{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2GSSJFHSJTPOMWL6F5U33QAZNH","short_pith_number":"pith:2GSSJFHS","canonical_record":{"source":{"id":"1709.10350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-29T11:52:26Z","cross_cats_sorted":[],"title_canon_sha256":"0d3ee6dc37877642713f503c65cf5accff0ae939e1756b8a5f70adf9ee76035a","abstract_canon_sha256":"a2f0838cb8a57fb04c5c1beb277450f942928184480afdc4af0c16d6fe848223"},"schema_version":"1.0"},"canonical_sha256":"d1a52494f24cdee6597e2f69bdc01969d3be1fb95848ef8b247f0dec079a7c3e","source":{"kind":"arxiv","id":"1709.10350","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10350","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10350v1","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10350","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"2GSSJFHSJTPO","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2GSSJFHSJTPOMWL6","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2GSSJFHS","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2GSSJFHSJTPOMWL6F5U33QAZNH","target":"record","payload":{"canonical_record":{"source":{"id":"1709.10350","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-29T11:52:26Z","cross_cats_sorted":[],"title_canon_sha256":"0d3ee6dc37877642713f503c65cf5accff0ae939e1756b8a5f70adf9ee76035a","abstract_canon_sha256":"a2f0838cb8a57fb04c5c1beb277450f942928184480afdc4af0c16d6fe848223"},"schema_version":"1.0"},"canonical_sha256":"d1a52494f24cdee6597e2f69bdc01969d3be1fb95848ef8b247f0dec079a7c3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:03.447115Z","signature_b64":"VihtYlpECNsOACricVOE5t8e4NVXIpGScgw7FDFiDbxTGew0kDCxTJ9FAJvm7kQAwbJTf82vEd5RDTLGSEEcAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1a52494f24cdee6597e2f69bdc01969d3be1fb95848ef8b247f0dec079a7c3e","last_reissued_at":"2026-05-18T00:34:03.446453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:03.446453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.10350","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1mUQIVTosR88nHBTXjAXXsiJ/8xEze5/VsvyeqnQhjLQDL51+esSRodDF09SNIZcIosTwK8jC9jc4rgr62VwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:00:01.852716Z"},"content_sha256":"4768112b8eeae9001d3f56a3a0abdcc3f117ab250b3335ebc69436fcf052a436","schema_version":"1.0","event_id":"sha256:4768112b8eeae9001d3f56a3a0abdcc3f117ab250b3335ebc69436fcf052a436"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2GSSJFHSJTPOMWL6F5U33QAZNH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symplectic spaces and pairs of symmetric and nonsingular skew-symmetric matrices under congruence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mohamed A. Salim, Roger A. Horn, Victor A. Bovdi, Vladimir V. Sergeichuk","submitted_at":"2017-09-29T11:52:26Z","abstract_excerpt":"Let $\\mathbb F$ be a field of characteristic not $2$, and let $(A,B)$ be a pair of $n\\times n$ matrices over $\\mathbb F$, in which $A$ is symmetric and $B$ is skew-symmetric. A canonical form of $(A,B)$ with respect to congruence transformations $(S^TAS,S^TBS)$ was given by Sergeichuk (1988) up to classification of symmetric and Hermitian forms over finite extensions of $\\mathbb F$. We obtain a simpler canonical form of $(A,B)$ if $B$ is nonsingular. Such a pair $(A,B)$ defines a quadratic form on a symplectic space, that is, on a vector space with scalar product given by a nonsingular skew-sy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10350","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uqP9mURuHBcmXyDIlH63RYALVwGvAt1NiE5fO+nj7/6sYFC1/W1XpArFaltbNrlZgKabW4x5zCKTLvClbTd+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:00:01.853066Z"},"content_sha256":"221075ae2a46551ce5d6c81fe55a62dc0d71dbe0bfa66eb7f7c416e24e5da6d2","schema_version":"1.0","event_id":"sha256:221075ae2a46551ce5d6c81fe55a62dc0d71dbe0bfa66eb7f7c416e24e5da6d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH/bundle.json","state_url":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2GSSJFHSJTPOMWL6F5U33QAZNH/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":"2026-06-05T15:00:01Z","links":{"resolver":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH","bundle":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH/bundle.json","state":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2GSSJFHSJTPOMWL6F5U33QAZNH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2GSSJFHSJTPOMWL6F5U33QAZNH","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":"a2f0838cb8a57fb04c5c1beb277450f942928184480afdc4af0c16d6fe848223","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-29T11:52:26Z","title_canon_sha256":"0d3ee6dc37877642713f503c65cf5accff0ae939e1756b8a5f70adf9ee76035a"},"schema_version":"1.0","source":{"id":"1709.10350","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.10350","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"arxiv_version","alias_value":"1709.10350v1","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10350","created_at":"2026-05-18T00:34:03Z"},{"alias_kind":"pith_short_12","alias_value":"2GSSJFHSJTPO","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2GSSJFHSJTPOMWL6","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2GSSJFHS","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:221075ae2a46551ce5d6c81fe55a62dc0d71dbe0bfa66eb7f7c416e24e5da6d2","target":"graph","created_at":"2026-05-18T00:34:03Z","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 $\\mathbb F$ be a field of characteristic not $2$, and let $(A,B)$ be a pair of $n\\times n$ matrices over $\\mathbb F$, in which $A$ is symmetric and $B$ is skew-symmetric. A canonical form of $(A,B)$ with respect to congruence transformations $(S^TAS,S^TBS)$ was given by Sergeichuk (1988) up to classification of symmetric and Hermitian forms over finite extensions of $\\mathbb F$. We obtain a simpler canonical form of $(A,B)$ if $B$ is nonsingular. Such a pair $(A,B)$ defines a quadratic form on a symplectic space, that is, on a vector space with scalar product given by a nonsingular skew-sy","authors_text":"Mohamed A. Salim, Roger A. Horn, Victor A. Bovdi, Vladimir V. Sergeichuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-29T11:52:26Z","title":"Symplectic spaces and pairs of symmetric and nonsingular skew-symmetric matrices under congruence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.10350","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":"sha256:4768112b8eeae9001d3f56a3a0abdcc3f117ab250b3335ebc69436fcf052a436","target":"record","created_at":"2026-05-18T00:34:03Z","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":"a2f0838cb8a57fb04c5c1beb277450f942928184480afdc4af0c16d6fe848223","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-09-29T11:52:26Z","title_canon_sha256":"0d3ee6dc37877642713f503c65cf5accff0ae939e1756b8a5f70adf9ee76035a"},"schema_version":"1.0","source":{"id":"1709.10350","kind":"arxiv","version":1}},"canonical_sha256":"d1a52494f24cdee6597e2f69bdc01969d3be1fb95848ef8b247f0dec079a7c3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1a52494f24cdee6597e2f69bdc01969d3be1fb95848ef8b247f0dec079a7c3e","first_computed_at":"2026-05-18T00:34:03.446453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:03.446453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VihtYlpECNsOACricVOE5t8e4NVXIpGScgw7FDFiDbxTGew0kDCxTJ9FAJvm7kQAwbJTf82vEd5RDTLGSEEcAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:03.447115Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.10350","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4768112b8eeae9001d3f56a3a0abdcc3f117ab250b3335ebc69436fcf052a436","sha256:221075ae2a46551ce5d6c81fe55a62dc0d71dbe0bfa66eb7f7c416e24e5da6d2"],"state_sha256":"ba878a506224ebc860f17dd7c620019c4c82c4deb16a63600beb08ef4d390c77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ix/eo0Upfh4a/Cw9zAdV1JepQvbqI0e1YcLvOFAiTknH8TjIjVQrBBGKNNyXcGRPYsHvldV/MimCIzwo+A3xBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:00:01.855067Z","bundle_sha256":"db18442cdc71c3930303b158d6a1e5f40280bd9291bcc465a700ab95ff1b5ec7"}}