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2541 bytes, as of the version from 2026-09-25 15:13 (current). Recorded here, not run.
{
"table": "T451",
"phase": "broaden natural arguments and synchronize coverage notes",
"baseline_revision": "fe8ded4800af7875a472fc4c4ca45e1e2f4f44d9069b9c1585f29436d703b9d8",
"archive_label": "draft-expansion-2026-09-24",
"authority": "The current website database and revisions; this computation archive is supporting evidence.",
"parameter_values": {
"beta": [
"1",
"2",
"4"
],
"s": [
"-1",
"-1/2",
"-1/3",
"-1/4",
"-10/3",
"-11/2",
"-11/3",
"-11/4",
"-13/3",
"-13/4",
"-14/3",
"-15/4",
"-16/3",
"-17/3",
"-17/4",
"-19/4",
"-2",
"-2/3",
"-21/4",
"-23/4",
"-3",
"-3/2",
"-3/4",
"-4",
"-4/3",
"-5",
"-5/2",
"-5/3",
"-5/4",
"-6",
"-7/2",
"-7/3",
"-7/4",
"-8/3",
"-9/2",
"-9/4",
"0",
"1",
"1/2",
"1/3",
"1/4",
"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 $\\beta=1,2,4$ at every rational $s=a/b$ in lowest terms with $-6\\leq s\\leq3$ and $1\\leq b\\leq4$ (165 entries). Integers, halves, thirds and quarters are included, and every density value has a distribution-function value at the same argument in the companion table. Other rational arguments and the far tails are not included; this is not a decimal interpolation mesh.",
"coverage_validated_against_every_cartesian_parameter_combination": true,
"before": 39,
"after": 165,
"comparison_counts": {
"same": 39,
"new": 126
},
"generator_sha256": "ff5320c572462e02d60e89c4287feba597acb4debda4b28512c0086791dadb6f",
"checks": "generator agreement checks",
"cross_checks": {
"finite_entries": 165,
"cdf_derivative_max_absolute_error": 4.953086029432091e-10
},
"allowed_prose_changes": [
[
"Data properties",
"complete-note"
],
[
"Comments",
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[
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"rigour details"
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"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"
}