# Argument selection for T708

The sole free parameter is `N`, an integer truncation level with natural domain
N >= 1, in increasing order. Category: `discrete_index`. There is no free
coupling, sampled rational dilation, root choice, or statistical quantile.

Báez-Duarte, math/0011254v1, §1.2 equation (1.17), defines
V_N = sum_{n=1}^N mu(n) rho_n - g_N rho_1, with g_N from (1.4).
Each N names a member of this prescribed arithmetic sequence. The correction
is at the fixed dilation 1; its coefficient is derived, not selected separately.
The output is its squared residual norm in L²((0,infinity),dx), targeting -chi.

Selection: every N=1,...,30, without pruning primes, composites, or repeated
nonsquarefree endpoints. The full prefix permits direct same-index comparison
with all current optimal-distance cases in T641, with the Selberg cases
N=2,...,30 in T642, and with the untapered baseline T706. The range is a
noncanonical practical cutoff, independently justified by these comparisons
and the manageable certified 30 by 30 Gram calculation. It is not a claim
of asymptotic completeness or a quota. No particular decimal appearance
influenced the selection. Breadth here is every successive truncation of one
named approximant; adding other named constructions would change the quantity
and belongs in separate tables.

The generator enumerates exactly this prefix, allows positive N beyond it,
and computes the same definition there. The Programs function accepts every
positive integer N; its example N=30 is within the stored prefix. The
completeness note says `no` and gives these exact bounds and rationale.
N=1 is retained as an exact normalization control, not made into another table.

Live candidate metadata and both tag pages were refreshed in discovery.py.
Related tables are context only, not independent evidence for these numbers.
The instruction archive is ../20261110T205245Z-build-skills/manifest.json,
retained verbatim as skill-manifest.json; bundle SHA-256
 d6661c2f21613524889fa3a57d3c95f8330344ca62e5a856211c08a282b7dbab.
This is the builder's justification; an independent critic must assess it.