when the table is
private. No checking command publishes or offers it.

The separate critique must freshly fingerprint the live selection and
`generate.py`, assess every parameter, perform its own numerical checks, and
write its own required -arguments.json sidecar with its reviewer_run. The
build-fingerprint.json artifact is a read-only baseline, not acceptance.
The required build.table.json handoff names only T625, the draft filled here.