{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:UJ3G2W4RZIJ3HQIZH5NXQHK6XX","short_pith_number":"pith:UJ3G2W4R","canonical_record":{"source":{"id":"1902.03819","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-11T11:18:42Z","cross_cats_sorted":[],"title_canon_sha256":"963ea8f742da1bc4d3f2ead2bf86debc98cb9cfc87eb719e820932ab61ef2bae","abstract_canon_sha256":"d4170e2bee882f436d54960d3fa59e6c4ddff28319e9558ec955b986bc04b878"},"schema_version":"1.0"},"canonical_sha256":"a2766d5b91ca13b3c1193f5b781d5ebdd4834ff16fea859abcf1205a2c53eba7","source":{"kind":"arxiv","id":"1902.03819","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03819","created_at":"2026-05-17T23:40:39Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03819v2","created_at":"2026-05-17T23:40:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03819","created_at":"2026-05-17T23:40:39Z"},{"alias_kind":"pith_short_12","alias_value":"UJ3G2W4RZIJ3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UJ3G2W4RZIJ3HQIZ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UJ3G2W4R","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:UJ3G2W4RZIJ3HQIZH5NXQHK6XX","target":"record","payload":{"canonical_record":{"source":{"id":"1902.03819","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-11T11:18:42Z","cross_cats_sorted":[],"title_canon_sha256":"963ea8f742da1bc4d3f2ead2bf86debc98cb9cfc87eb719e820932ab61ef2bae","abstract_canon_sha256":"d4170e2bee882f436d54960d3fa59e6c4ddff28319e9558ec955b986bc04b878"},"schema_version":"1.0"},"canonical_sha256":"a2766d5b91ca13b3c1193f5b781d5ebdd4834ff16fea859abcf1205a2c53eba7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:39.027665Z","signature_b64":"p3yN9Aga6vYGkaeH5kaShVutfpEPMHfWNmJc2nSXdkn6M0iSOD1VAt9DemMErGBQu6g7TBvePqZPjR4yScsxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2766d5b91ca13b3c1193f5b781d5ebdd4834ff16fea859abcf1205a2c53eba7","last_reissued_at":"2026-05-17T23:40:39.027263Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:39.027263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.03819","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pDCO+qMSU/O0TmAe7nmct45uG4oxUQbadvJd7j/cNzPxGX4YZovHC6ayPjzneckxVHiiA2zb5+6+1g65fZMMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T14:25:32.326617Z"},"content_sha256":"3b3856c4d95d6a184aab5ca926e0ce4a3ac071f58c628438f5d9fac09a1f86b1","schema_version":"1.0","event_id":"sha256:3b3856c4d95d6a184aab5ca926e0ce4a3ac071f58c628438f5d9fac09a1f86b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:UJ3G2W4RZIJ3HQIZH5NXQHK6XX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Emergent behavior of Cucker-Smale model with normalized weights and distributed time delays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cristina Pignotti, Young-Pil Choi","submitted_at":"2019-02-11T11:18:42Z","abstract_excerpt":"We study a Cucker-Smale-type flocking model with distributed time delay where individuals interact with each other through normalized communication weights. Based on a Lyapunov functional approach, we provide sufficient conditions for the velocity alignment behavior. We then show that as the number of individuals N tends to infinity, the N-particle system can be well approximated by a delayed Vlasov alignment equation. Furthermore, we also establish the global existence of measure-valued solutions for the delayed Vlasov alignment equation and its large-time asymptotic behavior."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03819","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":""},"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":"2026-05-17T23:40:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mMCRHPl66ACF7LHjcC/TDwtHxGw7owxa7ze4u+0DwwVq7lxsUWbx2w5Qvfj4MCXyVVgR9UP56QF9BXK17/vWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T14:25:32.326959Z"},"content_sha256":"66c41fdbc1bacbbdb46ae225798b91ed4ba69f0dd58db97c22226b23a8d249c3","schema_version":"1.0","event_id":"sha256:66c41fdbc1bacbbdb46ae225798b91ed4ba69f0dd58db97c22226b23a8d249c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJ3G2W4RZIJ3HQIZH5NXQHK6XX/bundle.json","state_url":"https://pith.science/pith/UJ3G2W4RZIJ3HQIZH5NXQHK6XX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJ3G2W4RZIJ3HQIZH5NXQHK6XX/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":"2026-07-01T14:25:32Z","links":{"resolver":"https://pith.science/pith/UJ3G2W4RZIJ3HQIZH5NXQHK6XX","bundle":"https://pith.science/pith/UJ3G2W4RZIJ3HQIZH5NXQHK6XX/bundle.json","state":"https://pith.science/pith/UJ3G2W4RZIJ3HQIZH5NXQHK6XX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJ3G2W4RZIJ3HQIZH5NXQHK6XX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UJ3G2W4RZIJ3HQIZH5NXQHK6XX","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":"d4170e2bee882f436d54960d3fa59e6c4ddff28319e9558ec955b986bc04b878","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-11T11:18:42Z","title_canon_sha256":"963ea8f742da1bc4d3f2ead2bf86debc98cb9cfc87eb719e820932ab61ef2bae"},"schema_version":"1.0","source":{"id":"1902.03819","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03819","created_at":"2026-05-17T23:40:39Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03819v2","created_at":"2026-05-17T23:40:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03819","created_at":"2026-05-17T23:40:39Z"},{"alias_kind":"pith_short_12","alias_value":"UJ3G2W4RZIJ3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UJ3G2W4RZIJ3HQIZ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UJ3G2W4R","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:66c41fdbc1bacbbdb46ae225798b91ed4ba69f0dd58db97c22226b23a8d249c3","target":"graph","created_at":"2026-05-17T23:40:39Z","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"},"paper":{"abstract_excerpt":"We study a Cucker-Smale-type flocking model with distributed time delay where individuals interact with each other through normalized communication weights. Based on a Lyapunov functional approach, we provide sufficient conditions for the velocity alignment behavior. We then show that as the number of individuals N tends to infinity, the N-particle system can be well approximated by a delayed Vlasov alignment equation. Furthermore, we also establish the global existence of measure-valued solutions for the delayed Vlasov alignment equation and its large-time asymptotic behavior.","authors_text":"Cristina Pignotti, Young-Pil Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-11T11:18:42Z","title":"Emergent behavior of Cucker-Smale model with normalized weights and distributed time delays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03819","kind":"arxiv","version":2},"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":"sha256:3b3856c4d95d6a184aab5ca926e0ce4a3ac071f58c628438f5d9fac09a1f86b1","target":"record","created_at":"2026-05-17T23:40:39Z","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":"d4170e2bee882f436d54960d3fa59e6c4ddff28319e9558ec955b986bc04b878","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-11T11:18:42Z","title_canon_sha256":"963ea8f742da1bc4d3f2ead2bf86debc98cb9cfc87eb719e820932ab61ef2bae"},"schema_version":"1.0","source":{"id":"1902.03819","kind":"arxiv","version":2}},"canonical_sha256":"a2766d5b91ca13b3c1193f5b781d5ebdd4834ff16fea859abcf1205a2c53eba7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2766d5b91ca13b3c1193f5b781d5ebdd4834ff16fea859abcf1205a2c53eba7","first_computed_at":"2026-05-17T23:40:39.027263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:39.027263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p3yN9Aga6vYGkaeH5kaShVutfpEPMHfWNmJc2nSXdkn6M0iSOD1VAt9DemMErGBQu6g7TBvePqZPjR4yScsxBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:39.027665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03819","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b3856c4d95d6a184aab5ca926e0ce4a3ac071f58c628438f5d9fac09a1f86b1","sha256:66c41fdbc1bacbbdb46ae225798b91ed4ba69f0dd58db97c22226b23a8d249c3"],"state_sha256":"bdc9c02ee64f6cee0801a4d39f83dc03573bcdb4a27fbe4fc97bfd575a748917"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OZWPg7+GXYyqVoXIMDLJ+PCII8gDBCVcVg0wdNCiXAg/qqy87yasJkycb3wQa1kPojsok+bieAtk4rd+ET/HAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T14:25:32.328935Z","bundle_sha256":"e8822737476a1a1b9badf829368f43fde93e9c40d65034b4c137d0064d9d4566"}}