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4080 bytes, as of the version from 2026-11-02 17:11 (current). Recorded here, not run.
{
"table": "T681",
"skill_manifest": "agents/runs/20261102T170711Z-repair-skills/manifest.json",
"skill_versions": [
{
"source": "local",
"file": "skill-local.md",
"sha256": "a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278"
},
{
"source": "live",
"file": "skill-live.md",
"sha256": "a2b28d9953264d7b0ca62663785c2952190c5be6d6d3597fd695d9a54d606278"
}
],
"generator_sha256": "2f6c214786ca7b4a772a0b53e90721c10fdab2bdfd22e9d7c0d9359e4493e337",
"program": "# Download https://numberdb.org/files/T681/generate.py?raw=1 as generate.py.\n# Install numberdb with sage -pip install numberdb, then run in Sage.\nfrom generate import moment\nmoment(15, 3, digits=100)",
"program_executes": true,
"enumerated_rows": 88,
"enumeration_matches_stored_order": true,
"checks": [
{
"n": 1,
"k": 2,
"stored": "0.8224670334241132182362075833230125946094749506033992188677791146850037352016004369168144503098793527",
"computed_ball": "[0.82246703342411321823620758332301259460947495060339921886777911468500373520160043691681445030987935265200215948116859533981436234350250389 +/- 4.50e-138]",
"independent_ball": "[0.82246703342411321823620758332301259460947495060339921886777911468500373520160043691681445030987935265200215948116859533981436234350250389396755147316543313841586665468388130254763 +/- 5.44e-180]",
"computed_accuracy_bits": 457,
"independent_accuracy_bits": 597,
"computed_and_independent_contained_in_stored_interval": true,
"overlap": true,
"independent_error_ulp_upper": "0.479978405188314046601856376564974961060324485268345668615841333453161186974523756445492857104291790125370378221158866038001259503700045917715744007290766328377625589816164516130680"
},
{
"n": 1,
"k": 3,
"stored": "-1.803085354739391428099607242267174986147479438510748322688407333012757308679469635279683810414002887",
"computed_ball": "[-1.80308535473939142809960724226717498614747943851074832268840733301275730867946963527968381041400288721929873669289107912773799399800992482 +/- 9.32e-139]",
"independent_ball": "[-1.80308535473939142809960724226717498614747943851074832268840733301275730867946963527968381041400288721929873669289107912773799399800992482066459525581185024218091267442404010007879 +/- 4.12e-180]",
"computed_accuracy_bits": 459,
"independent_accuracy_bits": 597,
"computed_and_independent_contained_in_stored_interval": true,
"overlap": true,
"independent_error_ulp_upper": "0.219298736692891079127737993998009924820664595255811850242180912674424040100078789146717787643678267628379010080913605646154804434662441903308765934371099165988945733573136164726957"
},
{
"n": 15,
"k": 3,
"stored": "-2.074855006906156013604465299651846058736303311353823345806231006222849692611915294016580960238021935",
"computed_ball": "[-2.07485500690615601360446529965184605873630331135382334580623100622284969261191529401658096023802193479483016667237941993970645351 +/- 5.92e-129]",
"independent_ball": "[-2.07485500690615601360446529965184605873630331135382334580623100622284969261191529401658096023802193479483016667237941993970645351481651020527281285704789128317930779994399698759 +/- 6.09e-177]",
"computed_accuracy_bits": 429,
"independent_accuracy_bits": 586,
"computed_and_independent_contained_in_stored_interval": true,
"overlap": true,
"independent_error_ulp_upper": "0.205169833327620580060293546485183489794727187142952108716820692200056003012416089354500011949285057717387890045106985601644100733769985296843744520487640609957384008451843512112850"
}
],
"precision_and_uncertainty": "Root angles are exact rational residues; 600-bit Arb enclosures propagate argument uncertainty through trig and Hurwitz zeta. Stored decimal intervals are checked with exact decimal centers and ULPs.",
"versions": {
"sage": "10.9",
"python": "3.12.3 (main, Mar 23 2026, 19:04:32) [GCC 13.3.0]"
}
}