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4199 bytes, as of the version from 2026-10-27 19:33. Recorded here, not run.
# Build handoff: Umemura polynomials for Painlevé III
Status: blocked, with empty unpublished draft T558. This run did not complete
a table, offer it, publish it, perform human review, or write a successful
build.table.json handoff. T558 is the sole draft claimed and may be resumed
after coordination; an owner can clear it if this proposal is abandoned.
Family numberdb-data#223 was read first and its current conventions followed:
monic normalization in x, mu retained as an indeterminate, integer index n.
The local/live policy archives were read and compared. Manifest:
`agents/runs/20261027T192330Z-build-skills/manifest.json`.
Both skill versions have SHA-256
`e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
The campaign argument gate and argument_review.py were also read.
The cheap corpus screen found no Umemura family. The x+y sample matches
unrelated symmetric-polynomial families; the next Umemura polynomial has no
match. The actual mu spelling causes a lookup HTTP 500. Public searches do
not expose the sibling drafts T556 and T557, which were read by authenticated
API using the T-numbers in the issue. Both tag pages contain the existing
polynomial, special functions and recurrence tags but no Painlevé equations
tag. That proposed tag would connect T443, T556, T557, T558, and the proposed
Okamoto family. No tags on published tables were changed.
Decisions not settled by the family: use the 2023 Clarkson–Law–Lin indexing
S_{-1}=S_0=1, S_1=x+mu, degree n(n+1)/2, and choose every n=0,...,5.
The family issue refers to recurrences "below" but contains no actual recurrence.
The convention was taken from equation (1.5) and Theorem 2.3 of the checked
paper, not inferred from a title. See argument-selection.md for the explicit
index-family and breadth assessment. Expanded S_5 has 959 characters;
S_6 has 2129. These are exact integer polynomials, so 100-digit approximation
is inapplicable.
All six computed polynomials passed dry_run.py and exact independent Wronskian
reconstruction over QQ[x,mu]. All five printed polynomials in the source's
Table 1 matched. Degree, monicity, integrality, mu=0, reverse-Bessel mu=1,
recurrence, logarithmic derivative and cleared Painlevé III equation checks
passed for every selected n. Known nonzero/zero and deliberately perturbed
controls passed. The Programs snippet was executed and matched all six values.
Numerical evidence and exact values are in numerical-evidence.json and
values.json; checks are in checks.py with the unchanged shared check.py.
Blocking cause: the NumberDB polynomial grammar accepts a single letter
followed by optional digits. It does not accept mu. The fill request failed
atomically with `A value in these entries cannot be read as a number. trailing
input at 'u'`. The post-failure authenticated read confirms zero entries.
The attempted prose update also failed because the full-document endpoint
rejects empty Numbers, even for an existing draft. The initial claim document
is therefore still the live prose; document.json is the proposed full document.
Its rigour note explicitly says readback and verify have not been performed.
The empty-draft audit is clean, but this certifies no entries and is not a
successful build audit. No generator verify or stored-value mathematical
checks were possible. No independent critique acceptance was written.
The family queue was marked skipped with the format blocker and T558 named,
so another campaign will not repeatedly attempt this unsupported convention.
The generator, check code, argument selection, exact computed values, proposed
document and build evidence are attached to T558 for recovery. They remain
working artifacts, not completed published data. Resolve the parser/family
convention mismatch first, reuse T558 rather than making a second title, then
fill, independently check readback, verify, audit, and obtain the controller's
separate critique before any offer. Changing variables or generator bytes
requires that future independent critique to assess the resulting selection.
Additional findings are recorded in lessons.md and environment-findings.md.
No source, pipeline, skill or Git changes were made.