{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q6H7OX7TMYKUTLM3NTZNM3N4HP","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":"8c0b5266fb299f1607891f4584eb28fa2c7262518098ce704741d9ae72ba7f03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-05T02:46:04Z","title_canon_sha256":"21ef4f2dc7f7216414ff55708ddd2f109d2e1f7c78086a961b2169e2958f9138"},"schema_version":"1.0","source":{"id":"1403.0991","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0991","created_at":"2026-05-18T01:44:19Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0991v1","created_at":"2026-05-18T01:44:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0991","created_at":"2026-05-18T01:44:19Z"},{"alias_kind":"pith_short_12","alias_value":"Q6H7OX7TMYKU","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q6H7OX7TMYKUTLM3","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q6H7OX7T","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:652719cc2a4de9c0677e2b3b494fb416b32067bc2dee142df6b843fecf7a4b0e","target":"graph","created_at":"2026-05-18T01:44:19Z","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 the large-time behavior of Eulerian systems augmented with non-local alignment. Such systems arise as hydrodynamic descriptions of agent-based models for self-organized dynamics, e.g., Cucker-Smale and Motsch-Tadmor models \\cite{CS,MT}. We prove that in analogy with the agent-based models, the presence of non-local alignment enforces \\emph{strong} solutions to self-organize into a macroscopic flock. This then raises the question of existence of such strong solutions. We address this question in one- and two-dimensional setups, proving global regularity for \\emph{sub-critical} initial ","authors_text":"Changhui Tan, Eitan Tadmor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-05T02:46:04Z","title":"Critical thresholds in flocking hydrodynamics\\\\with nonlocal alignment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0991","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:efd097c73376dd376e1364ecbc619a349db76c0278659095048ab0a4edc1a5df","target":"record","created_at":"2026-05-18T01:44:19Z","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":"8c0b5266fb299f1607891f4584eb28fa2c7262518098ce704741d9ae72ba7f03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-05T02:46:04Z","title_canon_sha256":"21ef4f2dc7f7216414ff55708ddd2f109d2e1f7c78086a961b2169e2958f9138"},"schema_version":"1.0","source":{"id":"1403.0991","kind":"arxiv","version":1}},"canonical_sha256":"878ff75ff3661549ad9b6cf2d66dbc3bef1073e1902848a0df55d3a1106e750e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"878ff75ff3661549ad9b6cf2d66dbc3bef1073e1902848a0df55d3a1106e750e","first_computed_at":"2026-05-18T01:44:19.907438Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:19.907438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l5Qc/dU0M/l6NaBXi9/dq3A7teY7JWWB1dutYgwy7ST8pKiBx/nqh5e1aSOCsDSXhqsHoE0E/aP6r/WG23YPDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:19.908135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0991","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efd097c73376dd376e1364ecbc619a349db76c0278659095048ab0a4edc1a5df","sha256:652719cc2a4de9c0677e2b3b494fb416b32067bc2dee142df6b843fecf7a4b0e"],"state_sha256":"6a506ebddb55d13e43e9bfa6f273c2d9ea9a982c3010b8b90752c4eb2f8ac90c"}