{
  "table": "T668",
  "stage": "repair",
  "run": "20261102T041628Z",
  "skill_manifest": "agents/runs/20261102T041628Z-repair-skills/manifest.json",
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  "change": {
    "section": "Comments.comment-extremal",
    "before": "These six cases are precisely the nonzero extremal weight-zero Jacobi cases with $m_X-1$ dividing $12$ CITE{CDH12}, Theorem 2.2. The other $17$ Niemeier root systems require additional constructions. Twined traces, with a nonidentity acting class, are not included. The integer keys such as A1^24 name the root system $A_1^{24}$; the exponent denotes the number of copies.",
    "after": "These six cases are precisely the nonzero extremal weight-zero Jacobi cases with $m_X-1$ dividing $12$ CITE{CDH12}, Theorem 2.2. The other $17$ Niemeier root systems require additional constructions. Twined traces, with a nonidentity acting class, are not included. The labels such as A1^24 name the root system $A_1^{24}$; the exponent denotes the number of copies."
  },
  "api_write": {
    "tid": "T668",
    "url": "Mathieu_and_umbral_moonshine_coefficients",
    "revision": "dd83e1cb655428bc7a26ec40bdcbec0a5924e5b24282a2b5d42b46d1d126cf2d",
    "unchanged": false,
    "merged": false,
    "reviewed": false
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  "audit": {
    "tid": "T668",
    "title": "Mathieu and umbral moonshine coefficients",
    "findings": [],
    "clean": true
  },
  "browser": {
    "status": 200,
    "url": "https://numberdb.org/T668",
    "comment": "These six cases are precisely the nonzero extremal weight-zero Jacobi cases with \n𝑚\n𝑋\n−\n1\n dividing \n12\n [1], Theorem 2.2. The other \n17\n Niemeier root systems require additional constructions. Twined traces, with a nonidentity acting class, are not included. The labels such as A1^24 name the root system \n𝐴\n1\n24\n; the exponent denotes the number of copies.",
    "math_errors": 0,
    "page_errors": [],
    "browser_version": "156.0.8078.4"
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    "table": "T668",
    "sage_version": "10.9",
    "skill_manifest": "agents/runs/20261102T041628Z-repair-skills/manifest.json",
    "symbolic_labels": [
      "A1^24",
      "A2^12",
      "A3^8",
      "A4^6",
      "A6^4",
      "A12^2"
    ],
    "parameter_type": "Symbolic",
    "enumeration_matches": true,
    "exact_generator_comparisons": 840,
    "zero_count": 6,
    "max_integer_characters": 10,
    "method": "Recomputed all stored integers with the unchanged attached generator; this is a reproducibility check, not a new independent mathematical critique.",
    "new_values": 0,
    "argument_uncertainty": "Not applicable: all arguments are exact discrete indices."
  },
  "sage_command": "agents/sage.sh \"$TMPDIR/check-repair.py\" \"$TMPDIR/generate.py\" \"$TMPDIR/document-before.json\" > \"$TMPDIR/check-repair.log\" 2>&1",
  "only_wording_changed": true,
  "values_and_order_unchanged": true,
  "before_selection_sha256": "9f5c0e0396f1e3f50a5d1778edcf9c308937d977cdd0497aafdaed8019167fe7",
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  "reviewed_generator_attachments_unchanged": {
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  "reason": "The selection fingerprint binds the entire Comments section, although no arguments, mathematical definitions, enumeration or generator sources changed.",
  "draft_remains_private": true,
  "offered": false,
  "published": false,
  "reviewed": false,
  "initial_attempt": "Stopped locally before any write because the browser editor did not expose the optional base revision. The authenticated API edit then followed an immediate full-document reread.",
  "artifact_sha256": {
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    "argument-selection.md": "10b12cd4099538c785ad939fdb7410f106d1fe15d31bf92e09336b562b612326",
    "change.txt": "179bef5cf319f0941beb92124c8078490455815d9296d217b50ffe18bfa4a72f",
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}