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4586 bytes, as of the version from 2026-10-27 01:12 (current). Recorded here, not run.
# Build handoff: T511
Draft: https://numberdb.org/T511
Title: Values of the irregular Coulomb wave function $G_\ell(\eta,\rho)$.
Family: numberdb-data issue #210. This build filled T511, claimed empty in this
run. It remains unpublished and has not been offered for review.
The table contains 88 rigorously enclosed values at 100 significant digits.
The parameter order is (ell, eta, rho). The parameter domain and initial
selection exactly follow the family: ell=0..3, eta=0,+/-1/2,+/-1,+/-2,
rho=1/2,1,2, with rho=5 at eta=2. Enumeration starts with the free case and
pairs positive and negative couplings by increasing magnitude. No selection
was added to meet an entry quota.
The sign and normalization are DLMF 33.2.7–11, equivalently the prescribed
cosine asymptotic condition. Principal powers and Tricomi U are used.
Sage had no direct Coulomb interface or python-flint, so the generator uses
Sage/Arb U with the gamma-ratio phase. This is mathematically equivalent to
the displayed DLMF phase formula; the checker verifies that equivalence.
All local checks passed before uploading any entries. The computation at
515 working bits retained at least 496 relative accuracy bits; the largest
radius was less than 2.711e-149. The 100-digit written intervals enclose all
computed balls; the longest stored decimal has 103 characters. Dry-run
exactness and disguised-exactness checks passed for all 88 entries.
The package verify() reported 88 matched, zero differing, missing or extra.
The checks were repeated on the database's actual decimals, with these counts:
- 88 enclosures contained in the written intervals.
- 88 mpmath comparisons at each of 150 and 200 digits, with precision agreement.
- 88 G differential-equation and Wronskian checks.
- 88 ascending derivative and 66 descending derivative checks.
- 66 order recurrence checks (ell=1..3; auxiliary ell=4 is computed).
- 12 independent free-case Bessel Y checks, including 3 cosine checks.
- 4 handbook values and 4 derivatives, within absolute 0.0001.
- 6 more precise printed mpmath value/derivative controls.
- 88 checks of Im H+=F and its derivative, with an independent product
normalization for F. The regular ODE and order recurrence also passed.
The checking methods enforce finite narrow enclosures. Known nonzero sine,
cosine and Wronskian controls run first; the reversed cosine sign is rejected.
An exact control checks the decimal uncertainty parser. Both published
Programs snippets were executed. The authenticated site audit is clean.
Three decisions not dictated by the formula itself:
1. 515 working bits suffice, as measured; the generator still has a bounded
precision escalation if an extension needs more.
2. Couplings are displayed in increasing absolute value, positive before negative.
3. The rounded handbook worked example is checked to absolute 0.0001, rather
than treating each printed final digit as certified. Its scan was inspected.
The live corpus search, already_here, already_asked, three api/lookup probes,
and both tag pages were checked. There was no existing irregular Coulomb
value table. Similar published tables T190 and T209 were read, including their
actual search-result URLs. T510 was read with authentication and is currently
a draft. It is linked by its supported stable T-number, not a guessed slug.
Publication order needs attention later: T511's companion links should resolve
publicly before a human publishes T511. This run performed no publication or
review action and made no change to T510 or any published table.
The existing special functions, special values and physics tags are used.
The absent quantum mechanics tag would connect T510, T511, T404, T406, T408,
and T411. It remains a proposal, not a new tag created by this build.
Reproducibility files are attached to the draft: generate.py, checks.py,
evidence.json, README.md, stored-checks.json and this handoff. The local
working directory also retains the source scan, skill comparison, screening,
dry-run output, raw numerical output, all scripts, and the stored document.
The exact software versions are Sage 10.9, numberdb 0.1.10, mpmath 1.4.1.
Two checker issues were resolved privately: MPFI membership is written with
`in`, and the Wronskian residual must subtract 1. The first read-back checker
also expected a list of entries; the API returns canonical nested mappings,
so it now uses the client's normalizer. No numeric value or mathematical
convention changed during these fixes. No source code in the snapshot was
changed. No Git operations or deployment were attempted.