Overview

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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Indexed 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" }