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# Argument selection for T94
At rational shifts $x=r/q$, Hurwitz values are the residue-class components of Dirichlet $L$-values CITE{SelectionDirichlet}. Nonpositive integer orders are Bernoulli-polynomial values, positive integer orders include the polygamma special values CITE{SelectionHurwitz}, and $s=1/2$ gives the components of central Dirichlet $L$-values. The rational shift is therefore an arithmetic parameter; this does not justify a separate continuous rational mesh in the order $s$.
Coverage: it holds every reduced shift $0<x<1$ of denominator at most $5$, at integer orders $-10\leq s\leq10$, $s\ne1$, and at $s=1/2$; these are finite conductor and integer-order reference bounds for the arithmetic families in CITE{argument-selection}; the $x=1$ group refers to the Riemann zeta table.
## Primary mathematical evidence
- DLMF 25.15.3: Dirichlet L-functions as Hurwitz sums: https://dlmf.nist.gov/25.15.E3
- DLMF 25.11: Hurwitz Zeta Function: https://dlmf.nist.gov/25.11
The mathematical deductions in the selection paragraph are distinguished from a source publishing this exact finite list. The range cutoff is a reference limit, not a theorem that every included dimension or order has a separate documented application.
## Reproduction and history
Run `python generate.py` to verify and `python checks.py T94 --live` for independent checks. Neither writes. The source uses exact rational arithmetic and certified Arb balls, with mpmath as a separate agreement check. Retained numeric strings and annotations are copied from, and verified against, the website export; the generator is not claimed to have authored those annotations. Removed sample identities and old attached sources remain in website revision history. No identity is reused for another argument.