{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EITRSP64AXEH3FHNLWTFMMANTV","short_pith_number":"pith:EITRSP64","canonical_record":{"source":{"id":"1708.07947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-26T08:06:02Z","cross_cats_sorted":[],"title_canon_sha256":"3484b9825757343ee6f338f08806e827afbff734ab10d52ba0a7f303f9d2a1e1","abstract_canon_sha256":"b8ec818dc09ac8acb31459fd82b491b96db099d513bd916767d193291d858352"},"schema_version":"1.0"},"canonical_sha256":"2227193fdc05c87d94ed5da656300d9d57fea4fbf3ae7627aba2f157ef20d95f","source":{"kind":"arxiv","id":"1708.07947","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07947","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07947v1","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07947","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"EITRSP64AXEH","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EITRSP64AXEH3FHN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EITRSP64","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EITRSP64AXEH3FHNLWTFMMANTV","target":"record","payload":{"canonical_record":{"source":{"id":"1708.07947","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-26T08:06:02Z","cross_cats_sorted":[],"title_canon_sha256":"3484b9825757343ee6f338f08806e827afbff734ab10d52ba0a7f303f9d2a1e1","abstract_canon_sha256":"b8ec818dc09ac8acb31459fd82b491b96db099d513bd916767d193291d858352"},"schema_version":"1.0"},"canonical_sha256":"2227193fdc05c87d94ed5da656300d9d57fea4fbf3ae7627aba2f157ef20d95f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:37.546187Z","signature_b64":"cpeD3U1xXUNiQB88GsTGsv9AxI7xHOjD+PibYNzE8V4sincD/aps2MPwcGtBRsD5PSHxlbZ7O8XEl1knv5O5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2227193fdc05c87d94ed5da656300d9d57fea4fbf3ae7627aba2f157ef20d95f","last_reissued_at":"2026-05-18T00:36:37.545715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:37.545715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.07947","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":"2026-05-18T00:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W3gBcLmWXLWE20RKMs8DkSw0q8Oh+WNlxx6NyAFMcL9AAiZJiumOh1dd7WavpWde+ZSOAG5KPbxxkWgLt6A5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:47:13.521631Z"},"content_sha256":"1c10649f7a21ed2f990e5e7454a7e71dc05614e49be3c0d95d508c3908dce72a","schema_version":"1.0","event_id":"sha256:1c10649f7a21ed2f990e5e7454a7e71dc05614e49be3c0d95d508c3908dce72a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EITRSP64AXEH3FHNLWTFMMANTV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solutions to Linear Bimatrix Equations with Applications to Pole Assignment of Complex-Valued Linear Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bin Zhou","submitted_at":"2017-08-26T08:06:02Z","abstract_excerpt":"We study in this paper solutions to several kinds of linear bimatrix equations arising from pole assignment and stability analysis of complex-valued linear systems, which have several potential applications in control theory, particularly, can be used to model second-order linear systems in a very dense manner. These linear bimatrix equations include generalized Sylvester bimatrix equations, Sylvester bimatrix equations, Stein bimatrix equations, and Lyapunov bimatrix equations. Complete and explicit solutions are provided in terms of the bimatrices that are coefficients of the equations/syste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07947","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":"2026-05-18T00:36:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ESGrA3fRJwLevQjmjvHMnhyxnRB3wM4T8QOQXia55r7bVY0AqSDhECAbP91B+GOikaLehTVk9PoVjU5OSuqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:47:13.521983Z"},"content_sha256":"f5c5a7bee3ad3591d328bd403867db343e2150888f74e3c4a9efe611644ca22b","schema_version":"1.0","event_id":"sha256:f5c5a7bee3ad3591d328bd403867db343e2150888f74e3c4a9efe611644ca22b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EITRSP64AXEH3FHNLWTFMMANTV/bundle.json","state_url":"https://pith.science/pith/EITRSP64AXEH3FHNLWTFMMANTV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EITRSP64AXEH3FHNLWTFMMANTV/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":"2026-06-02T20:47:13Z","links":{"resolver":"https://pith.science/pith/EITRSP64AXEH3FHNLWTFMMANTV","bundle":"https://pith.science/pith/EITRSP64AXEH3FHNLWTFMMANTV/bundle.json","state":"https://pith.science/pith/EITRSP64AXEH3FHNLWTFMMANTV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EITRSP64AXEH3FHNLWTFMMANTV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EITRSP64AXEH3FHNLWTFMMANTV","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":"b8ec818dc09ac8acb31459fd82b491b96db099d513bd916767d193291d858352","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-26T08:06:02Z","title_canon_sha256":"3484b9825757343ee6f338f08806e827afbff734ab10d52ba0a7f303f9d2a1e1"},"schema_version":"1.0","source":{"id":"1708.07947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07947","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07947v1","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07947","created_at":"2026-05-18T00:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"EITRSP64AXEH","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EITRSP64AXEH3FHN","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EITRSP64","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:f5c5a7bee3ad3591d328bd403867db343e2150888f74e3c4a9efe611644ca22b","target":"graph","created_at":"2026-05-18T00:36:37Z","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":"We study in this paper solutions to several kinds of linear bimatrix equations arising from pole assignment and stability analysis of complex-valued linear systems, which have several potential applications in control theory, particularly, can be used to model second-order linear systems in a very dense manner. These linear bimatrix equations include generalized Sylvester bimatrix equations, Sylvester bimatrix equations, Stein bimatrix equations, and Lyapunov bimatrix equations. Complete and explicit solutions are provided in terms of the bimatrices that are coefficients of the equations/syste","authors_text":"Bin Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-26T08:06:02Z","title":"Solutions to Linear Bimatrix Equations with Applications to Pole Assignment of Complex-Valued Linear Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07947","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":"sha256:1c10649f7a21ed2f990e5e7454a7e71dc05614e49be3c0d95d508c3908dce72a","target":"record","created_at":"2026-05-18T00:36:37Z","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":"b8ec818dc09ac8acb31459fd82b491b96db099d513bd916767d193291d858352","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-26T08:06:02Z","title_canon_sha256":"3484b9825757343ee6f338f08806e827afbff734ab10d52ba0a7f303f9d2a1e1"},"schema_version":"1.0","source":{"id":"1708.07947","kind":"arxiv","version":1}},"canonical_sha256":"2227193fdc05c87d94ed5da656300d9d57fea4fbf3ae7627aba2f157ef20d95f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2227193fdc05c87d94ed5da656300d9d57fea4fbf3ae7627aba2f157ef20d95f","first_computed_at":"2026-05-18T00:36:37.545715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:37.545715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cpeD3U1xXUNiQB88GsTGsv9AxI7xHOjD+PibYNzE8V4sincD/aps2MPwcGtBRsD5PSHxlbZ7O8XEl1knv5O5Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:37.546187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c10649f7a21ed2f990e5e7454a7e71dc05614e49be3c0d95d508c3908dce72a","sha256:f5c5a7bee3ad3591d328bd403867db343e2150888f74e3c4a9efe611644ca22b"],"state_sha256":"21270ce529a29cc34787388909707f96028adf0b689e97a1e392d3d2d164c54c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tb+WhtUIzfW5ZVPgGp2IKoZqpbdubzEl68LPyHlq04JKhsXGatoMwak3BajON+BkRzyo4eOzfi/v3FDEXu9bAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:47:13.524051Z","bundle_sha256":"ec9236a56ea3f50cfb9cd3a4bf0f6c01b758bbc8a4f98c7a2b262878fd23f6bd"}}