{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:5AQFV5AWACBZ5ZOQE2NH6WT3JK","short_pith_number":"pith:5AQFV5AW","canonical_record":{"source":{"id":"0911.0379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-11-02T18:20:28Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"1e0ee03fbb16403e9478a2c173f9e4ec632853d6181a5ff0a683f65ef7470d06","abstract_canon_sha256":"ee9f4d3a5a45b190fb0c31abe3ad0506da8d7d4fa2ce8623e4d77f300fcc27e4"},"schema_version":"1.0"},"canonical_sha256":"e8205af41600839ee5d0269a7f5a7b4a8be15af5f7aa6f3a781ccc37d04f24b8","source":{"kind":"arxiv","id":"0911.0379","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0379","created_at":"2026-05-18T03:16:06Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0379v3","created_at":"2026-05-18T03:16:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0379","created_at":"2026-05-18T03:16:06Z"},{"alias_kind":"pith_short_12","alias_value":"5AQFV5AWACBZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5AQFV5AWACBZ5ZOQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5AQFV5AW","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:5AQFV5AWACBZ5ZOQE2NH6WT3JK","target":"record","payload":{"canonical_record":{"source":{"id":"0911.0379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-11-02T18:20:28Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"1e0ee03fbb16403e9478a2c173f9e4ec632853d6181a5ff0a683f65ef7470d06","abstract_canon_sha256":"ee9f4d3a5a45b190fb0c31abe3ad0506da8d7d4fa2ce8623e4d77f300fcc27e4"},"schema_version":"1.0"},"canonical_sha256":"e8205af41600839ee5d0269a7f5a7b4a8be15af5f7aa6f3a781ccc37d04f24b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:06.767428Z","signature_b64":"L02FrnUymC6CrutOTE+tFKUEXcMHJz77j77zaI0qjTPCMbOSMDcp1A5Kd0MZRSMgZTumUI42PLAsqxu7C9BiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8205af41600839ee5d0269a7f5a7b4a8be15af5f7aa6f3a781ccc37d04f24b8","last_reissued_at":"2026-05-18T03:16:06.766951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:06.766951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.0379","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:16:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hWEZJX9ZreQTFUxRCJcKqigaAZtvf3kZUCPaulRJbAbAgMYLcZObFR4A2LubE8LsknDOD8+LahO+5rEhaDcZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:31:26.267679Z"},"content_sha256":"d138f0e360fa1338f70603f755077f66a34534451bb0269d85da2472dda1a610","schema_version":"1.0","event_id":"sha256:d138f0e360fa1338f70603f755077f66a34534451bb0269d85da2472dda1a610"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:5AQFV5AWACBZ5ZOQE2NH6WT3JK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Conjugacy Classes in the orthogonal and symplectic groups over algebraically closed fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.GR","authors_text":"Krishnendu Gongopadhyay","submitted_at":"2009-11-02T18:20:28Z","abstract_excerpt":"Let $\\F$ be an algebraically closed field. Let $\\V$ be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form $B$ over $\\F$. Suppose the characteristic of $\\F$ is \\emph{large}, i.e. either zero or greater than the dimension of $\\V$. Let $I(\\V, B)$ denote the group of isometries. Using the Jacobson-Morozov lemma we give a new and simple proof of the fact that two elements in $I(\\V,B)$ are conjugate if and only if they have the same elementary divisors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0379","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:16:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XO5kbb0xIqdKpGfUbiaGtP81mUufxABR+rS6JqSN962q6HeB95A6Dcym1aI6/mFRQnZ9LQ/k0/UZ8MFg+oT4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:31:26.268019Z"},"content_sha256":"ec2afe179aa5a5208880d4fbf272b2996a229865b45f76ffedbdea3b15fa016f","schema_version":"1.0","event_id":"sha256:ec2afe179aa5a5208880d4fbf272b2996a229865b45f76ffedbdea3b15fa016f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5AQFV5AWACBZ5ZOQE2NH6WT3JK/bundle.json","state_url":"https://pith.science/pith/5AQFV5AWACBZ5ZOQE2NH6WT3JK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5AQFV5AWACBZ5ZOQE2NH6WT3JK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T14:31:26Z","links":{"resolver":"https://pith.science/pith/5AQFV5AWACBZ5ZOQE2NH6WT3JK","bundle":"https://pith.science/pith/5AQFV5AWACBZ5ZOQE2NH6WT3JK/bundle.json","state":"https://pith.science/pith/5AQFV5AWACBZ5ZOQE2NH6WT3JK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5AQFV5AWACBZ5ZOQE2NH6WT3JK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:5AQFV5AWACBZ5ZOQE2NH6WT3JK","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":"ee9f4d3a5a45b190fb0c31abe3ad0506da8d7d4fa2ce8623e4d77f300fcc27e4","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-11-02T18:20:28Z","title_canon_sha256":"1e0ee03fbb16403e9478a2c173f9e4ec632853d6181a5ff0a683f65ef7470d06"},"schema_version":"1.0","source":{"id":"0911.0379","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.0379","created_at":"2026-05-18T03:16:06Z"},{"alias_kind":"arxiv_version","alias_value":"0911.0379v3","created_at":"2026-05-18T03:16:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.0379","created_at":"2026-05-18T03:16:06Z"},{"alias_kind":"pith_short_12","alias_value":"5AQFV5AWACBZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"5AQFV5AWACBZ5ZOQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"5AQFV5AW","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:ec2afe179aa5a5208880d4fbf272b2996a229865b45f76ffedbdea3b15fa016f","target":"graph","created_at":"2026-05-18T03:16:06Z","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":"Let $\\F$ be an algebraically closed field. Let $\\V$ be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form $B$ over $\\F$. Suppose the characteristic of $\\F$ is \\emph{large}, i.e. either zero or greater than the dimension of $\\V$. Let $I(\\V, B)$ denote the group of isometries. Using the Jacobson-Morozov lemma we give a new and simple proof of the fact that two elements in $I(\\V,B)$ are conjugate if and only if they have the same elementary divisors.","authors_text":"Krishnendu Gongopadhyay","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-11-02T18:20:28Z","title":"On the Conjugacy Classes in the orthogonal and symplectic groups over algebraically closed fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.0379","kind":"arxiv","version":3},"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:d138f0e360fa1338f70603f755077f66a34534451bb0269d85da2472dda1a610","target":"record","created_at":"2026-05-18T03:16:06Z","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":"ee9f4d3a5a45b190fb0c31abe3ad0506da8d7d4fa2ce8623e4d77f300fcc27e4","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-11-02T18:20:28Z","title_canon_sha256":"1e0ee03fbb16403e9478a2c173f9e4ec632853d6181a5ff0a683f65ef7470d06"},"schema_version":"1.0","source":{"id":"0911.0379","kind":"arxiv","version":3}},"canonical_sha256":"e8205af41600839ee5d0269a7f5a7b4a8be15af5f7aa6f3a781ccc37d04f24b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8205af41600839ee5d0269a7f5a7b4a8be15af5f7aa6f3a781ccc37d04f24b8","first_computed_at":"2026-05-18T03:16:06.766951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:06.766951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L02FrnUymC6CrutOTE+tFKUEXcMHJz77j77zaI0qjTPCMbOSMDcp1A5Kd0MZRSMgZTumUI42PLAsqxu7C9BiCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:06.767428Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.0379","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d138f0e360fa1338f70603f755077f66a34534451bb0269d85da2472dda1a610","sha256:ec2afe179aa5a5208880d4fbf272b2996a229865b45f76ffedbdea3b15fa016f"],"state_sha256":"95f9a5b058416bc8390df7581620edaa1febafbaadaad339f9580a74c4f0bdc3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4xSqCRaihCRXlLdvfhhh38BK2UFuKUYW/yHmRFkNHcRwEVFuUgYoG3ErJby6XCsJwXJYhbH+KuVQxF/aKMJDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:31:26.270105Z","bundle_sha256":"74ffd8ce4a45b3c526673b9344a9f2a089ac9bf4d43175fd2644ecda200852ac"}}