{"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"}