{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BPS2IJ42VE2YJO6ZCARA5LG6KP","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":"41bca4157fba40d038281dbd0d6f9ff4a9bddffc1d90923184f2662fbb18efcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-17T14:47:38Z","title_canon_sha256":"fa9814a45300ad834745f828cde00216e12e2e2cdb1447b8fddeb83669f9dfde"},"schema_version":"1.0","source":{"id":"1707.05190","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05190","created_at":"2026-05-18T00:40:09Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05190v1","created_at":"2026-05-18T00:40:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05190","created_at":"2026-05-18T00:40:09Z"},{"alias_kind":"pith_short_12","alias_value":"BPS2IJ42VE2Y","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BPS2IJ42VE2YJO6Z","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BPS2IJ42","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:1ba1b4b36ca353b9fb0d4697972aeb651bde83ffec40684f94b474e8190e584d","target":"graph","created_at":"2026-05-18T00:40:09Z","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 hydrodynamic Cucker-Smale-type model with time delay in communication and information processing, in which agents interact with each other through normalized communication weights. The model consists of a pressureless Euler system with time delayed non-local alignment forces. We resort to its Lagrangian formulation and prove the existence of its global in time classical solutions. Moreover, we derive a sufficient condition for the asymptotic flocking behavior of the solutions. Finally, we show the presence of a critical phenomenon for the Eulerian system posed in the spatially one-d","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":"2017-07-17T14:47:38Z","title":"Hydrodynamic 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":"1707.05190","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":"sha256:19b21987c1a5c40822df3143e312203013f3a40c1f537b10a6475cda61c3f59e","target":"record","created_at":"2026-05-18T00:40:09Z","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":"41bca4157fba40d038281dbd0d6f9ff4a9bddffc1d90923184f2662fbb18efcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-17T14:47:38Z","title_canon_sha256":"fa9814a45300ad834745f828cde00216e12e2e2cdb1447b8fddeb83669f9dfde"},"schema_version":"1.0","source":{"id":"1707.05190","kind":"arxiv","version":1}},"canonical_sha256":"0be5a4279aa93584bbd910220eacde53f3044558a078fb8781c185c0090db349","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0be5a4279aa93584bbd910220eacde53f3044558a078fb8781c185c0090db349","first_computed_at":"2026-05-18T00:40:09.235991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:09.235991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y0WEHk9VLMTuYkoqgikQTxoipLH+P2SIxF/x6/3OnhoGuR0mm89o3YMDojKxpHIw/FzH4QZO98xHnJxBIuMhDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:09.236781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05190","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19b21987c1a5c40822df3143e312203013f3a40c1f537b10a6475cda61c3f59e","sha256:1ba1b4b36ca353b9fb0d4697972aeb651bde83ffec40684f94b474e8190e584d"],"state_sha256":"61693be55858536f3a62fb85c7fc481ea6b7f8c5877628ef16c48ca2ed7e8174"}