{
  "table": "T441",
  "phase": "broaden natural arguments and synchronize coverage notes",
  "baseline_revision": "af734441109d93c589cc10630ca9f7507dbd769b9ddc3a476e15cf7119cc34cc",
  "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). The selection includes integers, halves, thirds and quarters in the central region and adjoining tails, with the same arguments as the density table. It is not complete over all real or rational arguments and does not cover the far tails.",
  "coverage_validated_against_every_cartesian_parameter_combination": true,
  "before": 39,
  "after": 165,
  "comparison_counts": {
    "same": 39,
    "new": 126
  },
  "generator_sha256": "5f9397ca71caa792698d36fecc2ff76de4b9557695eafc80cdc831b94f276cfd",
  "checks": "generator agreement checks",
  "cross_checks": {
    "finite_entries": 165,
    "cdf_range_and_monotonicity": true
  },
  "allowed_prose_changes": [
    [
      "Data properties",
      "complete-note"
    ],
    [
      "Comments",
      "comment-range"
    ],
    [
      "Data properties",
      "rigour details"
    ]
  ],
  "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"
}