{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:B2GZ2RBFHQ57ITXX76IWLOCTTL","short_pith_number":"pith:B2GZ2RBF","schema_version":"1.0","canonical_sha256":"0e8d9d44253c3bf44ef7ff9165b8539ae75ed39cc948463bc9e9479295b23fcd","source":{"kind":"arxiv","id":"1605.02411","version":3},"attestation_state":"computed","paper":{"title":"Convergence Analysis of Classes of Asymmetric Networks of Cucker-Smale Type with Deterministic Perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.OC","authors_text":"Christoforos Somarakis, Evripidis Paraskevas, John S. Baras, Nader Motee","submitted_at":"2016-05-09T04:02:53Z","abstract_excerpt":"We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence of identical internal dynamics. The second model describes a similar population of agents that perform velocity alignment with the restriction of collision-free orbits. Although qualitatively different, we explain how these two non-trivial types of perturbations are analyzed under a unified framework. Rigorous analysis is conducted towards establishing new su"},"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":"1605.02411","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-09T04:02:53Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"20ab1d75cd81831b5bb6b910dae73425c3619d781e9b844865bfefd8dd77dbc3","abstract_canon_sha256":"be1ff2b4ced02b2e44b2065f9b3ff6e5fbcf36a095705378729e0703ca78a29d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:53.315897Z","signature_b64":"qux2DWOSp+mLJj3JQgyAkDRI2sk7GYwpijci+LS7JShOmTvDYFMPOMgGNC9YUu+auaFsgWWYfD+6CMxdP7thAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e8d9d44253c3bf44ef7ff9165b8539ae75ed39cc948463bc9e9479295b23fcd","last_reissued_at":"2026-05-18T00:33:53.315257Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:53.315257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence Analysis of Classes of Asymmetric Networks of Cucker-Smale Type with Deterministic Perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.OC","authors_text":"Christoforos Somarakis, Evripidis Paraskevas, John S. Baras, Nader Motee","submitted_at":"2016-05-09T04:02:53Z","abstract_excerpt":"We introduce and discuss two nonlinear perturbed extensions of the Cucker-Smale model with asymmetric coupling weights. The first model assumes a finite collection of autonomous agents aiming to perform a consensus process in the presence of identical internal dynamics. The second model describes a similar population of agents that perform velocity alignment with the restriction of collision-free orbits. Although qualitatively different, we explain how these two non-trivial types of perturbations are analyzed under a unified framework. Rigorous analysis is conducted towards establishing new su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02411","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.02411","created_at":"2026-05-18T00:33:53.315391+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.02411v3","created_at":"2026-05-18T00:33:53.315391+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02411","created_at":"2026-05-18T00:33:53.315391+00:00"},{"alias_kind":"pith_short_12","alias_value":"B2GZ2RBFHQ57","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"B2GZ2RBFHQ57ITXX","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"B2GZ2RBF","created_at":"2026-05-18T12:30:07.202191+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/B2GZ2RBFHQ57ITXX76IWLOCTTL","json":"https://pith.science/pith/B2GZ2RBFHQ57ITXX76IWLOCTTL.json","graph_json":"https://pith.science/api/pith-number/B2GZ2RBFHQ57ITXX76IWLOCTTL/graph.json","events_json":"https://pith.science/api/pith-number/B2GZ2RBFHQ57ITXX76IWLOCTTL/events.json","paper":"https://pith.science/paper/B2GZ2RBF"},"agent_actions":{"view_html":"https://pith.science/pith/B2GZ2RBFHQ57ITXX76IWLOCTTL","download_json":"https://pith.science/pith/B2GZ2RBFHQ57ITXX76IWLOCTTL.json","view_paper":"https://pith.science/paper/B2GZ2RBF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.02411&json=true","fetch_graph":"https://pith.science/api/pith-number/B2GZ2RBFHQ57ITXX76IWLOCTTL/graph.json","fetch_events":"https://pith.science/api/pith-number/B2GZ2RBFHQ57ITXX76IWLOCTTL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B2GZ2RBFHQ57ITXX76IWLOCTTL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B2GZ2RBFHQ57ITXX76IWLOCTTL/action/storage_attestation","attest_author":"https://pith.science/pith/B2GZ2RBFHQ57ITXX76IWLOCTTL/action/author_attestation","sign_citation":"https://pith.science/pith/B2GZ2RBFHQ57ITXX76IWLOCTTL/action/citation_signature","submit_replication":"https://pith.science/pith/B2GZ2RBFHQ57ITXX76IWLOCTTL/action/replication_record"}},"created_at":"2026-05-18T00:33:53.315391+00:00","updated_at":"2026-05-18T00:33:53.315391+00:00"}