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2187 bytes, as of the version from 2026-09-24 20:53 (current). Recorded here, not run.
{
"table": "T424",
"phase": "broaden natural arguments and synchronize coverage notes",
"baseline_revision": "85caea3b1cc1a3002d8956abf29055fbbfcdab85418358761e0dfb85429f66a2",
"archive_label": "draft-expansion-2026-09-24",
"authority": "The current website database and revisions; this computation archive is supporting evidence.",
"parameter_values": {
"m": [
"1/2",
"1/3",
"1/4",
"1/5",
"1/6",
"1/8",
"2/3",
"2/5",
"3/4",
"3/5",
"4/5",
"5/6",
"7/8"
],
"u": [
"1",
"1/2",
"1/3",
"1/4",
"1/6",
"1/8",
"11/4",
"2",
"2/3",
"3",
"3/2",
"3/4",
"4/3",
"5/2",
"5/3",
"5/4",
"7/3",
"7/4",
"8/3",
"9/4"
]
},
"coverage_note": "it holds $m\\in\\{1/8,1/6,1/5,1/4,1/3,2/5,1/2,3/5,2/3,3/4,4/5,5/6,7/8\\}$ and every rational $u=a/b$ in lowest terms with $0<u\\leq3$ and $1\\leq b\\leq4$, together with $u=1/6,1/8$ (260 entries). The moduli form complementary pairs $m,1-m$ around $m=1/2$; the arguments are simple rationals and extend beyond the first quarter period for each selected modulus. These are not arguments proportional to $K(m)$, and no completeness over all rational pairs is claimed.",
"coverage_validated_against_every_cartesian_parameter_combination": true,
"before": 35,
"after": 260,
"comparison_counts": {
"new": 225,
"same": 35
},
"generator_sha256": "020ce8a34999ed7c1f093e478f59a782ae2ac8b765b960068b52d045d9f54fde",
"checks": "check_identities",
"cross_checks": {
"finite_entries": 260,
"independent_mpmath_all_entries": true,
"each_modulus_quarter_period_below_argument_maximum": true
},
"allowed_prose_changes": [
[
"Data properties",
"complete-note"
]
],
"preserved": "Definitions, formulas, parameters, normalization conventions, rigour levels, references, unrelated prose, draft status and every pre-existing entry.",
"previous_selection_retained_in_revision_history": true,
"engine": "codex-cli",
"model": "gpt-5.2",
"session": "019c3fb0-a459-7fa3-9d1b-82994c678238"
}