{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OQWLL2HV3ZUI3RX3RYUNGLEFMH","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":"507a6421f7ee4e62b540b8df12bcd501eae1e5c88b61b3d2c558ba5ef03a54e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-27T13:52:57Z","title_canon_sha256":"d95cc8fb41f702a19ef56d6ccf39909cd6b330d05295949df6eb3d3fab873ee8"},"schema_version":"1.0","source":{"id":"1505.07316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07316","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07316v1","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07316","created_at":"2026-05-18T01:12:08Z"},{"alias_kind":"pith_short_12","alias_value":"OQWLL2HV3ZUI","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OQWLL2HV3ZUI3RX3","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OQWLL2HV","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:5ab761cbaf9dce02bed3bfb14d2932288da2f7fde94a1fa96c64f9a321975e59","target":"graph","created_at":"2026-05-18T01:12:08Z","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 include alignment interactions in a well-studied first-order attractive-repulsive macroscopic model for aggregation. The distinctive feature of the extended model is that the equation that specifies the velocity in terms of the population density, becomes {\\em implicit}, and can have non-unique solutions. We investigate the well-posedness of the model and show rigorously how it can be obtained as a macroscopic limit of a second-order kinetic equation. We work within the space of probability measures with compact support and use mass transportation ideas and the characteristic method as esse","authors_text":"Changhui Tan, Razvan C. Fetecau, Weiran Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-27T13:52:57Z","title":"First-order aggregation models with alignment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07316","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":"sha256:09f0429215b5872c116639d71208da257e65c702b77a33a86dd7ec5e09bef458","target":"record","created_at":"2026-05-18T01:12:08Z","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":"507a6421f7ee4e62b540b8df12bcd501eae1e5c88b61b3d2c558ba5ef03a54e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-27T13:52:57Z","title_canon_sha256":"d95cc8fb41f702a19ef56d6ccf39909cd6b330d05295949df6eb3d3fab873ee8"},"schema_version":"1.0","source":{"id":"1505.07316","kind":"arxiv","version":1}},"canonical_sha256":"742cb5e8f5de688dc6fb8e28d32c8561cdf07e182d2b6dc5d349d881bd691e65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"742cb5e8f5de688dc6fb8e28d32c8561cdf07e182d2b6dc5d349d881bd691e65","first_computed_at":"2026-05-18T01:12:08.496416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:08.496416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kz25DeO3A+lOyFKRuGdO9/fkZHoEvUtmqKm33gSZS1bxiQkm2fN0nked87grDOPKS++JTF+Zq1C4LkA4+NogDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:08.496937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09f0429215b5872c116639d71208da257e65c702b77a33a86dd7ec5e09bef458","sha256:5ab761cbaf9dce02bed3bfb14d2932288da2f7fde94a1fa96c64f9a321975e59"],"state_sha256":"99bb2560cdf8a0a79de5c5121aa90985cc6e165535e1ac1d1699c07bed8f02c5"}