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# Build handoff: T456
Table: [Quantiles of the Kolmogorov distribution](https://numberdb.org/T456).
Family: numberdb-data #197. Run: 20261016T065906Z-build.
Status: filled draft, unpublished, not offered for review. Separate critique
and repair stages remain the controller's responsibility.
## What was built
Fourteen lower-tail quantiles of the limiting scaled two-sided
Kolmogorov-Smirnov statistic, in ascending exact-rational probability order.
The probability selection and kappa_p notation follow the family. Every
entry has 100 significant digits with proven enclosures. The domain is
0 < p < 1; the finite selection and its significance-level motivation are
stated separately in Data properties.
The draft was claimed empty as T456 before numerical work. It was filled
once. A subsequent metadata edit supplied the dedicated parameter-selection
field requested by audit; no numbers changed.
## Checks actually run
- Repository dry_run.py: all 14 entries, exactness/enclosure check, generator
named imports, value lengths and block size. No complaints.
- Arb rational-endpoint bisection with an alternating-series tail bound.
Working precision: 461 bits, with adaptive increases if needed. The least
retained precision was 110 decimal digits before rounding to 100.
- Independent MPFI transformed-positive-series evaluation at 560 bits with
a geometric tail bound. For all 14 written intervals, F(lower) < p < F(upper).
- Known nonzero control F(sqrt(pi/2)) = Gamma(1/4)/(2*pi)^(3/4): both CDF
implementations overlapped the independent gamma value, with all widths
less than 1e-135. Also F(0)=0.
- Every interval shifted upward by 100 last-place units was rejected by a
positive lower-endpoint residual. Strict monotonicity and upper-tail
conversion passed over all entries.
- mpmath theta inversion at 130 working digits: every value was within one
last-place unit of its stored decimal; maximum was 0.498562752659 units.
- SciPy 1.17.1 ppf: maximum absolute difference 1.7763568394002505e-15.
- Generator.verify(sample=None): 14/14 matched, 0 differing, 0 missing, 0 extra.
- The independent checks were repeated against every value fetched from the
website. All 14 passed; stored-evidence.json records them. The final saved
document's values were also compared exactly with those checked strings.
- Authenticated site audit: clean=true, findings=[] after the single metadata
finding was addressed. audit-initial.json preserves the original finding.
Final written values: maximum 102 characters, approximately 1.90 KB as
measured by the shared measure helper.
## Decisions and limits for the next stage
The two-sided KS statistic uses p=1-alpha, without halving alpha. No new
probability grid, finite-sample correction, or one-sided-statistic convention
was introduced. The mpmath and SciPy Programs examples were exercised.
The probability theory tag exists and is used. The statistics tag exists
but currently has no tables, so it was not activated by this build. T452,
T453, T454, T455 and T456 would together justify that subject heading.
T454 and T455 are filled drafts readable with the bot key; their unauthenticated
pages returned 404. The family requests links among its tables, so T456 links
them with verified stable T-number identifiers. These dependencies must be
resolved before T456 is published. No studentized-range table was found;
there is no invented link to that remaining proposal.
The family queue was not marked built by this stage. The controller can do
that after the separate critique/repair workflow; no issue was closed or
commented on. No review, offer, or publication endpoint was called.
## Reproduction and evidence
The website attachments include generate.py, checks.py, the shared check.py,
numerical-evidence.json, stored-evidence.json, audit.json, build-notes.md and
this handoff. Download them together; the generator gives installation and
run commands in its opening docstring. Verification of a private draft needs
a key authorised to read it. All numerical work here ran via agents/sage.sh.
The artifact directory also preserves the proposal, both skill versions,
screening results, neighbour documents and addresses, document snapshots,
fill responses, dry-run output, source notes, lesson proposals and deployment
observations. environment-notes.md explains the cache permission failure
before the successful fill. No source, skill or pipeline files were edited;
no commits, pushes or deployments were made.