{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XXF3ZGHQ2PDTJN2ZN6VRKLDRZI","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":"ddeaa7838659be1bd4b55c8bb4c745f20355d7c903b8242b9e29186e431cf3ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-13T08:47:25Z","title_canon_sha256":"27b753e75e4bd67a584d837e331c01d80f5eaf6bda0d1acae937f78b8fa9cab1"},"schema_version":"1.0","source":{"id":"1903.05360","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.05360","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"arxiv_version","alias_value":"1903.05360v1","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.05360","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"pith_short_12","alias_value":"XXF3ZGHQ2PDT","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XXF3ZGHQ2PDTJN2Z","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XXF3ZGHQ","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:d90ffa488f7da2e5ae9f8b36644e3a15bfcd6288a97e72e2e8f3824bff0d62ac","target":"graph","created_at":"2026-05-17T23:43:56Z","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":"The T-congruence Sylvester equation is the matrix equation $AX+X^{\\mathrm{T}}B=C$, where $A\\in\\mathbb{R}^{m\\times n}$, $B\\in\\mathbb{R}^{n\\times m}$, and $C\\in\\mathbb{R}^{m\\times m}$ are given, and $X\\in\\mathbb{R}^{n\\times m}$ is to be determined. Recently, Oozawa et al. discovered a transformation that the matrix equation is equivalent to one of the well-studied matrix equations (the Lyapunov equation); however, the condition of the transformation seems to be too limited because matrices $A$ and $B$ are assumed to be square matrices ($m=n$). In this paper, two transformations are provided for ","authors_text":"Masaya Oozawa, Shao-Liang Zhang, Tomohiro Sogabe, Tomoya Kemmochi, Yuki Satake, Yuto Miyatake","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-13T08:47:25Z","title":"Relation between the T-congruence Sylvester equation and the generalized Sylvester equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.05360","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":"sha256:60ae52dc65444fd4f377a791c24d232c403031a83beadef8962ca9757ea62167","target":"record","created_at":"2026-05-17T23:43:56Z","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":"ddeaa7838659be1bd4b55c8bb4c745f20355d7c903b8242b9e29186e431cf3ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-13T08:47:25Z","title_canon_sha256":"27b753e75e4bd67a584d837e331c01d80f5eaf6bda0d1acae937f78b8fa9cab1"},"schema_version":"1.0","source":{"id":"1903.05360","kind":"arxiv","version":1}},"canonical_sha256":"bdcbbc98f0d3c734b7596fab152c71ca0149df471c099f0eae48e8a495572ab8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdcbbc98f0d3c734b7596fab152c71ca0149df471c099f0eae48e8a495572ab8","first_computed_at":"2026-05-17T23:43:56.213844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:56.213844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uBNUqpKxzZuLfaDlDSgBCA2unvpWVr1cwk61LmRhc5Faicf8knz1ACaVEKN1X5/Z0bLil3eeUA3l3zgCZoxYDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:56.214611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.05360","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60ae52dc65444fd4f377a791c24d232c403031a83beadef8962ca9757ea62167","sha256:d90ffa488f7da2e5ae9f8b36644e3a15bfcd6288a97e72e2e8f3824bff0d62ac"],"state_sha256":"1f0ace89a1e6e5ff9965af0cb401a374df4fb26d5dc2f7746061b85010abb51d"}