{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WUTSOGVZ24BWQ37OHPSV3RBCZL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"570f47f7e800bc8ab383ee450ebcfd5eaf11bf086eedef6bc9c5825ca9530cd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-13T10:01:46Z","title_canon_sha256":"d14db9dc0982a5b33a79ab9f380574e0a560e27cfe221198c294ead83c16657e"},"schema_version":"1.0","source":{"id":"1410.3244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3244","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3244v1","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3244","created_at":"2026-05-18T02:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"WUTSOGVZ24BW","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WUTSOGVZ24BWQ37O","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WUTSOGVZ","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:bed05adadc127eec84e27547aaf2f3abf7cdbe25a6affa3f48ae200a96a3fcd7","target":"graph","created_at":"2026-05-18T02:40:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present a partial classification of the pseudo $H$-type algebras with minimal admissible Clifford modules. Furthermore, we prove that the subspace $\\mathfrak{v}_{r,s}$ of $\\mathfrak{n}_{r,s}$ is strongly bracket generating if and only if $r=0$ or $s=0$. Additionally, we discuss the classification of pseudo $H$-type algebras related to non-equivalent irreducible Clifford modules.","authors_text":"Christian Autenried, Irina Markina, Kenro Furutani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-13T10:01:46Z","title":"Classification of pseudo $H$-type algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3244","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5e77caa5913521ec5ca83463dd57eb350dcfb1fc5bf2b95588de5db59ac140ff","target":"record","created_at":"2026-05-18T02:40:11Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"570f47f7e800bc8ab383ee450ebcfd5eaf11bf086eedef6bc9c5825ca9530cd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-10-13T10:01:46Z","title_canon_sha256":"d14db9dc0982a5b33a79ab9f380574e0a560e27cfe221198c294ead83c16657e"},"schema_version":"1.0","source":{"id":"1410.3244","kind":"arxiv","version":1}},"canonical_sha256":"b527271ab9d703686fee3be55dc422cafa9c93311c607af7ad68201b0c87b6ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b527271ab9d703686fee3be55dc422cafa9c93311c607af7ad68201b0c87b6ce","first_computed_at":"2026-05-18T02:40:11.709843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:11.709843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zq1XTxqfri1/ndKJ5QZ4klBVhROfbDS98vXf1OFJ4PXz0xVNScMyn6fI8NSXnMw2HgrLSP8ul+w81tdIqEQoCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:11.710353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e77caa5913521ec5ca83463dd57eb350dcfb1fc5bf2b95588de5db59ac140ff","sha256:bed05adadc127eec84e27547aaf2f3abf7cdbe25a6affa3f48ae200a96a3fcd7"],"state_sha256":"b6a5d23f397696818a0ca36e10eda0114c266bf6c906f59652d426b3f9bba732"}