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2666 bytes, as of the version from 2026-10-26 23:52 (current). Recorded here, not run.
# Source and corpus evidence
Family #216 was read first with `python3 agents/queue.py show 216`; the output
is in family-216.txt. Both archived skill versions, the local canonical skill,
and a fresh https://numberdb.org/skill download are byte-identical. See
../20261026T232323Z-build-skills/manifest.json and skill-read-evidence.json.
SHA-256: b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18.
The primary reference read through the web PDF reader was A. Voros,
*Airy function (exact WKB results for potentials of odd degree)*,
https://arxiv.org/pdf/math-ph/9811001, version 2 dated 26 August 2003.
Equation (5) defines the parity-sector spectral sums; equation (9) gives the
logarithmic determinant expansion. Section 3, equation (28), identifies
D+(z) = -2 sqrt(pi) Ai'(z), with a'_s = -lambda_(2s-2). Equation (29)
gives the regularized canonical product. Equations (43.2) and (43.3) state
Z+(2)=1/rho and Z+(3)=1 with rho=-Ai'(0)/Ai(0).
The direct shell download was refused with HTTP 403; no local PDF is claimed.
The web reader supplied the actual paper text, including those equations.
NIST DLMF https://dlmf.nist.gov/9.2 was read for the Airy equation and the
initial Gamma values; https://dlmf.nist.gov/9.9 was read for the negative,
real, ordered derivative zeros and their asymptotic growth. These fix the
operator normalization and lower convergence cutoff without an inferred scale.
`already_here` and `already_asked` were run from agents/table-ideas/screen.py;
see screening.json. No duplicate Neumann Airy zeta family was found.
api/lookup at 1.371721164 and 0.9408094762 returned no entries, whereas the
exact value 1 had many unrelated matches; it is not evidence of duplication.
T531 is the companion Dirichlet family and is a draft, not this same spectrum.
The final table links it by its documented stable T-number; no slug was guessed.
T57 stores the derivative-root locations, not these infinite sums.
T201 stores Ai' function values. The Gamma table was read by its actual search
result address. The source snippets and full table documents read are saved
as T531.json, T57.json, T201.json, and gamma-table.json.
Both pages of /tags were read: 73 distinct public tags. The existing tags
special values, special functions, analysis and physics fit this table.
There is no spectral zeta tag. Propose that tag for the four tables of #216:
Airy zeta values (T531), Airy derivative zeta values (T532), Bessel Rayleigh
sums and Rayleigh sums of Bessel derivatives. It was not created here.
No quantile, percentile or critical-value family was built. No source,
pipeline, skill, public table, or existing generator was edited.