{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:I3ALITU4YWAAHBFHOX7ITYWOBR","short_pith_number":"pith:I3ALITU4","schema_version":"1.0","canonical_sha256":"46c0b44e9cc5800384a775fe89e2ce0c6142c02e8b5383f1b079a61ad42325a7","source":{"kind":"arxiv","id":"2107.09292","version":2},"attestation_state":"computed","paper":{"title":"Cluster Consensus on Matrix-weighted Switching Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA","cs.SY"],"primary_cat":"eess.SY","authors_text":"Dewei Li, Haibin Shao, Lulu Pan, Mehran Mesbahi, Yugeng Xi","submitted_at":"2021-07-20T07:20:23Z","abstract_excerpt":"This paper examines the cluster consensus problem of multi-agent systems on matrix-weighted switching networks. Necessary and/or sufficient conditions under which cluster consensus can be achieved are obtained and quantitative characterization of the steady-state of the cluster consensus are provided as well. Specifically, if the underlying network switches amongst finite number of networks, a necessary condition for cluster consensus of multi-agent system on switching matrix-weighted networks is firstly presented, it is shown that the steady-state of the system lies in the intersection of the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2107.09292","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2021-07-20T07:20:23Z","cross_cats_sorted":["cs.MA","cs.SY"],"title_canon_sha256":"e72ed8289699a7699b597fcad943bc531f12d5861fb288bce5f2da8fbe67ba01","abstract_canon_sha256":"5d14ca4944497f51df3f01be2dd7029134a5403531854c25c5dc28df4181911d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:59:38.366591Z","signature_b64":"tK8SErGjyfjklpikUD1rLa+3/T1J2jw5J6f+lhvt8qMcd6tWd2OKAHIqteF5xmlkUqsaX9lbu5dCQ1mcOaB8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46c0b44e9cc5800384a775fe89e2ce0c6142c02e8b5383f1b079a61ad42325a7","last_reissued_at":"2026-07-05T02:59:38.366070Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:59:38.366070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cluster Consensus on Matrix-weighted Switching Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA","cs.SY"],"primary_cat":"eess.SY","authors_text":"Dewei Li, Haibin Shao, Lulu Pan, Mehran Mesbahi, Yugeng Xi","submitted_at":"2021-07-20T07:20:23Z","abstract_excerpt":"This paper examines the cluster consensus problem of multi-agent systems on matrix-weighted switching networks. Necessary and/or sufficient conditions under which cluster consensus can be achieved are obtained and quantitative characterization of the steady-state of the cluster consensus are provided as well. Specifically, if the underlying network switches amongst finite number of networks, a necessary condition for cluster consensus of multi-agent system on switching matrix-weighted networks is firstly presented, it is shown that the steady-state of the system lies in the intersection of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.09292","kind":"arxiv","version":2},"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/2107.09292/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2107.09292","created_at":"2026-07-05T02:59:38.366140+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.09292v2","created_at":"2026-07-05T02:59:38.366140+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.09292","created_at":"2026-07-05T02:59:38.366140+00:00"},{"alias_kind":"pith_short_12","alias_value":"I3ALITU4YWAA","created_at":"2026-07-05T02:59:38.366140+00:00"},{"alias_kind":"pith_short_16","alias_value":"I3ALITU4YWAAHBFH","created_at":"2026-07-05T02:59:38.366140+00:00"},{"alias_kind":"pith_short_8","alias_value":"I3ALITU4","created_at":"2026-07-05T02:59:38.366140+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I3ALITU4YWAAHBFHOX7ITYWOBR","json":"https://pith.science/pith/I3ALITU4YWAAHBFHOX7ITYWOBR.json","graph_json":"https://pith.science/api/pith-number/I3ALITU4YWAAHBFHOX7ITYWOBR/graph.json","events_json":"https://pith.science/api/pith-number/I3ALITU4YWAAHBFHOX7ITYWOBR/events.json","paper":"https://pith.science/paper/I3ALITU4"},"agent_actions":{"view_html":"https://pith.science/pith/I3ALITU4YWAAHBFHOX7ITYWOBR","download_json":"https://pith.science/pith/I3ALITU4YWAAHBFHOX7ITYWOBR.json","view_paper":"https://pith.science/paper/I3ALITU4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.09292&json=true","fetch_graph":"https://pith.science/api/pith-number/I3ALITU4YWAAHBFHOX7ITYWOBR/graph.json","fetch_events":"https://pith.science/api/pith-number/I3ALITU4YWAAHBFHOX7ITYWOBR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I3ALITU4YWAAHBFHOX7ITYWOBR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I3ALITU4YWAAHBFHOX7ITYWOBR/action/storage_attestation","attest_author":"https://pith.science/pith/I3ALITU4YWAAHBFHOX7ITYWOBR/action/author_attestation","sign_citation":"https://pith.science/pith/I3ALITU4YWAAHBFHOX7ITYWOBR/action/citation_signature","submit_replication":"https://pith.science/pith/I3ALITU4YWAAHBFHOX7ITYWOBR/action/replication_record"}},"created_at":"2026-07-05T02:59:38.366140+00:00","updated_at":"2026-07-05T02:59:38.366140+00:00"}