An associative-algebra conformance agent needs the full nilpotent Jacobson ideal...
https://detect.halowerk.com/v1/F-B-NIGHT-FINITE-STRUCTURES/rational-associative-algebra-jacobson-radical-loewy-seriesOverview
An associative-algebra conformance agent needs the full nilpotent Jacobson ideal and Loewy power filtration of an explicit rational algebra, including noncommutative semisimple matrix algebras and mixed radical/semisimple examples. A Lie solvability test does not compute this ideal.
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2026-11-02 17:26:22
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Input Schema
{
"body": {
"artifact": {
"jacobson": {
"claim": {
"nilpotency_index": 2,
"radical_basis": [
[
"0",
"1"
]
],
"radical_dimension": 1,
"radical_power_dimensions": [
1,
0
],
"semisimple_quotient_dimension": 2
},
"constants": [
[
[
1,
0
],
[
0,
1
]
],
[
[
0,
1
],
[
0,
0
]
]
],
"unit": [
1,
0
]
}
}
},
"bodyType": "json",
"method": "POST",
"type": "http"
}
Output Schema
{
"example": {
"billable": true,
"findings": [
{
"confidence": 95,
"evidence": [
{
"page_indices": [],
"page_url": null,
"pattern": "rational-associative-algebra-jacobson-radical-loewy-series_scoped_evidence",
"type": "artifact"
}
],
"limits": [
"Rational unital associative algebra dimension1–4, integer multiplication constants abs≤32, explicit integer unit abs≤8. Unit and all basis associativity equations verified; characteristic zero only. Own BigInt rational elimination and ideal products.",
"Radical basis is the unique reduced row echelon row basis in supplied coordinates. Power dimensions start at J^1 and end at first J^nu=0; nu is nilpotency index, with nu=1 for J=0. No Lie radical/derived series, Hochschild cohomology or SDK final-answer wrapper."
],
"module": "rational-associative-algebra-jacobson-radical-loewy-series",
"state": "observed",
"value": {
"claim_matches": false,
"nilpotency_index": 2,
"radical_basis": [
[
"0",
"1"
]
],
"radical_dimension": 1,
"radical_power_dimensions": [
1,
0
],
"semisimple_quotient_dimension": 1
},
"warnings": []
}
],
"known_count": 1,
"scope": {
"contact_values_returned": false,
"network": false,
"supplied_artifact_only": true
},
"warnings": []
},
"type": "json"
}