back to table · edit · history · where entries came from · files · download
6013 bytes, as of the version from 2026-10-27 06:27 (current). Recorded here, not run.
# Build handoff: T540
Built **Neumann spectral determinants of homogeneous oscillators**, private draft
https://numberdb.org/T540, permanent address
https://numberdb.org/Neumann_spectral_determinants_of_homogeneous_oscillators.
The claim succeeded, then the generator added exactly twelve entries, N=1,...,12,
at 100 significant digits with `rigour: proven`. No publication, review or offer
endpoint was called. The controller must run its separate critique and repair
stages before it decides to offer the draft. No independent acceptance sidecar
was created by this builder.
## Policy and family
Read issue #218 first using `agents/queue.py show 218`. The saved issue is
`family-218.md`. Canonical policy archive manifest:
`agents/runs/20261027T061240Z-build-skills/manifest.json`.
Both archived skills and the canonical snapshot have SHA-256
`e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c`.
`skill-evidence.json` records the manifest path/hash and the individual versions.
The gate protocol and `agents/argument_review.py` were read.
The single free parameter is the positive integer degree N, classified in the
builder justification as `discrete_index`. The noncanonical cutoff 12 preserves
both parities, the linear and harmonic controls, cubic and quartic cases, and
several further steep wells. Unit coefficients, Neumann boundary condition,
real logarithms of positive eigenvalues, and fixed zero additive shift are
explicit. Definition, generator, program and completeness note agree.
`argument-selection.md` is attached. No exploratory probability inputs or
statistical quantiles are involved.
## Corpus screening and relationships
`screening.json` records `already_here`, `already_asked`, and neighboring tables;
no existing Neumann determinant family was found. `final-screening.json` records
successful `api/lookup` queries around the N=1,2,4 determinants, all with zero
public matches, and checks of the four existing tags. The initial approximate
N=1 query was imprecise; the final query uses its actual digits. A draft is
invisible to public text/numeric search, so the successful unique-title claim
is the definitive collision check.
T539 contains the complementary Dirichlet determinants and remains private to
unauthenticated readers. Its document was read; the stable T-number is used in
HREF rather than guessing its canonical slug. The audit implementation confirms
that T-number cross-references resolve. Consider this draft relationship when
ordering human publication. T408, Airy derivative values at zero, Airy extrema,
Airy derivative zeta values, Gamma and Hurwitz zeta neighbors were read through
the database. Their public addresses and entry identities were checked.
The tag `spectral zeta` still does not exist. It would group T540 and T539 with
T531 (Airy zeta values), T532 (Airy derivative zeta values), T533 (Bessel Rayleigh
sums) and T535 (Rayleigh sums of Bessel derivatives), as already proposed in the
family. Existing `special values`, `analysis`, `physics`, `special functions`
were used; no new tag was created.
## Numerical evidence
- `dry-run.log`: clean, twelve entries, longest working-ball representation
146 characters, approximately 2.3 KiB working block.
- `offline-checks.json`: Gamma evaluations at 100 and 200 requested digits,
all twelve compared with an independent Bessel/ODE Wronskian reconstruction.
Minimum measured accuracy: 425 bits for the generator and 708 bits for the
independent 720-bit calculation with explicitly bounded series tails.
- Nonzero N=0 reconstruction control equals 1; Airy and harmonic anchors pass;
all twelve deliberate 10^(-90) perturbations are rejected.
- `stored-verification.json`: exact decimal interval containment for all twelve
stored values; stored products with T539 satisfy the sine identity;
`verify(sample=None)` gives 12/12 matched, zero differing/missing/extra.
- `audit.json`: `clean: true`, no findings, after the final prose update.
- `numerical-evidence.md`, source PDFs with hashes, and dependency versions
explain the methods and limitations. The reusable generator and verifier
are attached to T540 along with the argument justification and evidence.
An initially failing harmonic differentiation check was investigated. Default
mpmath tiny-step differentiation lost accuracy near s=0. Explicit controlled
steps converge with O(h²) error and agree to more than 100 digits. Diagnostic
and lesson artifacts are `zeta-diagnostic.log` and `lesson.md`. The certified
Gamma and Bessel checks were unaffected. An attempted stored check using an
unforwarded custom environment variable ran only offline; that output remains
as `stored-checks.json`. The authoritative readback is `stored-verification.json`,
which explicitly asserts both stored-data flags and the verify report.
## Reproduction and next stage
Download the attachments and run `sage -python checks.py` and
`sage -python dry_run.py generate.py`. With authorized draft-reading credentials,
run `sage -python checks.py --stored`. In this campaign use `agents/sage.sh`;
`run_stored.py` demonstrates passing the stored-check option through the wrapper.
All working files and numerical outputs live in this run's isolated work path.
No source, skill or pipeline files were changed; no commit or deployment ran.
The critic must independently evaluate the mathematics and selection, fingerprint
the live selection and all relevant attachments, and write its own required
arguments sidecar. `generate.py` alone implements the enumeration and value;
`argument-selection.md` gives the rationale. `checks.py`, `check.py`, `dry_run.py`,
`numerical-evidence.md`, and `skill-evidence.json` are also attached reproducibility
inputs. A builder fingerprint only confirms attachment bytes, not acceptance.
The controller handoff `agents/runs/20261027T061240Z-build.table.json` names only
T540, the draft filled by this run. Proposal completion remains the controller's
responsibility after its independent stages.