{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:K6WVGGWUF3D4X43ZUOVYB47MMK","short_pith_number":"pith:K6WVGGWU","canonical_record":{"source":{"id":"2204.12976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-04-27T14:41:04Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6dc6b4e24d2ec7f11b48994e1bf819cf01ff021b5f9810b747dbdc25a8d375cc","abstract_canon_sha256":"b32fc68a0f806c1b772fa0ba25d772a1a21c395164e2985225ae77645fa74d09"},"schema_version":"1.0"},"canonical_sha256":"57ad531ad42ec7cbf379a3ab80f3ec62af5f9387aeb08c5d1fdf0df38679ffab","source":{"kind":"arxiv","id":"2204.12976","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.12976","created_at":"2026-07-05T04:18:24Z"},{"alias_kind":"arxiv_version","alias_value":"2204.12976v1","created_at":"2026-07-05T04:18:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.12976","created_at":"2026-07-05T04:18:24Z"},{"alias_kind":"pith_short_12","alias_value":"K6WVGGWUF3D4","created_at":"2026-07-05T04:18:24Z"},{"alias_kind":"pith_short_16","alias_value":"K6WVGGWUF3D4X43Z","created_at":"2026-07-05T04:18:24Z"},{"alias_kind":"pith_short_8","alias_value":"K6WVGGWU","created_at":"2026-07-05T04:18:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:K6WVGGWUF3D4X43ZUOVYB47MMK","target":"record","payload":{"canonical_record":{"source":{"id":"2204.12976","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-04-27T14:41:04Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"6dc6b4e24d2ec7f11b48994e1bf819cf01ff021b5f9810b747dbdc25a8d375cc","abstract_canon_sha256":"b32fc68a0f806c1b772fa0ba25d772a1a21c395164e2985225ae77645fa74d09"},"schema_version":"1.0"},"canonical_sha256":"57ad531ad42ec7cbf379a3ab80f3ec62af5f9387aeb08c5d1fdf0df38679ffab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:18:24.800266Z","signature_b64":"BV6Vkdlszdcb3/9fp3d259GWJ3O6mRRbmgizpqkydSDSUfC0AcLgZz7YiNap3wUd5q0SRRtYqUvnH4X2BPM7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57ad531ad42ec7cbf379a3ab80f3ec62af5f9387aeb08c5d1fdf0df38679ffab","last_reissued_at":"2026-07-05T04:18:24.799795Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:18:24.799795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.12976","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":"2026-07-05T04:18:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0a3HwV87KYVeRrIPAVHED7Vh/D4cZj9y2ARZCdMMitBqVnSl8EQiV8f8+Uq/ph/5Zn8k42ugXi4RbvwyV6hZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T05:11:49.439197Z"},"content_sha256":"edf4e95bdd9a57191d5d3ea0bf58c1e013f5b27664c09c8cff4553116aed722e","schema_version":"1.0","event_id":"sha256:edf4e95bdd9a57191d5d3ea0bf58c1e013f5b27664c09c8cff4553116aed722e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:K6WVGGWUF3D4X43ZUOVYB47MMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing the Lyapunov operator \\varphi-functions, with an application to matrix-valued exponential integrators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Dongping Li, Xiuying Zhang, Yue Zhang","submitted_at":"2022-04-27T14:41:04Z","abstract_excerpt":"In this paper, we develop efficient and accurate evaluation for the Lyapunov operator function $\\varphi_l(\\mathcal{L}_A)[Q],$ where $\\varphi_l(\\cdot)$ is the function related to the exponential, $\\mathcal{L}_A$ is a Lyapunov operator and $Q$ is a symmetric and full-rank matrix. An important application of the algorithm is to the matrix-valued exponential integrators for matrix differential equations such as differential Lyapunov equations and differential Riccati equations. The method is exploited by using the modified scaling and squaring procedure combined with the truncated Taylor series. A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.12976","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.12976/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":"2026-07-05T04:18:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nLtB9UkSQ+FzsAaotrhSt3/r5sb20PBZ1Me9hlJNn5T2j/nvIx7+/dzdBDiVy5KOGA77pFWnPD/TctdPnozzCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T05:11:49.440026Z"},"content_sha256":"50a8ac6cd76c53a575dd98a238c4bc832e07f9c88cc41937c316f29784ef6389","schema_version":"1.0","event_id":"sha256:50a8ac6cd76c53a575dd98a238c4bc832e07f9c88cc41937c316f29784ef6389"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6WVGGWUF3D4X43ZUOVYB47MMK/bundle.json","state_url":"https://pith.science/pith/K6WVGGWUF3D4X43ZUOVYB47MMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6WVGGWUF3D4X43ZUOVYB47MMK/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":"2026-08-20T05:11:49Z","links":{"resolver":"https://pith.science/pith/K6WVGGWUF3D4X43ZUOVYB47MMK","bundle":"https://pith.science/pith/K6WVGGWUF3D4X43ZUOVYB47MMK/bundle.json","state":"https://pith.science/pith/K6WVGGWUF3D4X43ZUOVYB47MMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6WVGGWUF3D4X43ZUOVYB47MMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:K6WVGGWUF3D4X43ZUOVYB47MMK","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":"b32fc68a0f806c1b772fa0ba25d772a1a21c395164e2985225ae77645fa74d09","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-04-27T14:41:04Z","title_canon_sha256":"6dc6b4e24d2ec7f11b48994e1bf819cf01ff021b5f9810b747dbdc25a8d375cc"},"schema_version":"1.0","source":{"id":"2204.12976","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.12976","created_at":"2026-07-05T04:18:24Z"},{"alias_kind":"arxiv_version","alias_value":"2204.12976v1","created_at":"2026-07-05T04:18:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.12976","created_at":"2026-07-05T04:18:24Z"},{"alias_kind":"pith_short_12","alias_value":"K6WVGGWUF3D4","created_at":"2026-07-05T04:18:24Z"},{"alias_kind":"pith_short_16","alias_value":"K6WVGGWUF3D4X43Z","created_at":"2026-07-05T04:18:24Z"},{"alias_kind":"pith_short_8","alias_value":"K6WVGGWU","created_at":"2026-07-05T04:18:24Z"}],"graph_snapshots":[{"event_id":"sha256:50a8ac6cd76c53a575dd98a238c4bc832e07f9c88cc41937c316f29784ef6389","target":"graph","created_at":"2026-07-05T04:18:24Z","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/2204.12976/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we develop efficient and accurate evaluation for the Lyapunov operator function $\\varphi_l(\\mathcal{L}_A)[Q],$ where $\\varphi_l(\\cdot)$ is the function related to the exponential, $\\mathcal{L}_A$ is a Lyapunov operator and $Q$ is a symmetric and full-rank matrix. An important application of the algorithm is to the matrix-valued exponential integrators for matrix differential equations such as differential Lyapunov equations and differential Riccati equations. The method is exploited by using the modified scaling and squaring procedure combined with the truncated Taylor series. A","authors_text":"Dongping Li, Xiuying Zhang, Yue Zhang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-04-27T14:41:04Z","title":"Computing the Lyapunov operator \\varphi-functions, with an application to matrix-valued exponential integrators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.12976","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:edf4e95bdd9a57191d5d3ea0bf58c1e013f5b27664c09c8cff4553116aed722e","target":"record","created_at":"2026-07-05T04:18:24Z","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":"b32fc68a0f806c1b772fa0ba25d772a1a21c395164e2985225ae77645fa74d09","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-04-27T14:41:04Z","title_canon_sha256":"6dc6b4e24d2ec7f11b48994e1bf819cf01ff021b5f9810b747dbdc25a8d375cc"},"schema_version":"1.0","source":{"id":"2204.12976","kind":"arxiv","version":1}},"canonical_sha256":"57ad531ad42ec7cbf379a3ab80f3ec62af5f9387aeb08c5d1fdf0df38679ffab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57ad531ad42ec7cbf379a3ab80f3ec62af5f9387aeb08c5d1fdf0df38679ffab","first_computed_at":"2026-07-05T04:18:24.799795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:18:24.799795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BV6Vkdlszdcb3/9fp3d259GWJ3O6mRRbmgizpqkydSDSUfC0AcLgZz7YiNap3wUd5q0SRRtYqUvnH4X2BPM7Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:18:24.800266Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.12976","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:edf4e95bdd9a57191d5d3ea0bf58c1e013f5b27664c09c8cff4553116aed722e","sha256:50a8ac6cd76c53a575dd98a238c4bc832e07f9c88cc41937c316f29784ef6389"],"state_sha256":"03ce505a165f3571ae04ddd929067283f035ac09e65e8f60f1472056a9f73208"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+cM8f8QiZfxI1odPaH/wOGYJ5RDjVSBzpdB5uW2PGrjpK+bUh460mFJ34c/nPAI93c+2xeulX7vUGkoiiSWPBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T05:11:49.447536Z","bundle_sha256":"4404618f790c34d2a79d87d4cb02e383f8e275a11c35467ac9eeae2db6bc0d21"}}