{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AWOGQA3VMUGXFNTF4AR5TWGQB4","short_pith_number":"pith:AWOGQA3V","schema_version":"1.0","canonical_sha256":"059c680375650d72b665e023d9d8d00f11d4072b2262db595a1d5b3be893c907","source":{"kind":"arxiv","id":"1407.8318","version":1},"attestation_state":"computed","paper":{"title":"Conjugacy classes of $n$-tuples in semi-simple Jordan algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Hannah Bergner","submitted_at":"2014-07-31T08:51:14Z","abstract_excerpt":"Let $J$ be a finite-dimensional semi-simple Jordan algebra over an algebraically closed field of characteristic $0$. In this article, the diagonal action of the automorphism group of $J$ on the $n$-fold product $J\\times\\ldots \\times J$ is studied. In particular, it is shown that the orbit through an $n$-tuple $x=(x_1,,\\ldots,x_n)$ is closed if and only if the Jordan subalgebra generated by the elements $x_1,\\ldots, x_n$ is semi-simple."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.8318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-31T08:51:14Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"798b0eb33c1e06d87a962ec92ea96a7d2fefbb570b8ca6cb81b56dc7d1fbbe67","abstract_canon_sha256":"833dc2cf29f8e670cb3bf02a461014eb5c884861a523cbe434a8bd734297e14f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:05.412162Z","signature_b64":"RXcK/L3yNx6SkLtkL/fGjWPcfflTCW5bpiiX9hjpJC2qwc5Q1AH3eoI7XqLl/c+DDunJVABz/EwRCCjgeRUBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"059c680375650d72b665e023d9d8d00f11d4072b2262db595a1d5b3be893c907","last_reissued_at":"2026-05-18T02:46:05.411672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:05.411672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conjugacy classes of $n$-tuples in semi-simple Jordan algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Hannah Bergner","submitted_at":"2014-07-31T08:51:14Z","abstract_excerpt":"Let $J$ be a finite-dimensional semi-simple Jordan algebra over an algebraically closed field of characteristic $0$. In this article, the diagonal action of the automorphism group of $J$ on the $n$-fold product $J\\times\\ldots \\times J$ is studied. In particular, it is shown that the orbit through an $n$-tuple $x=(x_1,,\\ldots,x_n)$ is closed if and only if the Jordan subalgebra generated by the elements $x_1,\\ldots, x_n$ is semi-simple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8318","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.8318","created_at":"2026-05-18T02:46:05.411777+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.8318v1","created_at":"2026-05-18T02:46:05.411777+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8318","created_at":"2026-05-18T02:46:05.411777+00:00"},{"alias_kind":"pith_short_12","alias_value":"AWOGQA3VMUGX","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AWOGQA3VMUGXFNTF","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AWOGQA3V","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AWOGQA3VMUGXFNTF4AR5TWGQB4","json":"https://pith.science/pith/AWOGQA3VMUGXFNTF4AR5TWGQB4.json","graph_json":"https://pith.science/api/pith-number/AWOGQA3VMUGXFNTF4AR5TWGQB4/graph.json","events_json":"https://pith.science/api/pith-number/AWOGQA3VMUGXFNTF4AR5TWGQB4/events.json","paper":"https://pith.science/paper/AWOGQA3V"},"agent_actions":{"view_html":"https://pith.science/pith/AWOGQA3VMUGXFNTF4AR5TWGQB4","download_json":"https://pith.science/pith/AWOGQA3VMUGXFNTF4AR5TWGQB4.json","view_paper":"https://pith.science/paper/AWOGQA3V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.8318&json=true","fetch_graph":"https://pith.science/api/pith-number/AWOGQA3VMUGXFNTF4AR5TWGQB4/graph.json","fetch_events":"https://pith.science/api/pith-number/AWOGQA3VMUGXFNTF4AR5TWGQB4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AWOGQA3VMUGXFNTF4AR5TWGQB4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AWOGQA3VMUGXFNTF4AR5TWGQB4/action/storage_attestation","attest_author":"https://pith.science/pith/AWOGQA3VMUGXFNTF4AR5TWGQB4/action/author_attestation","sign_citation":"https://pith.science/pith/AWOGQA3VMUGXFNTF4AR5TWGQB4/action/citation_signature","submit_replication":"https://pith.science/pith/AWOGQA3VMUGXFNTF4AR5TWGQB4/action/replication_record"}},"created_at":"2026-05-18T02:46:05.411777+00:00","updated_at":"2026-05-18T02:46:05.411777+00:00"}