{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2GSSJFHSJTPOMWL6F5U33QAZNH","short_pith_number":"pith:2GSSJFHS","schema_version":"1.0","canonical_sha256":"d1a52494f24cdee6597e2f69bdc01969d3be1fb95848ef8b247f0dec079a7c3e","source":{"kind":"arxiv","id":"1709.10350","version":1},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.10350","created_at":"2026-05-18T00:34:03.446568+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.10350v1","created_at":"2026-05-18T00:34:03.446568+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.10350","created_at":"2026-05-18T00:34:03.446568+00:00"},{"alias_kind":"pith_short_12","alias_value":"2GSSJFHSJTPO","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2GSSJFHSJTPOMWL6","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2GSSJFHS","created_at":"2026-05-18T12:30:55.937587+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH","json":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH.json","graph_json":"https://pith.science/api/pith-number/2GSSJFHSJTPOMWL6F5U33QAZNH/graph.json","events_json":"https://pith.science/api/pith-number/2GSSJFHSJTPOMWL6F5U33QAZNH/events.json","paper":"https://pith.science/paper/2GSSJFHS"},"agent_actions":{"view_html":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH","download_json":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH.json","view_paper":"https://pith.science/paper/2GSSJFHS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.10350&json=true","fetch_graph":"https://pith.science/api/pith-number/2GSSJFHSJTPOMWL6F5U33QAZNH/graph.json","fetch_events":"https://pith.science/api/pith-number/2GSSJFHSJTPOMWL6F5U33QAZNH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH/action/storage_attestation","attest_author":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH/action/author_attestation","sign_citation":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH/action/citation_signature","submit_replication":"https://pith.science/pith/2GSSJFHSJTPOMWL6F5U33QAZNH/action/replication_record"}},"created_at":"2026-05-18T00:34:03.446568+00:00","updated_at":"2026-05-18T00:34:03.446568+00:00"}