{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:2KKH3SBSUJRMW6OU52EWAYWMOZ","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":"0747539698d7513fae2742d49cbe370aed80fe6e90aca5dc52adefd8084bd1e0","cross_cats_sorted":["hep-th","math-ph","math.MP","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1996-12-17T09:54:56Z","title_canon_sha256":"d650ee204376dbadaf5a9a4d0e732ba66e811bcdcd08ef6d26c12b6aa071c3d7"},"schema_version":"1.0","source":{"id":"q-alg/9612021","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9612021","created_at":"2026-07-04T15:21:07Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9612021v2","created_at":"2026-07-04T15:21:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9612021","created_at":"2026-07-04T15:21:07Z"},{"alias_kind":"pith_short_12","alias_value":"2KKH3SBSUJRM","created_at":"2026-07-04T15:21:07Z"},{"alias_kind":"pith_short_16","alias_value":"2KKH3SBSUJRMW6OU","created_at":"2026-07-04T15:21:07Z"},{"alias_kind":"pith_short_8","alias_value":"2KKH3SBS","created_at":"2026-07-04T15:21:07Z"}],"graph_snapshots":[{"event_id":"sha256:8562764105055d3a201a65a83cb63aa62753c7ae7d170908e51e2a66a3d6eb44","target":"graph","created_at":"2026-07-04T15:21:07Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/q-alg/9612021/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the central extensions of a whole family of Lie algebras, obtained by the method of graded contractions from so(N+1), N arbitrary. All the inhomogeneous orthogonal and pseudo-orthogonal algebras are members of this family, as well as a large number of other non-semisimple algebras, all of which have at least a semidirect structure (in some cases two or more). The dimensions of their second cohomology groups H^2(G,R) and the explicit expression of their central extensions are given.","authors_text":"F. J. Herranz, J. A. de Azcarraga, J. C. Perez Bueno, M. Santander","cross_cats":["hep-th","math-ph","math.MP","math.QA"],"headline":"","license":"","primary_cat":"q-alg","submitted_at":"1996-12-17T09:54:56Z","title":"Central Extensions of the Quasi-orthogonal Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9612021","kind":"arxiv","version":2},"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:ad687a92ad3ba334a1008e0afc1908fcd1ed7c2e50cead97d4cc5c5cbf8e5d80","target":"record","created_at":"2026-07-04T15:21:07Z","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":"0747539698d7513fae2742d49cbe370aed80fe6e90aca5dc52adefd8084bd1e0","cross_cats_sorted":["hep-th","math-ph","math.MP","math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1996-12-17T09:54:56Z","title_canon_sha256":"d650ee204376dbadaf5a9a4d0e732ba66e811bcdcd08ef6d26c12b6aa071c3d7"},"schema_version":"1.0","source":{"id":"q-alg/9612021","kind":"arxiv","version":2}},"canonical_sha256":"d2947dc832a262cb79d4ee896062cc76743c4f45fb34795f8c0376e6f0d14135","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2947dc832a262cb79d4ee896062cc76743c4f45fb34795f8c0376e6f0d14135","first_computed_at":"2026-07-04T15:21:07.512883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:21:07.512883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1U/i5nnsnPmY4GD+CiRAnxV6CPLcLlib9jUa6wOS1fM/xDDyfupG+cejGBRoykHQ9F6Ph1dgTWgAkP3ItGzwDg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:21:07.513254Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-alg/9612021","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad687a92ad3ba334a1008e0afc1908fcd1ed7c2e50cead97d4cc5c5cbf8e5d80","sha256:8562764105055d3a201a65a83cb63aa62753c7ae7d170908e51e2a66a3d6eb44"],"state_sha256":"3db7a838659eb09aacf952ec4695b37a91957eac6ff9440ecd7c475b7b62b6af"}