{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:5JD4AXABEYFS2ARTT47YJVQ7Y5","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":"d94933f05932a1f265e0adb7dc2cb69dbe0cd47e2d531f4d00a967eca0d81292","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2008-01-16T20:34:12Z","title_canon_sha256":"905d3353b9ed523c3df07f2a625cb7d739cb59827e44af5799189b4e91be140c"},"schema_version":"1.0","source":{"id":"0801.2566","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.2566","created_at":"2026-05-18T02:16:01Z"},{"alias_kind":"arxiv_version","alias_value":"0801.2566v2","created_at":"2026-05-18T02:16:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.2566","created_at":"2026-05-18T02:16:01Z"},{"alias_kind":"pith_short_12","alias_value":"5JD4AXABEYFS","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"5JD4AXABEYFS2ART","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"5JD4AXAB","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:881a93d05a8230993c941b22cc9ecb8c4d9c81b1175685555a6b87099c942978","target":"graph","created_at":"2026-05-18T02:16:01Z","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 classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel's first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady-state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly-supported population h","authors_text":"A.J. Bernoff, A.J. Leverentz, C.M. Topaz","cross_cats":["nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2008-01-16T20:34:12Z","title":"Asymptotic dynamics of attractive-repulsive swarms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.2566","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:f2486aa1b432b482678435d43405c6ce1af815fe02310756d4c9bd9789e82c57","target":"record","created_at":"2026-05-18T02:16:01Z","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":"d94933f05932a1f265e0adb7dc2cb69dbe0cd47e2d531f4d00a967eca0d81292","cross_cats_sorted":["nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2008-01-16T20:34:12Z","title_canon_sha256":"905d3353b9ed523c3df07f2a625cb7d739cb59827e44af5799189b4e91be140c"},"schema_version":"1.0","source":{"id":"0801.2566","kind":"arxiv","version":2}},"canonical_sha256":"ea47c05c01260b2d02339f3f84d61fc7513cff5b35f41f81cde2a31c9096e0fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea47c05c01260b2d02339f3f84d61fc7513cff5b35f41f81cde2a31c9096e0fb","first_computed_at":"2026-05-18T02:16:01.839007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:01.839007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2/Yk6aRgF3jZieJ5zi/XAAhIQN74+iv125oG+svstnkW2JjdGWnMsSjLoaqRWD81lJH2W+o/OkdnEgYI50XMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:01.839508Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.2566","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2486aa1b432b482678435d43405c6ce1af815fe02310756d4c9bd9789e82c57","sha256:881a93d05a8230993c941b22cc9ecb8c4d9c81b1175685555a6b87099c942978"],"state_sha256":"3acd97ad37c3e5e5312505480b64ed402103c8d083f7e9bb93e94448202d0688"}