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5791 bytes, as of the version from 2026-10-27 01:05 (current). Recorded here, not run.
# Build handoff: T515, Values of the Scorer function Hi
Draft: https://numberdb.org/T515
Long address returned by creation: https://numberdb.org/Values_of_the_Scorer_function_Hi
Family: numberdb-data#211. Build stamp: 20261026T122728Z.
The table contains nine real values at x = 0, 1/2, -1/2, 1, -1, 2, -2, 10, -10, in that order, each written to 100 significant digits with rigour `proven`. The domain is all rational x; the finite selection and its rationale are in the completeness note. The normalisation, argument selection, ordering, and positive forcing sign follow the family without changes. Computational choices left open by the proposal were 665 working bits, a 10^-150 cutoff for each of the three Taylor tails, and independent quadrature truncated at T=12 with its explicit positive tail bound.
No publication, offering for review, or human review action was taken. The controller must run the separate critique and repair stages. The proposal queue was not marked built during this build stage. No other table was edited. No source, pipeline, skill, or git changes were made.
## Screening and sources
The family was read first. Both the local and live skill were read; the stricter local range guidance was followed. `already_here` returned no Scorer matches; `already_asked('Scorer')` returned #211. Authenticated API lookups around Hi(0), Hi(-1), and Hi(-10) returned no hits. The first raw API lookup attempt used the wrong record shape and was replaced by the client's successful `search_real_ball` requests. The two tag pages confirmed `special functions` and `special values`; both are applied.
T514 already holds the Gi companion as a draft and was read through the authenticated table API. Public search does not show it. It is linked by the verified permanent identifier HREF{T514}, which the site audit accepts, rather than by an invented slug. The Bi and Gamma addresses were read from live search results and their documents were inspected. No request provenance was put in mathematical prose.
DLMF 9.12, in particular equations 9.12.1, 9.12.6, 9.12.7, 9.12.11, and 9.12.20, fixes the conventions and relations. The mpmath Scorer Hi documentation supplies independent evaluations and the ±10 reference arguments. DLMF was readable through the web tool, although a direct urllib attempt to archive its HTML returned 403; this did not prevent reading the source. The live skill is preserved in `live-skill.md`.
The absent tag `Airy functions` remains worth proposing: T55, T56, T57, T58, T198, T201, T202, T203, T514, and T515 would share it. No tag was created.
## Numerical evidence
- The dry run computed all nine values, found finite exact-or-enclosed values, and found no suspicious exact-looking decimals or entry-prose problems.
- The entire Taylor series uses enclosed gamma initial conditions and geometric bounds separately for each residue class modulo three. Minimum final relative accuracy: 494 bits.
- An independent Arb integral of exp(x*t-t^3/3)/pi on [0,12], augmented by exp(12*x-576)/(pi*(144-x)), agreed with every Taylor enclosure. Minimum relative accuracy: 517 bits. The largest omitted integral tail bound was less than 2.176e-201, at x=10.
- Quadrature controls returned integral_0^3 t^2 dt = 9 and integral_0^1 exp(-t) dt = 1-exp(-1); the deliberately wrong answer 8 was rejected.
- mpmath at 150 and 200 dps agreed for all nine arguments. Independently differentiated mpmath Hi checked Hi''-x*Hi=1/pi, and reversing the forcing sign was rejected at every argument. mpmath Gi and Arb Bi checked Gi+Hi=Bi.
- Initial values, positivity, and monotonicity on the selected arguments passed. The derivative initial value was independently checked by mpmath.
- After filling, all nine stored decimal intervals contained the narrow independent certified integral enclosures. The ODE and sum relation also passed on the stored intervals. `verify(sample=None)` reported 9/9 matched, 0 differing, 0 missing, 0 extra.
- The final written values are at most 103 characters; the generic measurement helper estimates a 1.22 KB entries block. The dry run's 217-character maximum measures the higher-precision working ball, not its 100-digit serialized value.
- The authenticated site audit returned `clean: true`, with no findings.
The attached generator, independent checks, common check helper, dry-run helper, and numerical evidence reproduce these results. `checks.py` was corrected after the first read-back attempt to accept both scalar and annotated Numbers leaves; no numerical values were corrected. There are separate revisions for the empty claim, filling and initial attachments, final mathematical prose, and the corrected check plus final evidence. All nine values were sent once.
## Reproduction
On a laptop with Sage and numberdb, download the attached files into one directory, then run:
sage -python dry_run.py generate.py
sage -python checks.py
sage -python checks.py --stored
sage -python generate.py
While the table is a draft, reading its values requires an authorized NumberDB key, supplied via NUMBERDB_API_KEY. On this campaign builder, all Sage calls used `agents/sage.sh`; authenticated calls piped the key from NUMBERDB_KEY_FILE into stdin with NUMBERDB_KEY_FROM_STDIN=1. The package's `Generator.publish()` operation was used only to fill entries and attach source to the existing draft; it does not publish the table.
Versions: Sage 10.9, numberdb 0.1.10, mpmath 1.4.1. `evidence.json` preserves every written value, working ball, independent integral ball, tail bound, and achieved accuracy. `checks-stored-final.log` preserves the successful read-back checks. `lessons.md` records the document-shape and checker API lessons. The controller handoff is `../20261026T122728Z-build.table.json`.