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82139 bytes, as of the version from 2026-10-30 10:45 (current). Recorded here, not run.
{
"table": "T623",
"sage_version": "10.9",
"skill_evidence": {
"manifest": "agents/runs/20261030T103826Z-repair-skills/manifest.json",
"local_sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199",
"live_sha256": "28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199"
},
"scope": "Repair verification only; no independent argument-review verdict.",
"method": "Exact cyclotomic cotangent sum, live T622 eta differences, and unchanged generator comparison.",
"precision": "Exact rationals; no approximate argument or rounding uncertainty.",
"controls": [
[
2,
1,
1,
"0"
],
[
3,
1,
1,
"1/3"
],
[
3,
2,
1,
"-1/3"
],
[
4,
1,
2,
"1"
],
[
7,
2,
0,
"0"
]
],
"checked_rows": 550,
"all_passed": true,
"results": [
{
"p": 2,
"q": 1,
"u": 1,
"rho": "0",
"eta_difference": "0",
"exact_cyclotomic_match": true
},
{
"p": 3,
"q": 1,
"u": 1,
"rho": "1/3",
"eta_difference": "1/3",
"exact_cyclotomic_match": true
},
{
"p": 3,
"q": 2,
"u": 1,
"rho": "-1/3",
"eta_difference": "-1/3",
"exact_cyclotomic_match": true
},
{
"p": 4,
"q": 1,
"u": 1,
"rho": "1/2",
"eta_difference": "1/2",
"exact_cyclotomic_match": true
},
{
"p": 4,
"q": 1,
"u": 2,
"rho": "1",
"eta_difference": "1",
"exact_cyclotomic_match": true
},
{
"p": 4,
"q": 3,
"u": 1,
"rho": "-1/2",
"eta_difference": "-1/2",
"exact_cyclotomic_match": true
},
{
"p": 4,
"q": 3,
"u": 2,
"rho": "-1",
"eta_difference": "-1",
"exact_cyclotomic_match": true
},
{
"p": 5,
"q": 1,
"u": 1,
"rho": "3/5",
"eta_difference": "3/5",
"exact_cyclotomic_match": true
},
{
"p": 5,
"q": 1,
"u": 2,
"rho": "7/5",
"eta_difference": "7/5",
"exact_cyclotomic_match": true
},
{
"p": 5,
"q": 2,
"u": 1,
"rho": "-1/5",
"eta_difference": "-1/5",
"exact_cyclotomic_match": true
},
{
"p": 5,
"q": 2,
"u": 2,
"rho": "1/5",
"eta_difference": "1/5",
"exact_cyclotomic_match": true
},
{
"p": 5,
"q": 4,
"u": 1,
"rho": "-3/5",
"eta_difference": "-3/5",
"exact_cyclotomic_match": true
},
{
"p": 5,
"q": 4,
"u": 2,
"rho": "-7/5",
"eta_difference": "-7/5",
"exact_cyclotomic_match": true
},
{
"p": 6,
"q": 1,
"u": 1,
"rho": "2/3",
"eta_difference": "2/3",
"exact_cyclotomic_match": true
},
{
"p": 6,
"q": 1,
"u": 2,
"rho": "5/3",
"eta_difference": "5/3",
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},
{
"p": 6,
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"u": 3,
"rho": "2",
"eta_difference": "2",
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},
{
"p": 6,
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"u": 1,
"rho": "-2/3",
"eta_difference": "-2/3",
"exact_cyclotomic_match": true
},
{
"p": 6,
"q": 5,
"u": 2,
"rho": "-5/3",
"eta_difference": "-5/3",
"exact_cyclotomic_match": true
},
{
"p": 6,
"q": 5,
"u": 3,
"rho": "-2",
"eta_difference": "-2",
"exact_cyclotomic_match": true
},
{
"p": 7,
"q": 1,
"u": 1,
"rho": "5/7",
"eta_difference": "5/7",
"exact_cyclotomic_match": true
},
{
"p": 7,
"q": 1,
"u": 2,
"rho": "13/7",
"eta_difference": "13/7",
"exact_cyclotomic_match": true
},
{
"p": 7,
"q": 1,
"u": 3,
"rho": "17/7",
"eta_difference": "17/7",
"exact_cyclotomic_match": true
},
{
"p": 7,
"q": 2,
"u": 1,
"rho": "-1/7",
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},
{
"p": 7,
"q": 2,
"u": 2,
"rho": "3/7",
"eta_difference": "3/7",
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},
{
"p": 7,
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"u": 3,
"rho": "5/7",
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},
{
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"u": 1,
"rho": "-3/7",
"eta_difference": "-3/7",
"exact_cyclotomic_match": true
},
{
"p": 7,
"q": 3,
"u": 2,
"rho": "-5/7",
"eta_difference": "-5/7",
"exact_cyclotomic_match": true
},
{
"p": 7,
"q": 3,
"u": 3,
"rho": "1/7",
"eta_difference": "1/7",
"exact_cyclotomic_match": true
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{
"p": 7,
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{
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"eta_difference": "-13/7",
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},
{
"p": 7,
"q": 6,
"u": 3,
"rho": "-17/7",
"eta_difference": "-17/7",
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},
{
"p": 8,
"q": 1,
"u": 1,
"rho": "3/4",
"eta_difference": "3/4",
"exact_cyclotomic_match": true
},
{
"p": 8,
"q": 1,
"u": 2,
"rho": "2",
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{
"p": 8,
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"rho": "11/4",
"eta_difference": "11/4",
"exact_cyclotomic_match": true
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{
"p": 8,
"q": 1,
"u": 4,
"rho": "3",
"eta_difference": "3",
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},
{
"p": 8,
"q": 3,
"u": 1,
"rho": "1/4",
"eta_difference": "1/4",
"exact_cyclotomic_match": true
},
{
"p": 8,
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"rho": "0",
"eta_difference": "0",
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"eta_difference": "1/4",
"exact_cyclotomic_match": true
},
{
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"rho": "1",
"eta_difference": "1",
"exact_cyclotomic_match": true
},
{
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"rho": "-1/4",
"eta_difference": "-1/4",
"exact_cyclotomic_match": true
},
{
"p": 8,
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"u": 2,
"rho": "0",
"eta_difference": "0",
"exact_cyclotomic_match": true
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{
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{
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{
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"rho": "-3/4",
"eta_difference": "-3/4",
"exact_cyclotomic_match": true
},
{
"p": 8,
"q": 7,
"u": 2,
"rho": "-2",
"eta_difference": "-2",
"exact_cyclotomic_match": true
},
{
"p": 8,
"q": 7,
"u": 3,
"rho": "-11/4",
"eta_difference": "-11/4",
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},
{
"p": 8,
"q": 7,
"u": 4,
"rho": "-3",
"eta_difference": "-3",
"exact_cyclotomic_match": true
},
{
"p": 9,
"q": 1,
"u": 1,
"rho": "7/9",
"eta_difference": "7/9",
"exact_cyclotomic_match": true
},
{
"p": 9,
"q": 1,
"u": 2,
"rho": "19/9",
"eta_difference": "19/9",
"exact_cyclotomic_match": true
},
{
"p": 9,
"q": 1,
"u": 3,
"rho": "3",
"eta_difference": "3",
"exact_cyclotomic_match": true
},
{
"p": 9,
"q": 1,
"u": 4,
"rho": "31/9",
"eta_difference": "31/9",
"exact_cyclotomic_match": true
},
{
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"eta_difference": "5/9",
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{
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{
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"rho": "-1",
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{
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{
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"q": 8,
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{
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{
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"rho": "-3",
"eta_difference": "-3",
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},
{
"p": 9,
"q": 8,
"u": 4,
"rho": "-31/9",
"eta_difference": "-31/9",
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},
{
"p": 10,
"q": 1,
"u": 1,
"rho": "4/5",
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{
"p": 10,
"q": 1,
"u": 2,
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{
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"q": 1,
"u": 3,
"rho": "16/5",
"eta_difference": "16/5",
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},
{
"p": 10,
"q": 1,
"u": 4,
"rho": "19/5",
"eta_difference": "19/5",
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{
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"q": 1,
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"rho": "4",
"eta_difference": "4",
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{
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{
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{
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"rho": "0",
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{
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{
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{
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"u": 1,
"rho": "9/11",
"eta_difference": "9/11",
"exact_cyclotomic_match": true
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{
"p": 11,
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{
"p": 11,
"q": 1,
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{
"p": 11,
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{
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{
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{
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"q": 2,
"u": 2,
"rho": "7/11",
"eta_difference": "7/11",
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{
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{
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{
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{
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{
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{
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{
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{
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{
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{
"p": 11,
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"u": 4,
"rho": "-3/11",
"eta_difference": "-3/11",
"exact_cyclotomic_match": true
},
{
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"q": 7,
"u": 5,
"rho": "-15/11",
"eta_difference": "-15/11",
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{
"p": 11,
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"u": 1,
"rho": "-9/11",
"eta_difference": "-9/11",
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{
"p": 11,
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"u": 2,
"rho": "-25/11",
"eta_difference": "-25/11",
"exact_cyclotomic_match": true
},
{
"p": 11,
"q": 10,
"u": 3,
"rho": "-37/11",
"eta_difference": "-37/11",
"exact_cyclotomic_match": true
},
{
"p": 11,
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"u": 4,
"rho": "-45/11",
"eta_difference": "-45/11",
"exact_cyclotomic_match": true
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{
"p": 11,
"q": 10,
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"rho": "-49/11",
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{
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"rho": "5/6",
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{
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{
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{
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{
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{
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"rho": "5",
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{
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{
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{
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{
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{
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{
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{
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