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5001 bytes, as of the version from 2026-11-02 04:21 (current). Recorded here, not run.
{
"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,
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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 \nš\nš\nā\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 \nš“\n1\n24\n; the exponent denotes the number of copies.",
"math_errors": 0,
"page_errors": [],
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},
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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,
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"fresh_independent_critique_required": true,
"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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}