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2916 bytes, as of the version from 2026-10-28 15:11 (current). Recorded here, not run.
# Argument selection for Gram points (T583)
The sole free parameter is the integer phase-crossing index n, with domain
n >= -1. Its role is `discrete_index`. The quantity is the unique root g_n
in [7,infinity) of theta(g_n)=n*pi, with the analytic log-gamma branch real
at 1/4. This is the same normalization used by family issue 230 and FLINT's
`acb_dirichlet_gram_point` documentation. No real coupling, probability,
normalization selector or second quantity is varied.
The finite selection is every integer -1 <= n <= 200, in increasing order.
This is an initial segment of an intrinsically defined phase-crossing sequence,
not an exploratory sample of real arguments. Gram points occur in the isolation
and counting of Riemann-zeta zeros (FLINT, Gram points and counting zeros;
mpmath, siegelz and grampoint). The segment includes the initial positive
landmarks and extends into the range where Gram's sign rule fails. Including
consecutive ordinary crossings together with the exceptional ones permits
comparison of neighboring intervals without restricting the table to named
exceptions. The endpoint 200 is a practical, noncanonical reference cutoff;
it is not a special mathematical index and does not depend on numeral notation.
Breadth was assessed before depth: this table has one landmark family and no
secondary parameter. The low-height endpoint g_-1 and the nonzero g_0 must
both be included. Zero heights, stationary heights, and values of Hardy Z are
separate quantities and belong in separate tables; adding them here would not
improve coverage of this named object. There is no missing second argument
slice to justify before extending this consecutive prefix. A larger prefix
could be added later, but is not needed for this bounded initial reference.
The generator's default enumeration is exactly range(-1, 201). Its output
is 202 certified real enclosures, serialized to 100 significant digits.
Numerical evidence records the actual length and block size. The completeness
note must name this same prefix, its initial-landmark coverage and its
noncanonical cutoff. No `reference_sample` policy is needed for a genuine
integer phase index. The independent critique must assess this classification
and bind its verdict to the website selection and generator source hashes.
This file is the builder's justification, not an independent acceptance.
Sources checked:
- https://flintlib.org/doc/acb_dirichlet/index.html, “Gram points and Turing's
method”, especially acb_dirichlet_gram_point and the good-Gram-block bound.
- https://mpmath.org/doc/current/functions/zeta.html, “siegelz”,
“siegeltheta”, and “grampoint”.
Instruction provenance: agents/runs/20261028T143558Z-build-skills/manifest.json.
Both archived canonical skill versions have SHA-256
e37efb7e2ededf6c1d7134c673f152f648f26e0267c556aebdf3ec65765d8b4c.
The same manifest is attached as skill-manifest.json.