{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5YZYK6TAQ2GRNA22ZXOOZBVVG2","short_pith_number":"pith:5YZYK6TA","canonical_record":{"source":{"id":"1807.07840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-07-20T13:52:05Z","cross_cats_sorted":[],"title_canon_sha256":"27725c9adf29ba364b408d6a1aa04b8e14299c63d770ef65973d1928d18d98ff","abstract_canon_sha256":"b120a662f0b0bb8bbfa98e744dd6b479bb7773c647bcc329d488f86e857630ee"},"schema_version":"1.0"},"canonical_sha256":"ee33857a60868d16835acddcec86b536847814d8cf470d0cf5cdeade76aa27b9","source":{"kind":"arxiv","id":"1807.07840","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07840","created_at":"2026-05-18T00:10:15Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07840v1","created_at":"2026-05-18T00:10:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07840","created_at":"2026-05-18T00:10:15Z"},{"alias_kind":"pith_short_12","alias_value":"5YZYK6TAQ2GR","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5YZYK6TAQ2GRNA22","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5YZYK6TA","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5YZYK6TAQ2GRNA22ZXOOZBVVG2","target":"record","payload":{"canonical_record":{"source":{"id":"1807.07840","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-07-20T13:52:05Z","cross_cats_sorted":[],"title_canon_sha256":"27725c9adf29ba364b408d6a1aa04b8e14299c63d770ef65973d1928d18d98ff","abstract_canon_sha256":"b120a662f0b0bb8bbfa98e744dd6b479bb7773c647bcc329d488f86e857630ee"},"schema_version":"1.0"},"canonical_sha256":"ee33857a60868d16835acddcec86b536847814d8cf470d0cf5cdeade76aa27b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:15.500817Z","signature_b64":"Brt6205YbCBVABAf2V7cju1OdYk8LzUFk5dTcDXN9vVtAFDyje4MXHErK2jvQ4YccqSworNIxwhBw+xpPK1UCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee33857a60868d16835acddcec86b536847814d8cf470d0cf5cdeade76aa27b9","last_reissued_at":"2026-05-18T00:10:15.500065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:15.500065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.07840","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":"2026-05-18T00:10:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Y5klcvgq/30Kq31sHiWbuzFTFGJSF+1cgonMbZ8K0JcriLwfdWSs8g63PiODz+uZWRSos3Jos56+mWXq32fCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:56:25.416932Z"},"content_sha256":"5d58f87442458cc0bd8ca36d1e332e96f513743e145fbb664dec510b05e31a30","schema_version":"1.0","event_id":"sha256:5d58f87442458cc0bd8ca36d1e332e96f513743e145fbb664dec510b05e31a30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5YZYK6TAQ2GRNA22ZXOOZBVVG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Synchronization of Dynamical Systems over Directed Switching Topologies: An Algebraic and Geometric Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Jiahu Qin, Long Wang, Qichao Ma, Xinghuo Yu","submitted_at":"2018-07-20T13:52:05Z","abstract_excerpt":"In this paper, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on the switching topologies is imposed, which allows them to be directed and jointly connected. We propose a novel analysis framework from both algebraic and geometric perspectives to justify the attractiveness of the synchronization manifold. Specifically, it is proven that the complementary space of the synchronization manifold can be spanned by certain subspa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07840","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":"2026-05-18T00:10:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2dzHMVKxJLy57a/AQUR+CIfJWWOJlRt3PoqyXXO1rMwujNl/030N45KECgs2SJDXmRTZYABehPLl0967XbKDBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:56:25.417352Z"},"content_sha256":"2ac00a0ee1ef20a6ae8ba208f430a7ca521d720bdf3572a05e130325bf4c9bb8","schema_version":"1.0","event_id":"sha256:2ac00a0ee1ef20a6ae8ba208f430a7ca521d720bdf3572a05e130325bf4c9bb8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5YZYK6TAQ2GRNA22ZXOOZBVVG2/bundle.json","state_url":"https://pith.science/pith/5YZYK6TAQ2GRNA22ZXOOZBVVG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5YZYK6TAQ2GRNA22ZXOOZBVVG2/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":"2026-05-27T12:56:25Z","links":{"resolver":"https://pith.science/pith/5YZYK6TAQ2GRNA22ZXOOZBVVG2","bundle":"https://pith.science/pith/5YZYK6TAQ2GRNA22ZXOOZBVVG2/bundle.json","state":"https://pith.science/pith/5YZYK6TAQ2GRNA22ZXOOZBVVG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5YZYK6TAQ2GRNA22ZXOOZBVVG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5YZYK6TAQ2GRNA22ZXOOZBVVG2","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":"b120a662f0b0bb8bbfa98e744dd6b479bb7773c647bcc329d488f86e857630ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-07-20T13:52:05Z","title_canon_sha256":"27725c9adf29ba364b408d6a1aa04b8e14299c63d770ef65973d1928d18d98ff"},"schema_version":"1.0","source":{"id":"1807.07840","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07840","created_at":"2026-05-18T00:10:15Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07840v1","created_at":"2026-05-18T00:10:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07840","created_at":"2026-05-18T00:10:15Z"},{"alias_kind":"pith_short_12","alias_value":"5YZYK6TAQ2GR","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5YZYK6TAQ2GRNA22","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5YZYK6TA","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:2ac00a0ee1ef20a6ae8ba208f430a7ca521d720bdf3572a05e130325bf4c9bb8","target":"graph","created_at":"2026-05-18T00:10:15Z","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":"In this paper, we aim to investigate the synchronization problem of dynamical systems, which can be of generic linear or Lipschitz nonlinear type, communicating over directed switching network topologies. A mild connectivity assumption on the switching topologies is imposed, which allows them to be directed and jointly connected. We propose a novel analysis framework from both algebraic and geometric perspectives to justify the attractiveness of the synchronization manifold. Specifically, it is proven that the complementary space of the synchronization manifold can be spanned by certain subspa","authors_text":"Jiahu Qin, Long Wang, Qichao Ma, Xinghuo Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-07-20T13:52:05Z","title":"On Synchronization of Dynamical Systems over Directed Switching Topologies: An Algebraic and Geometric Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07840","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":"sha256:5d58f87442458cc0bd8ca36d1e332e96f513743e145fbb664dec510b05e31a30","target":"record","created_at":"2026-05-18T00:10:15Z","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":"b120a662f0b0bb8bbfa98e744dd6b479bb7773c647bcc329d488f86e857630ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-07-20T13:52:05Z","title_canon_sha256":"27725c9adf29ba364b408d6a1aa04b8e14299c63d770ef65973d1928d18d98ff"},"schema_version":"1.0","source":{"id":"1807.07840","kind":"arxiv","version":1}},"canonical_sha256":"ee33857a60868d16835acddcec86b536847814d8cf470d0cf5cdeade76aa27b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee33857a60868d16835acddcec86b536847814d8cf470d0cf5cdeade76aa27b9","first_computed_at":"2026-05-18T00:10:15.500065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:15.500065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Brt6205YbCBVABAf2V7cju1OdYk8LzUFk5dTcDXN9vVtAFDyje4MXHErK2jvQ4YccqSworNIxwhBw+xpPK1UCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:15.500817Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07840","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d58f87442458cc0bd8ca36d1e332e96f513743e145fbb664dec510b05e31a30","sha256:2ac00a0ee1ef20a6ae8ba208f430a7ca521d720bdf3572a05e130325bf4c9bb8"],"state_sha256":"40a8d55077fdf1e689e4a22664de09f06005622d2282586f0ba82ef0cba51eb0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f2ugL9tmkuM7zgpYa6lGw2sfFFQHyDXJzoJPfqBnLDN/H/QJI2JgeH8f6UMCZ7eeQrKrYNQQVcMMzANb6yqFAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:56:25.419796Z","bundle_sha256":"c43167d1dbea7f177346d98c541df7f1fb0bed857454aa768a443c7955790d28"}}