{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5PJUB3ST5KZJG2IDJCD2GCWNBB","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":"abafa19c0c02ad2c3bf0d1e73908b643a0b50768e13143a9ef079e1b7e4c087e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-24T08:29:45Z","title_canon_sha256":"bd656b04f7afad73abeee1dbb47f72f8a4541432676a3faf718cc52eb9d84120"},"schema_version":"1.0","source":{"id":"1608.06747","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06747","created_at":"2026-05-18T01:07:57Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06747v1","created_at":"2026-05-18T01:07:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06747","created_at":"2026-05-18T01:07:57Z"},{"alias_kind":"pith_short_12","alias_value":"5PJUB3ST5KZJ","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5PJUB3ST5KZJG2ID","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5PJUB3ST","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:b24f9b71bc4e5b06b8a1bb6630cecb86a68f7073726105d96a254b84ab03e949","target":"graph","created_at":"2026-05-18T01:07:57Z","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 system with time delay in which agents interact with each other through normalized communication weights. We construct a Lyapunov functional for the system and provide sufficient conditions for asymptotic flocking, i.e., convergence to a common velocity vector. We also carry out a rigorous limit passage to the mean-field limit of the particle system as the number of particles tends to infinity.For the resulting Vlasov-type equation we prove the existence, stability and large-time behavior of measure-valued solutions. This is, to our best knowledge, the first such r","authors_text":"Jan Haskovec, Young-Pil Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-24T08:29:45Z","title":"Cucker-Smale model with normalized communication weights and time delay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06747","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:b9bca4c0f3e5b12121fe465a1d14977ff6023f4eceb8c7d6c824c896cafe04a3","target":"record","created_at":"2026-05-18T01:07:57Z","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":"abafa19c0c02ad2c3bf0d1e73908b643a0b50768e13143a9ef079e1b7e4c087e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-08-24T08:29:45Z","title_canon_sha256":"bd656b04f7afad73abeee1dbb47f72f8a4541432676a3faf718cc52eb9d84120"},"schema_version":"1.0","source":{"id":"1608.06747","kind":"arxiv","version":1}},"canonical_sha256":"ebd340ee53eab29369034887a30acd086843f3e13a50c1e2d2132f0b1bf6452f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebd340ee53eab29369034887a30acd086843f3e13a50c1e2d2132f0b1bf6452f","first_computed_at":"2026-05-18T01:07:57.619595Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:57.619595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U99bbzmJyHkGIgJ5P+klIN7RRGDN6QyatkkgWes1PqmBf/gAWXXrHpsXJszwR2+zP7lxzktHSxanh6l+/v7zDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:57.620119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06747","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9bca4c0f3e5b12121fe465a1d14977ff6023f4eceb8c7d6c824c896cafe04a3","sha256:b24f9b71bc4e5b06b8a1bb6630cecb86a68f7073726105d96a254b84ab03e949"],"state_sha256":"9dde6819c70519cad896bbe0e5018cf4e16507b640bb5d67b0e56db9d26420d9"}