{"paper":{"title":"The catastrophes of algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A real finite-dimensional unital associative algebra associates with a vector space of pseudo-Finsler norms linked to its normalized trace forms by an integral transform.","cross_cats":[],"primary_cat":"math.RA","authors_text":"Fred Greensite","submitted_at":"2023-06-26T18:23:27Z","abstract_excerpt":"A parametrized collection of flat (conic pseudo-)Finsler spaces is derived from application of a particular transform procedure to the space of normalized trace forms of a real finite-dimensional unital associative algebra. The associated collection of co-(pseudo-)Finsler symplectic manifolds is thereby indexed by an inherited set of parameters that control the Lagrangian submanifold dynamics. Largrangian submanifolds are defined with respect to the indicatrix H(q,p)=1/2, with the t=0 slice such that q is fixed by the unit Euclidean sphere in configuration space and p is directed inward. The w"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that a real finite-dimensional unital associative algebra is naturally associated with a vector space of pseudo-Finsler norms whose members are linked to the algebra's space of normalized trace forms through an integral transform.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The integral transform produces well-defined pseudo-Finsler norms to which the Hamiltonian formalism can be applied, and that repeating the procedure on the Cuntz-Quillen tower captures the full influence of the Jacobson radical to yield useful invariants (abstract, paragraph beginning 'Since components of the space of trace forms...').","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Finite-dimensional real unital associative algebras are linked to pseudo-Finsler norms through integral transforms from trace forms, allowing Hamiltonian formalism and Cuntz-Quillen towers to produce catastrophe-based invariants.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A real finite-dimensional unital associative algebra associates with a vector space of pseudo-Finsler norms linked to its normalized trace forms by an integral transform.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b8d92c6c71c5b8feebfd58faedb53c76b4c1ba7d6414aa848cad0bbd39a7e75c"},"source":{"id":"2306.14995","kind":"arxiv","version":44},"verdict":{"id":"8dc5db3f-1776-4c8e-b660-ed6b456f3d34","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-24T08:18:27.886748Z","strongest_claim":"We show that a real finite-dimensional unital associative algebra is naturally associated with a vector space of pseudo-Finsler norms whose members are linked to the algebra's space of normalized trace forms through an integral transform.","one_line_summary":"Finite-dimensional real unital associative algebras are linked to pseudo-Finsler norms through integral transforms from trace forms, allowing Hamiltonian formalism and Cuntz-Quillen towers to produce catastrophe-based invariants.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The integral transform produces well-defined pseudo-Finsler norms to which the Hamiltonian formalism can be applied, and that repeating the procedure on the Cuntz-Quillen tower captures the full influence of the Jacobson radical to yield useful invariants (abstract, paragraph beginning 'Since components of the space of trace forms...').","pith_extraction_headline":"A real finite-dimensional unital associative algebra associates with a vector space of pseudo-Finsler norms linked to its normalized trace forms by an integral transform."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.14995/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}