{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FEXKN7W3CIJRYWMYIWSGZ3C6VM","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":"46cccf834a64faf3401944cbb6078ae698eab2993339b9f646ed441d605c8955","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-08T04:33:29Z","title_canon_sha256":"835bb8d60bf54f60b292087d57d5a0a324acc7abc860d9441d68513e92eb9df7"},"schema_version":"1.0","source":{"id":"1305.1715","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1715","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1715v2","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1715","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"FEXKN7W3CIJR","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FEXKN7W3CIJRYWMY","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FEXKN7W3","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:732a58bcbc8c4f6bcfb50b144b9b8444479b9e55ff495e2a22ed85528ab65f48","target":"graph","created_at":"2026-05-18T01:22:25Z","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":"In this paper we study two models for crowd motion and herding. Each of the models is of Keller-Segel type and involves two parabolic equations, one for the evolution of the density and one for the evolution of a mean field potential. We classify all radial stationary solutions, prove multiplicity results and establish some qualitative properties of these solutions, which are characterized as critical points of an energy functional. A notion of variational stability is associated to such solutions. The dynamical stability in a neighborhood of a stationary solution is also studied in terms of t","authors_text":"Gaspard Jankowiak (CEREMADE), Jean Dolbeault (CEREMADE), Peter Markowich (DAMTP)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-08T04:33:29Z","title":"Stationary solutions of Keller-Segel type crowd motion and herding models: multiplicity and dynamical stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1715","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":"sha256:98be7381e552e7429097a9403004303c6d79130f4763f0771c1b564476437479","target":"record","created_at":"2026-05-18T01:22:25Z","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":"46cccf834a64faf3401944cbb6078ae698eab2993339b9f646ed441d605c8955","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-08T04:33:29Z","title_canon_sha256":"835bb8d60bf54f60b292087d57d5a0a324acc7abc860d9441d68513e92eb9df7"},"schema_version":"1.0","source":{"id":"1305.1715","kind":"arxiv","version":2}},"canonical_sha256":"292ea6fedb12131c599845a46cec5eab2307c2a6d4bec540269a432532319b7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"292ea6fedb12131c599845a46cec5eab2307c2a6d4bec540269a432532319b7c","first_computed_at":"2026-05-18T01:22:25.409145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:25.409145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rwjr0oz7MVOcP/T/fwM/OVX4i9KNIEjuQ6pdvQLv57CYCwZnWiuhYvcf/ebMcOF/cV3YezhP/8pTjHycFK7HDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:25.409795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1715","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98be7381e552e7429097a9403004303c6d79130f4763f0771c1b564476437479","sha256:732a58bcbc8c4f6bcfb50b144b9b8444479b9e55ff495e2a22ed85528ab65f48"],"state_sha256":"89cc9785b977166303671955c06e31d331746c0a0ce8a6b1e7948b5ca53ebb71"}