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4868 bytes, as of the version from 2026-11-10 22:01 (current). Recorded here, not run.
# Build handoff: T706
Private populated draft: https://numberdb.org/T706
Title: Untapered Möbius approximation errors in the Nyman–Beurling criterion.
Owner: zeta3. Build run: 20261110T195231Z, codex-cli / gpt-6-astra.
Proposal #313; contributes to wanted #273. No issue is declared fully answered.
Scope completed: every N=1,...,30 at 100 significant digits, type R, rigour
proven. The quantity is ||chi+sum_(n=1)^N mu(n){1/(nx)}||^2 in
L^2((0,infinity),dx). The full exterior tail is included. The sole integer
parameter and noncanonical comparative prefix are justified in the attached
argument-selection.md. No other table was created, edited, or retagged.
## Numerical and source evidence
- Inspected source versions and passages are recorded in research.md,
derivation.md and source-archives.json. Source pages remain in this work
directory. The notational change F_n (2002) = S_n (2000) is explicit.
- generate.py uses the published finite cotangent kernel with exact rationals
and Arb balls. All 30 norms retain at least 444 bits at 461 working bits;
maximum generator radius 7.2968621e-136.
- checks.py and integral_kernel.py freshly check all 465 symmetric Gram entries
and all 30 norms using the period integral and an explicit series remainder
at 720 bits. Maximum independent norm radius below 6.05e-151. Whole-residual
integrals at N=1,2,3,6 independently check the target terms and full domain.
Known-answer, perturbed-value, wide-ball and NaN controls pass as intended.
Numerical evidence includes exact rational endpoints, dependencies and hashes.
- Every stored decimal strictly contains both independently computed
enclosures. verify_stored.py checks all 30, two closed forms, repetitions,
exterior-tail contributions and independently solved optimal lower bounds.
stored-verification.json has 30 checked entries and no failures.
- Generator verify(sample=None): 30/30 matched, zero differing/missing/extra.
Standalone Programs code agrees on all 30 entries. Existing deterministic
dry_run.py/check.py passed type, finite-enclosure, exactness-pattern,
import, prose and size checks (30 entries, 5.7 KB raw ball block).
- Audit is clean. Its sole earlier finding was a missing install command in
generate.py's docstring. The command was added; numerical-evidence.json
records both source hashes and the checked identity of executable ASTs.
No mathematical code or stored value changed after validation.
## Presentation and provenance
Stored content was inspected through the live NumberDB preview renderer in
26 sections/entry groups; browser-check.json and screenshots record the final
MathJax/citation check. The actual private /T706 route requires a browser login
and returned 404; no login session was available. Preview uses the same stored
prose, formulas, parameters, and all 30 numbers, with references carried into
relevant excerpts. Four companion links resolve. This limitation is explicit
rather than a claim to have viewed the authenticated full-page route.
All attachments were read back byte-for-byte. History confirms both URLs
https://github.com/numberdb/numberdb-data/issues/313 and
https://github.com/numberdb/numberdb-data/issues/273 in the initial creation
and later amended run messages, with actual engine/model attribution.
metadata-final.json, attachment-readback.json and fingerprint.json bind the
current document and sources. fingerprint.json is not an acceptance sidecar.
Instruction archive read:
../20261110T195231Z-build-skills/manifest.json (also attached as
skill-manifest.json), manifest SHA-256
c5ee30e128246f511fb7c0e8e37f8b7d2419d5fad25227688a6111fdf9686049;
matching local/live bundle SHA-256
d6661c2f21613524889fa3a57d3c95f8330344ca62e5a856211c08a282b7dbab.
All archived resource hashes were checked. No later differing skill was read.
Family research and reusable code/checkpoints are preserved at
/home/ubuntu/numberdb-campaign-20261110-pilot/control/families/family-313/
T706-build-20261110T195231Z/; its manifest.json hashes the copied files.
The concise shared research.md distinguishes checked build facts from pending
independent review. Deployment findings are in environment-notes.md; no live
skill or source infrastructure was changed.
## Controller action
Obtain fresh independent scientific validation and argument-selection review
bound to the final revision and all relevant generator files. This builder has
written neither verdict nor an -arguments.json sidecar. T706 remains in_progress,
unpublished, unreviewed, and unoffered. The controller alone may advance it.
The proposal remains claimed pending that process. No supervisor checkpoint,
completion receipt, or review state was modified by this build.
The exact machine handoff is ../20261110T195231Z-build.table.json with only
{"tid":"T706"}. It names the sole draft filled by this run.