# Argument selection for Airy derivative zeta values (T532)

The only parameter is the integer inverse-power order n, with domain n >= 2.
The table stores Z_N(n) = Tr(H^(-n)) for H = -d²/dx² + x on x >= 0,
with u'(0) = 0 and decay at infinity. The kinetic coefficient and potential
slope are 1; the energy shift is 0. There is no independently sampled coupling,
scale, boundary condition, or continuous argument.

The integers are intrinsic: they index powers of the inverse operator and
Taylor coefficients of its logarithmic spectral determinant Ai'(z)/Ai'(0).
They do not sample a continuous zeta function merely because it can be evaluated.
Voros, Section 3, equations (28), (29), (43.2) and (43.3), explicitly identifies
the even-parity Airy spectrum and its inverse-power sum rules. The Neumann
half-line spectrum is this even sector without a degeneracy multiplier.
Source: https://arxiv.org/pdf/math-ph/9811001 (revised version, 2003).

The derivative zeros satisfy -a'_k ~ [3*pi*(k-3/4)/2]^(2/3), so convergence
requires n > 3/2. Thus 2 is the smallest allowed integer; n = 1 would require
analytic continuation and is outside this table's definition.
Source: NIST DLMF 9.9(i), 9.9.8 and 9.9.19, https://dlmf.nist.gov/9.9.

The selection is every n from 2 through 20, in increasing order, as requested
by family #216. The endpoint 20 is an editorial prefix, not a distinguished
mathematical boundary. It supplies the low-order moments and subsequent
spectral-determinant coefficients without making a large listing. The default
generator enumeration, Programs, and completeness note must state this same
selection. Z_N(3) = 1 is proved by the Airy equation and independently stated
by Voros (43.3); it is stored exactly.

This is the builder's justification, not the independent argument-selection
verdict. The separate critique must evaluate n and bind its judgment to the
live document and generate.py (the generator has no local source dependencies).
The checks are attached separately as checks.py with the shared check.py.

Instruction evidence: ../20261026T232323Z-build-skills/manifest.json records
both archived skill versions. Both have SHA-256
b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18.
The canonical local skill and a fresh live /skill read were byte-identical.
The same manifest is attached to the draft as skill-manifest.json.