# Numerical evidence for T532, Airy derivative zeta values Build run: 20261026T232323Z-build. This is builder evidence, not an independent critique, an argument-selection acceptance, or a publication decision. Instruction manifest: `/home/ubuntu/numberdb-campaign-20261026-hundred/repo-natural-arguments-v2/agents/runs/20261026T232323Z-build-skills/manifest.json`. Both archived skill versions were read and were identical to the canonical local file and a fresh live /skill read. Their SHA-256 is `b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18`. The manifest is attached as skill-manifest.json; skill-read-evidence.json records the fresh hashes. The stricter combined instructions were followed. The sole argument n is the inverse-operator power, n >= 2. All orders 2..20 are included, in increasing order. This is an editorial initial segment of a discrete spectral family; no continuous parameter or adjustable scale is sampled. See argument-selection.md and Voros, Section 3, equations (28), (29), (43.2), (43.3), https://arxiv.org/pdf/math-ph/9811001. The generator represents every Z_N(n) as an exact polynomial in Gamma(1/3)/(3^(1/3) Gamma(2/3)), using rational arithmetic. Its final Arb substitution uses 429 bits (100 digits plus a 96-bit guard). Across the 18 nonrational entries the minimum relative accuracy was 421 bits and the largest relative radius was 7.336470736913143e-128. Z_N(3)=1 remains an exact integer by the Airy equation and Voros (43.3). Every entry was recomputed at 628 bits. SageMath 10.9 and numberdb 0.1.10 were used. The independent check computes Ai(z)/Ai'(z) directly with Arb at 600 bits on 512 points of |z|=1/2, then extracts coefficients by discrete Fourier sums. It does not use the generator's recurrence, polynomial coefficients or Gamma initialization. An explicit alias error of 2/(2^512-1), less than 1.5e-154, is included in every enclosure. The derivation and the proof that the nearest pole has modulus greater than 1 are in checks.py. Before the Airy computation the same coefficient extractor recovered all 19 requested coefficients of 3+2z+z^5, including its nonzero coefficients. Every ball's real and imaginary components were checked for finiteness and small radius. Results: * Shared dry_run.py: 19 entries passed exactness, ring-import and prose checks, with no exact value disguised as a decimal. * All 19 values agreed with the higher-precision rerun and independent Cauchy enclosures. The Cauchy enclosures fit inside each written 100-digit interval; the exact entry was checked by its symbolic identity and by inclusion of 1 in the independent enclosure. * Low-order identities, the full recurrence, positivity, strict decrease and strict log convexity passed. The reflection-form Gamma expression supplied a separately written initial-constant check. * Values read back through numberdb.table('T532') passed those identities and independent-enclosure containment checks again. The exact stored spelling at n=3 is `1`. * The Programs section read from the live document was executed and agreed with the independent computation at every selected order. * Generator.verify(sample=None): 19/19 matched, 0 differing, 0 missing, 0 extra. The read-back check took about 0.89 seconds after Sage startup. * The stored values have maximum length 102 characters; the shared measurement of their flat block is about 2.47 KiB before the one entry comment. The larger dry-run size (3.3 KiB) measures full working balls. * The authenticated site audit returned clean=true and no findings. Full values, independent enclosures, measurements and read-back results are in numerical-results.json. The raw dry-run and check logs are retained in the run work directory, including the two checker interface errors corrected before its first successful control. No failed comparison between two numerical methods was discarded. The independent critique must still assess the mathematical derivation, source interpretation and argument selection. The Cauchy computation is independent in algorithm and initialization, but uses the same Arb library; it is not an independent software-library check. No finite root sum was presented as a 100-digit infinite-sum computation. The remote audit does not perform the optional outward-link check.