{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O65VJHBJDSNSMZFQP4ZGC5SNTH","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":"4c86a619fe4c6497b439fbacdca14d8313118ddb783f8ca77b7dc184d13a688b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-14T17:56:31Z","title_canon_sha256":"9848e5059a62c543596bfef69c2f1824025348d244c821b660b706e89484a593"},"schema_version":"1.0","source":{"id":"1407.3746","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3746","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3746v2","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3746","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"O65VJHBJDSNS","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O65VJHBJDSNSMZFQ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O65VJHBJ","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:461fd81c89d9f37fd6bd1e58b191bca6cc2f06ef3d120172bc8941fcf1df0042","target":"graph","created_at":"2026-05-18T02:30:15Z","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":"A first characterization of the isomorphism classes of $k$-involutions for any reductive algebraic group defined over a perfect field was given in \\cite{Helm2000} using $3$ invariants. In \\cite{HWD04,Helm-Wu2002} a full classification of all $k$-involutions on $\\text{SL}(n,k)$ for $k$ algebraically closed, the real numbers, the $p$-adic numbers or a finite field was provided. In this paper, we find analogous results to develop a detailed characterization of the $k$-involutions of $\\text{SO}(n,k,\\beta)$, where $\\beta$ is any non-degenerate symmetric bilinear form and $k$ is any field not of cha","authors_text":"Aloysius G. Helminck, Christopher E. Dometrius, Ling Wu, Robert W. Benim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-14T17:56:31Z","title":"Isomorphy Classes of $k$-Involutions of $\\text{SO}(n, k,\\beta)$, $n > 2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3746","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":"sha256:01ba91c9a57dd9ebdab17dd6cb36bc26d632dbad9378f12793d58402ca4cb602","target":"record","created_at":"2026-05-18T02:30:15Z","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":"4c86a619fe4c6497b439fbacdca14d8313118ddb783f8ca77b7dc184d13a688b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-14T17:56:31Z","title_canon_sha256":"9848e5059a62c543596bfef69c2f1824025348d244c821b660b706e89484a593"},"schema_version":"1.0","source":{"id":"1407.3746","kind":"arxiv","version":2}},"canonical_sha256":"77bb549c291c9b2664b07f3261764d99df6897213aa950e94342a633aea4c606","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77bb549c291c9b2664b07f3261764d99df6897213aa950e94342a633aea4c606","first_computed_at":"2026-05-18T02:30:15.488687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:15.488687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xoDE/oA9RGjIKamMaHRhKVB8Vsec3qaPFN/SBiH08Hs3uU8r042ToEYeAo6o6t+iMpO7DwV+Mbhk/QftddpuDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:15.489119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.3746","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01ba91c9a57dd9ebdab17dd6cb36bc26d632dbad9378f12793d58402ca4cb602","sha256:461fd81c89d9f37fd6bd1e58b191bca6cc2f06ef3d120172bc8941fcf1df0042"],"state_sha256":"8530c9efcc1cc6e6dc9e3a82e7a44ef2f5328d7a8abe7f8e299359de8a15efa3"}