{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VTLOFV4U2YZU35YVG2343AI32R","short_pith_number":"pith:VTLOFV4U","canonical_record":{"source":{"id":"2402.13491","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-21T03:03:11Z","cross_cats_sorted":[],"title_canon_sha256":"8e487d69496eafa9596de4d3b83cbb87162dc7befd277bfef1c03953462ca921","abstract_canon_sha256":"151eabd77df542da5103d7b3306feda47891f07efe80df5081c650a834e26547"},"schema_version":"1.0"},"canonical_sha256":"acd6e2d794d6334df71536b7cd811bd47336befc3dc5d5149d104c2ea53829ad","source":{"kind":"arxiv","id":"2402.13491","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.13491","created_at":"2026-07-05T11:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"2402.13491v5","created_at":"2026-07-05T11:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.13491","created_at":"2026-07-05T11:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"VTLOFV4U2YZU","created_at":"2026-07-05T11:39:39Z"},{"alias_kind":"pith_short_16","alias_value":"VTLOFV4U2YZU35YV","created_at":"2026-07-05T11:39:39Z"},{"alias_kind":"pith_short_8","alias_value":"VTLOFV4U","created_at":"2026-07-05T11:39:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VTLOFV4U2YZU35YVG2343AI32R","target":"record","payload":{"canonical_record":{"source":{"id":"2402.13491","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-21T03:03:11Z","cross_cats_sorted":[],"title_canon_sha256":"8e487d69496eafa9596de4d3b83cbb87162dc7befd277bfef1c03953462ca921","abstract_canon_sha256":"151eabd77df542da5103d7b3306feda47891f07efe80df5081c650a834e26547"},"schema_version":"1.0"},"canonical_sha256":"acd6e2d794d6334df71536b7cd811bd47336befc3dc5d5149d104c2ea53829ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:39:39.729747Z","signature_b64":"HdaWYHVN0J2psooZZwozOlexmggSLA6Fd1WbbFdRg8Dtyol/DellqdANF2/U/O+ciUurLosYJkzeLqwjb3puCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acd6e2d794d6334df71536b7cd811bd47336befc3dc5d5149d104c2ea53829ad","last_reissued_at":"2026-07-05T11:39:39.729263Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:39:39.729263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2402.13491","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lX9MmO3OzAQf+0LKaF20R+tsyZQ29nbZY0O9wqmmaTqXWkT2jOq2ZlfMf6IaiYjDpD0kQNrnMDEXfb3auPVZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:35:11.874414Z"},"content_sha256":"36303d68bc2305ed30760e4fe94ac8e113c2a26a294b688bb3421f5c098a1110","schema_version":"1.0","event_id":"sha256:36303d68bc2305ed30760e4fe94ac8e113c2a26a294b688bb3421f5c098a1110"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VTLOFV4U2YZU35YVG2343AI32R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic Riccati Tensor Equations with Applications in Multilinear Control Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Guofeng Zhang, Shih Yu Chang, Yimin Wei, Yuchao Wang","submitted_at":"2024-02-21T03:03:11Z","abstract_excerpt":"In a recent paper by Chen et al. [8], the authors initiated the control-theoretic study of a class of discrete-time multilinear time-invariant (MLTI) control systems, where system states, inputs, and outputs are all tensors endowed with the Einstein product. They established criteria for fundamental system-theoretic notions such as stability, reachability, and observability through tensor decomposition. Building on this new research direction, the purpose of our paper is to extend the study to continuous-time MLTI control systems. Specifically, we define Hamiltonian tensors and symplectic tens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.13491","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.13491/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sKAwguiWBA/viVeSqbzLDPnIpqCtGuZ9Ub9qLJAp1MLJTkvp+2YkfwvtOqxeFcBihReIs7Gb6PU6vKswc80rAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:35:11.874925Z"},"content_sha256":"b4ae3477fefb7c309c034abfc971ba277c958aad086d7da983e75ae178ab1995","schema_version":"1.0","event_id":"sha256:b4ae3477fefb7c309c034abfc971ba277c958aad086d7da983e75ae178ab1995"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VTLOFV4U2YZU35YVG2343AI32R/bundle.json","state_url":"https://pith.science/pith/VTLOFV4U2YZU35YVG2343AI32R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VTLOFV4U2YZU35YVG2343AI32R/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":"2026-08-05T21:35:11Z","links":{"resolver":"https://pith.science/pith/VTLOFV4U2YZU35YVG2343AI32R","bundle":"https://pith.science/pith/VTLOFV4U2YZU35YVG2343AI32R/bundle.json","state":"https://pith.science/pith/VTLOFV4U2YZU35YVG2343AI32R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VTLOFV4U2YZU35YVG2343AI32R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VTLOFV4U2YZU35YVG2343AI32R","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":"151eabd77df542da5103d7b3306feda47891f07efe80df5081c650a834e26547","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-21T03:03:11Z","title_canon_sha256":"8e487d69496eafa9596de4d3b83cbb87162dc7befd277bfef1c03953462ca921"},"schema_version":"1.0","source":{"id":"2402.13491","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.13491","created_at":"2026-07-05T11:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"2402.13491v5","created_at":"2026-07-05T11:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.13491","created_at":"2026-07-05T11:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"VTLOFV4U2YZU","created_at":"2026-07-05T11:39:39Z"},{"alias_kind":"pith_short_16","alias_value":"VTLOFV4U2YZU35YV","created_at":"2026-07-05T11:39:39Z"},{"alias_kind":"pith_short_8","alias_value":"VTLOFV4U","created_at":"2026-07-05T11:39:39Z"}],"graph_snapshots":[{"event_id":"sha256:b4ae3477fefb7c309c034abfc971ba277c958aad086d7da983e75ae178ab1995","target":"graph","created_at":"2026-07-05T11:39:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2402.13491/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a recent paper by Chen et al. [8], the authors initiated the control-theoretic study of a class of discrete-time multilinear time-invariant (MLTI) control systems, where system states, inputs, and outputs are all tensors endowed with the Einstein product. They established criteria for fundamental system-theoretic notions such as stability, reachability, and observability through tensor decomposition. Building on this new research direction, the purpose of our paper is to extend the study to continuous-time MLTI control systems. Specifically, we define Hamiltonian tensors and symplectic tens","authors_text":"Guofeng Zhang, Shih Yu Chang, Yimin Wei, Yuchao Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-21T03:03:11Z","title":"Algebraic Riccati Tensor Equations with Applications in Multilinear Control Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.13491","kind":"arxiv","version":5},"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":"sha256:36303d68bc2305ed30760e4fe94ac8e113c2a26a294b688bb3421f5c098a1110","target":"record","created_at":"2026-07-05T11:39:39Z","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":"151eabd77df542da5103d7b3306feda47891f07efe80df5081c650a834e26547","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-02-21T03:03:11Z","title_canon_sha256":"8e487d69496eafa9596de4d3b83cbb87162dc7befd277bfef1c03953462ca921"},"schema_version":"1.0","source":{"id":"2402.13491","kind":"arxiv","version":5}},"canonical_sha256":"acd6e2d794d6334df71536b7cd811bd47336befc3dc5d5149d104c2ea53829ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acd6e2d794d6334df71536b7cd811bd47336befc3dc5d5149d104c2ea53829ad","first_computed_at":"2026-07-05T11:39:39.729263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:39.729263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HdaWYHVN0J2psooZZwozOlexmggSLA6Fd1WbbFdRg8Dtyol/DellqdANF2/U/O+ciUurLosYJkzeLqwjb3puCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:39.729747Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.13491","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36303d68bc2305ed30760e4fe94ac8e113c2a26a294b688bb3421f5c098a1110","sha256:b4ae3477fefb7c309c034abfc971ba277c958aad086d7da983e75ae178ab1995"],"state_sha256":"f52588b9d57303a58dbee28181699d4b2073ab7925b4478e36398d6ce327c4a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K+0RnhNizo+qof66Om7lSdFDpSc+yYcX4yf2AdjdpDlDFKExkjQFpvkURlFaK/+JxnjBFQLCZpgOhfRV+uzNCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T21:35:11.880762Z","bundle_sha256":"541207cbae34382f7913768a1804722b942561b7deb245d006397b38d8fac90d"}}