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2361 bytes, as of the version from 2026-11-01 09:03 (current). Recorded here, not run.
# Argument selection for Báez-Duarte coefficients (T644)
The only free parameter is the integer coefficient index k, with domain k >= 0.
Its category is `discrete_index`: it is the order of a finite difference of
reciprocal even zeta values, and the index of the reciprocal-zeta expansion
in Pochhammer polynomials. It is not a sampled continuous input. The signs
and indexing follow Báez-Duarte, arXiv:math/0307215, equation (1.1) and
Proposition 2.1. Cisło and Wolf, arXiv:0807.2971, equations (4), (7), (10),
and (14), use the same convention and relate these coefficients to the Riesz
function. Both primary sources were read for this build.
We retain every k from 0 through 256, in increasing order. A consecutive
initial segment covers the finite-difference orders needed for binomial
inversion and the initial coefficients in the generating-function relation.
There are no missing intermediate orders, no second argument, no coupled
mesh, and no restriction to the three simplest closed forms. The other
quantities in family #283, Riesz function values and the alternating sum,
remain separate tables. This reviews breadth within the named sequence
without absorbing those companions or introducing generalized transforms.
The cutoff 256 is practical and noncanonical. Difference errors can grow as
2^k; one working bit per order plus 80 extra bits supports 100 significant
digits while keeping the full segment inexpensive to reproduce. The measured generator minimum is 398 relative accuracy bits, comfortably
exceeding the requested 100 significant digits. Serialized values have at most
106 characters; the 257-entry block is about 36 KB.
This is not a claim that 256 has intrinsic mathematical significance or that
finite coefficients test the asymptotic Riemann-hypothesis criterion.
No exploratory reference group or continuous probability parameter is used.
The generator default, Programs snippet, and completeness note all cover
exactly k = 0,...,256. Extending the range does not change the domain.
Policy evidence: agents/runs/20261101T072807Z-build-skills/manifest.json.
The local and live archived skills both have SHA-256
`a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278`.
This build's justification is not the separate independent argument review.
The controller must obtain that review before offering the draft.